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swrup 2025-11-11 02:07:51 +01:00
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(library
(name mirage_crypto_ec)
(public_name mirage-crypto-ec)
(libraries eqaf mirage-crypto-rng digestif)
(foreign_stubs
(language c)
(names p256_stubs np256_stubs p384_stubs np384_stubs p521_stubs np521_stubs
curve25519_stubs)
(include_dirs ../src/native)
(flags
(:standard -DNDEBUG)
(:include cflags_optimized.sexp))))
(env
(dev
(c_flags (:include cflags_warn.sexp))))
(include_subdirs unqualified)
(rule
(targets cflags_optimized.sexp cflags_warn.sexp)
(action
(run ../config/cfg.exe)))

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(include_subdirs no)
(executable
(name gen_tables)
(libraries mirage_crypto_ec))

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open Format
let print_header name =
printf
{|
/*
Pre-computed %d-bit multiples of the generator point G for the curve %s,
used for speeding up its scalar multiplication in point_operations.h.
Generated by %s
*/|}
Sys.word_size name Sys.argv.(0)
let pp_array elem_fmt fmt arr =
let fout = fprintf fmt in
let len = Array.length arr in
fout "@[<2>{@\n";
for i = 0 to len - 1 do
elem_fmt fmt arr.(i);
if i < len - 1 then printf ",@ " else printf ""
done;
fout "@]@,}"
let div_round_up a b = (a / b) + if a mod b = 0 then 0 else 1
let pp_string_words ~wordsize fmt str =
assert (String.length str * 8 mod wordsize = 0);
let limbs = String.length str * 8 / wordsize in
(* Truncate at the beginning (little-endian) *)
let bytes = Bytes.unsafe_of_string str in
(* let bytes = rev_str_bytes str in *)
fprintf fmt "@[<2>{@\n";
for i = 0 to limbs - 1 do
let index = i * (wordsize / 8) in
(if wordsize = 64 then
let w = Bytes.get_int64_le bytes index in
fprintf fmt "%#016Lx" w
else
let w = Bytes.get_int32_le bytes index in
fprintf fmt "%#08lx" w);
if i < limbs - 1 then printf ",@ " else printf ""
done;
fprintf fmt "@]@,}"
let check_shape tables =
let fe_len = String.length tables.(0).(0).(0) in
let table_len = fe_len * 2 in
assert (Array.length tables = table_len);
Array.iter
(fun x ->
assert (Array.length x = 15);
Array.iter
(fun x ->
assert (Array.length x = 3);
Array.iter (fun x -> assert (String.length x = fe_len)) x)
x)
tables
let print_tables tables ~wordsize =
let fe_len = String.length tables.(0).(0).(0) in
printf "@[<2>static WORD generator_table[%d][15][3][LIMBS] = @," (fe_len * 2);
pp_array
(pp_array (pp_array (pp_string_words ~wordsize)))
std_formatter tables;
printf "@];@,"
let print_toplevel name wordsize (module P : Mirage_crypto_ec.Dh_dsa) =
let tables = P.Dsa.Precompute.generator_tables () in
assert (wordsize = Sys.word_size);
check_shape tables;
print_header name;
if wordsize = 64 then
printf
"@[<v>#ifndef ARCH_64BIT@,\
#error \"Cannot use 64-bit tables on a 32-bit architecture\"@,\
#endif@,\
@]"
else
printf
"@[<v>#ifdef ARCH_64BIT@,\
#error \"Cannot use 32-bit tables on a 64-bit architecture\"@,\
#endif@,\
@]";
print_tables ~wordsize tables
let curves =
Mirage_crypto_ec.
[
("p256", (module P256 : Dh_dsa));
("p384", (module P384));
("p521", (module P521));
]
let usage () =
printf "Usage: gen_tables [%a] [64 | 32]@."
(pp_print_list
~pp_sep:(fun fmt () -> pp_print_string fmt " | ")
pp_print_string)
(List.map fst curves)
let go =
let name, curve, wordsize =
try
let name, curve =
List.find (fun (name, _) -> name = Sys.argv.(1)) curves
in
(name, curve, int_of_string Sys.argv.(2))
with _ ->
usage ();
exit 1
in
print_toplevel name wordsize curve

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{1 Implementation }
The goal of this document is to describe how the library is implemented.
{2 Field operations}
These are implemented in [Field_element], which is a binding over
[p256_{32,64}.h]. These are files extracted from Coq code in
{{:https://github.com/mit-plv/fiat-crypto}this repository}.
This module uses
{{:https://en.wikipedia.org/wiki/Montgomery_modular_multiplication} Montgomery
Modular Multiplication}. Instead of storing a number [a], operations are done
on [aR] where R = 2{^256}.
It is possible to check that these files correspond to the extracted ones in
the upstream repository by running [dune build @check_vendors].
These files are part of the trusted computing base. That is, using this package
relies on the fact that they implemented the correct algorithms. To go further,
one can re-run the extraction process from Coq sources, see
{{:https://github.com/mirage/fiat/issues/41}#41}.
{2 Point operations}
Points (see the [Point] module) are stored using projective coordinates (X : Y
: Z):
- Z=0 corresponds to the point at infinity
- for Z≠0, this corresponds to a point with affine coordinates (X/Z{^2},
Y/Z{^3})
Doubling and addition are implemented as C stubs in [p256_stubs.c] using code
that comes from BoringSSL, Google's fork of OpenSSL. Fiat code has been design
in part to be included in BoringSSL, so this does not require any particular
glue code.
Some operations are implemented manually, in particular:
- conversion to affine coordinates, as described above. This relies on a field
inversion primitive from BoringSSL, that is exposed in [Field_element].
- point verification (bound checking and making sure that the equation is
satisfied).
There is no automated way to check that the BoringSSL part is identical to that
in the upstream repository (nor to update it).
{2 Scalar multiplication}
Implemented by hand using the
{{:https://cr.yp.to/bib/2003/joye-ladder.pdf}Montgomery Powering Ladder}.
Instead of branching based on key bits, constant-time selection (as defined in
fiat code) is used.
The following references discuss this algorithm:
- {{:https://cryptojedi.org/peter/data/eccss-20130911b.pdf}Scalar-multiplication algorithms, Peter Schwabe, ECC 2013 Summer School}
- {{:https://eprint.iacr.org/2017/293.pdf}Montgomery curves and the Montgomery
ladder, Daniel J. Bernstein and Tanja Lange}
For the special case of base scalar multiplication (where the generator point of
the curve specifically is multiplied by a scalar), instead an algorithm
(implemented by hand in C) using pre-computed tables of point doubling is used
(tables are in `native/p*_tables_32|64.c`).
The key for this algorithm being constant-time is the function selecting values
from the tables, which conceals what value it selects by exploring the whole
table in the same order no matter the input, using const-time selection (as
defined in fiat code). See `native/point_operations.h`.
{2 Key exchange}
Key exchange consists in
- validating the public key as described in
{{:https://tools.ietf.org/html/rfc8446#section-4.2.8.2}RFC 8446 §4.2.8.2};
- computing scalar multiplication;
- returning the encoded x coordinate of the result.
This is implemented by hand and checked against common errors using test
vectors from {{:https://github.com/google/wycheproof}project Wycheproof}.

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(** {1 Elliptic curve cryptography} *)
(** Mirage-crypto-ec implements public key cryptography with named elliptic
curves. Ephemeral key exchanges with {{!Dh}Diffie-Hellman} and
{{!Dsa}digital signatures (ECDSA)} are implemented.
The arithmetic operations uses code generated by
{{:https://github.com/mit-plv/fiat-crypto}fiat-crypto} which is proven to
consume a constant amount of time, independent of the input values.
*)
type error = [
| `Invalid_range
| `Invalid_format
| `Invalid_length
| `Not_on_curve
| `At_infinity
| `Low_order
]
(** The type for errors. *)
val pp_error : Format.formatter -> error -> unit
(** Pretty printer for errors *)
exception Message_too_long
(** Raised if the provided message is too long for the curve. *)
(** Diffie-Hellman key exchange. *)
module type Dh = sig
type secret
(** Type for private keys. *)
val secret_of_octets : ?compress:bool -> string ->
(secret * string, error) result
(** [secret_of_octets ~compress secret] decodes the provided buffer as
{!secret}. If [compress] is provided and [true] (defaults to [false]),
the shared part will be compressed. May result in an error if the buffer
had an invalid length or was not in bounds. *)
val secret_to_octets : secret -> string
(** [secret_to_octets secret] encodes the provided secret into a freshly
allocated buffer. *)
val gen_key : ?compress:bool -> ?g:Mirage_crypto_rng.g -> unit ->
secret * string
(** [gen_key ~compress ~g ()] generates a private and a public key for
Ephemeral Diffie-Hellman. If [compress] is provided and [true] (defaults
to [false]), the shared part will be compressed. The returned key pair
MUST only be used for a single key exchange.
The generated private key is checked to be greater than zero and lower
than the group order meaning the public key cannot be the point at
inifinity. *)
val key_exchange : secret -> string -> (string, error) result
(** [key_exchange secret received_public_key] performs Diffie-Hellman key
exchange using your secret and the data received from the other party.
Returns the shared secret or an error if the received data is wrongly
encoded, doesn't represent a point on the curve or represent the point
at infinity.
The shared secret is returned as is i.e. not stripped from leading 0x00
bytes.
The public key encoding is described
{{:http://www.secg.org/sec1-v2.pdf}in SEC 1} from SECG. *)
end
(** Digital signature algorithm. *)
module type Dsa = sig
type priv
(** The type for private keys. *)
type pub
(** The type for public keys. *)
val byte_length : int
(** [byte_length] is the size of a ECDSA signature in bytes. *)
val bit_length : int
(** [bit_length] is the number of significant bits in a ECDSA signature *)
(** {2 Serialisation} *)
val priv_of_octets : string -> (priv, error) result
(** [priv_of_octets buf] decodes a private key from the buffer [buf]. If the
provided data is invalid, an error is returned. *)
val priv_to_octets : priv -> string
(** [priv_to_octets p] encode the private key [p] to a buffer. *)
val pub_of_octets : string -> (pub, error) result
(** [pub_of_octets buf] decodes a public key from the buffer [buf]. If the
provided data is invalid, an error is returned. *)
val pub_to_octets : ?compress:bool -> pub -> string
(** [pub_to_octets ~compress p] encodes the public key [p] into a buffer.
If [compress] is provided and [true] (default [false]), the compressed
representation is returned. *)
(** {2 Deriving the public key} *)
val pub_of_priv : priv -> pub
(** [pub_of_priv p] extracts the public key from the private key [p]. *)
(** {2 Key generation} *)
val generate : ?g:Mirage_crypto_rng.g -> unit -> priv * pub
(** [generate ~g ()] generates a key pair. *)
(** {2 Cryptographic operations} *)
val sign : key:priv -> ?k:string -> string -> string * string
(** [sign ~key ~k digest] signs the message [digest] using the private
[key]. The [digest] is not processed further - it should be the hash of
the message to sign. If [k] is not provided, it is computed using the
deterministic construction from RFC 6979. The result is a pair of [r]
and [s].
Warning: there {{:https://www.hertzbleed.com/2h2b.pdf}are}
{{:https://www.hertzbleed.com/hertzbleed.pdf}attacks} that recover the
private key from a power and timing analysis of the RFC 6979 computation
of [k] - thus it is advised to provide a good nonce ([k]) explicitly,
which is independent of key and digest.
@raise Invalid_argument if [k] is not suitable or not in range.
@raise Message_too_long if the bit size of [msg] exceeds the curve. *)
val verify : key:pub -> string * string -> string -> bool
(** [verify ~key (r, s) digest] verifies the signature [r, s] on the message
[digest] with the public [key]. The return value is [true] if verification
was successful, [false] otherwise. If the message has more bits than the
group order, the result is false. *)
(** [K_gen] can be instantiated over a hashing module to obtain an RFC6979
compliant [k]-generator for that hash. *)
module K_gen (H : Digestif.S) : sig
val generate : key:priv -> string -> string
(** [generate ~key digest] deterministically takes the given private key
and message digest to a [k] suitable for seeding the signing process. *)
end
(** {2 Misc} *)
(** Operations to precompute useful data meant to be hardcoded in
[mirage-crypto-ec] before compilation *)
module Precompute : sig
val generator_tables : unit -> string array array array
(** Return an array of shape (Fe_length * 2, 15, 3) containing multiples of
the generator point for the curve. Useful only to bootstrap tables
necessary for scalar multiplication. *)
end
end
(** Elliptic curve with Diffie-Hellman and DSA. *)
module type Dh_dsa = sig
(** Diffie-Hellman key exchange. *)
module Dh : Dh
(** Digital signature algorithm. *)
module Dsa : Dsa
end
(** The NIST P-256 curve, also known as SECP256R1. *)
module P256 : Dh_dsa
(** The NIST P-384 curve, also known as SECP384R1. *)
module P384 : Dh_dsa
(** The NIST P-521 curve, also known as SECP521R1. *)
module P521 : Dh_dsa
(** Curve 25519 Diffie-Hellman, also known as X25519. *)
module X25519 : Dh
(** Curve 25519 DSA, also known as Ed25519. *)
module Ed25519 : sig
type priv
(** The type for private keys. *)
type pub
(** The type for public keys. *)
(** {2 Serialisation} *)
val priv_of_octets : string -> (priv, error) result
(** [priv_of_octets buf] decodes a private key from the buffer [buf]. If the
provided data is invalid, an error is returned. *)
val priv_to_octets : priv -> string
(** [priv_to_octets p] encode the private key [p] to a buffer. *)
val pub_of_octets : string -> (pub, error) result
(** [pub_of_octets buf] decodes a public key from the buffer [buf]. If the
provided data is invalid, an error is returned. *)
val pub_to_octets : pub -> string
(** [pub_to_octets p] encodes the public key [p] into a buffer. *)
(** {2 Deriving the public key} *)
val pub_of_priv : priv -> pub
(** [pub_of_priv p] extracts the public key from the private key [p]. *)
(** {2 Key generation} *)
val generate : ?g:Mirage_crypto_rng.g -> unit -> priv * pub
(** [generate ~g ()] generates a key pair. *)
(** {2 Cryptographic operations} *)
val sign : key:priv -> string -> string
(** [sign ~key msg] signs the message [msg] using the private [key]. The
result is the concatenation of [r] and [s], as specified in RFC 8032. *)
val verify : key:pub -> string -> msg:string -> bool
(** [verify ~key signature msg] verifies the [signature] on the message
[msg] with the public [key]. The return value is [true] if verification
was successful, [false] otherwise. *)
end

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# This file is part of mirage-crypto-ec, and used to generate C files
# As a prerequisite, fiat-crypto (https://github.com/mit-plv/fiat-crypto)
# needs to be cloned and "make standalone-ocaml" invoked
# The lowest bound of fiat-crypto is git commit
# dabaf4b3132e8bb4a3f5fcd8366eec6ac9bb4232 (July 16th 2021)
# Generated on FreeBSD 12.2p2 with coq 8.13.1 (OCaml 4.12.0)
# with fiat-crypto 2a07751f37af74edeac47b19bd51810bc99b91a1 (May 29th 2022)
WBW_MONT ?= ../../../fiat-crypto/src/ExtractionOCaml/word_by_word_montgomery --static --use-value-barrier --inline-internal
UNSAT_SOLINAS ?= ../../../fiat-crypto/src/ExtractionOCaml/unsaturated_solinas --static --use-value-barrier --inline-internal
N_FUNCS=mul add opp from_montgomery to_montgomery one msat divstep_precomp divstep to_bytes from_bytes selectznz
GEN_TABLE=../../_build/default/ec/gen_tables/gen_tables.exe
# The NIST curve P-256 (AKA SECP256R1)
P256="2^256 - 2^224 + 2^192 + 2^96 - 1"
.PHONY: p256_64.h
p256_64.h:
$(WBW_MONT) p256 64 $(P256) > $@
.PHONY: p256_32.h
p256_32.h:
$(WBW_MONT) p256 32 $(P256) > $@
# The group order N of P-256
P256N="0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551"
.PHONY: np256_64.h
np256_64.h:
$(WBW_MONT) np256 64 $(P256N) $(N_FUNCS) > $@
.PHONY: np256_32.h
np256_32.h:
$(WBW_MONT) np256 32 $(P256N) $(N_FUNCS) > $@
.PHONY: p256_tables_64.h
p256_tables_64.h:
$(GEN_TABLE) p256 64 > $@
.PHONY: p256_tables_32.h
p256_tables_32.h:
$(GEN_TABLE) p256 32 > $@
.PHONY: p256
p256: p256_64.h p256_32.h np256_64.h np256_32.h
p256_tables: p256_tables_64.h p256_tables_32.h
# The NIST curve P-384 (AKA SECP384R1)
P384="2^384 - 2^128 - 2^96 + 2^32 - 1"
.PHONY: p384_64.h
p384_64.h:
$(WBW_MONT) p384 64 $(P384) > $@
.PHONY: p384_32.h
p384_32.h:
$(WBW_MONT) p384 32 $(P384) > $@
# The group order N of P-384
P384N="0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973"
.PHONY: np384_64.h
np384_64.h:
$(WBW_MONT) np384 64 $(P384N) $(N_FUNCS) > $@
.PHONY: np384_32.h
np384_32.h:
$(WBW_MONT) np384 32 $(P384N) $(N_FUNCS) > $@
.PHONY: p384_tables_64.h
p384_tables_64.h:
$(GEN_TABLE) p384 64 > $@
.PHONY: p384_tables_32.h
p384_tables_32.h:
$(GEN_TABLE) p384 32 > $@
.PHONY: p384
p384: p384_64.h p384_32.h np384_64.h np384_32.h
p384_tables: p384_tables_64.h p384_tables_32.h
# The NIST curve P-521 (AKA SECP521R1)
P521="2^521 - 1"
.PHONY: p521_64.h
p521_64.h:
$(WBW_MONT) p521 64 $(P521) > $@
.PHONY: p521_32.h
p521_32.h:
$(WBW_MONT) p521 32 $(P521) > $@
# The group order N of P-521
P521N="0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
.PHONY: np521_64.h
np521_64.h:
$(WBW_MONT) np521 64 $(P521N) $(N_FUNCS) > $@
.PHONY: np521_32.h
np521_32.h:
$(WBW_MONT) np521 32 $(P521N) $(N_FUNCS) > $@
.PHONY: p521_tables_64.h
p521_tables_64.h:
$(GEN_TABLE) p521 64 > $@
.PHONY: p521_tables_32.h
p521_tables_32.h:
$(GEN_TABLE) p521 32 > $@
.PHONY: p521
p521: p521_64.h p521_32.h np521_64.h np521_32.h
p521_tables: p521_tables_64.h p521_tables_32.h
# 25519
25519="2^255 - 19"
25519_FUNS=carry_mul carry_square carry add sub opp selectznz to_bytes from_bytes carry_scmul121666
.PHONY: curve25519_64.h
curve25519_64.h:
$(UNSAT_SOLINAS) 25519 64 '(auto)' $(25519) $(25519_FUNS) > $@
.PHONY: curve25519_32.h
curve25519_32.h:
$(UNSAT_SOLINAS) 25519 32 '(auto)' $(25519) $(25519_FUNS) > $@
.PHONY: curve25519
curve25519: curve25519_64.h curve25519_32.h
.PHONY: tables
tables: p256_tables p384_tables p521_tables
.PHONY: clean
clean:
$(RM) p256_32.h p256_64.h np256_32.h np256_64.h
$(RM) p384_32.h p384_64.h np384_32.h np384_64.h
$(RM) p521_32.h p521_64.h np521_32.h np521_64.h
$(RM) curve25519_32.h curve25519_64.h
.PHONY: clean_tables
clean_tables:
$(RM) p256_tables_32.h p256_tables_64.h
$(RM) p384_tables_32.h p384_tables_64.h
$(RM) p521_tables_32.h p521_tables_64.h
.PHONY: all
all: p256 p384 p521 curve25519

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# Generated code from fiat
This directory includes several files ("p*.h") that are generated by
[fiat](https://github.com/mit-plv/fiat-crypto). The GNUmakefile provides
targets to generate these files.
The file "inversion_template.h" is copied from the fiat-crypto repository
at e31a36d5f1b20134e67ccc5339d88f0ff3cb0f86 (inversion-c/inversion_template.c),
and has some modifications: the "inversion" function is declared "static",
and the convenience function "inversion" is provided.
The "*_stubs.c" files are handcrafted.
The "p*_tables_32/64.c" are generated from `../gen_tables` (see each file's
header) and contain pre-computed data to speed up scalar multiplication for
ECDSA. The 64- and 32-bit tables must be respectively generated from a 64-bit or
32-bit build of `gen_tables`.
# Code from BoringSSL
The code in "curve25519_tables.h", and large parts of
"curve25519_stubs.c" and "point_operations.h" (excluding scalar multiplication)
originate from BoringSSL. Minor adjustments have been done manually.

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/* Autogenerated: '../fiat-crypto/src/ExtractionOCaml/unsaturated_solinas' --static --use-value-barrier --inline-internal 25519 64 '(auto)' '2^255 - 19' carry_mul carry_square carry add sub opp selectznz to_bytes from_bytes carry_scmul121666 */
/* curve description: 25519 */
/* machine_wordsize = 64 (from "64") */
/* requested operations: carry_mul, carry_square, carry, add, sub, opp, selectznz, to_bytes, from_bytes, carry_scmul121666 */
/* n = 5 (from "(auto)") */
/* s-c = 2^255 - [(1, 19)] (from "2^255 - 19") */
/* tight_bounds_multiplier = 1 (from "") */
/* */
/* Computed values: */
/* carry_chain = [0, 1, 2, 3, 4, 0, 1] */
/* eval z = z[0] + (z[1] << 51) + (z[2] << 102) + (z[3] << 153) + (z[4] << 204) */
/* bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) */
/* balance = [0xfffffffffffda, 0xffffffffffffe, 0xffffffffffffe, 0xffffffffffffe, 0xffffffffffffe] */
#include <stdint.h>
typedef unsigned char fiat_25519_uint1;
typedef signed char fiat_25519_int1;
#if defined(__GNUC__) || defined(__clang__)
# define FIAT_25519_FIAT_EXTENSION __extension__
# define FIAT_25519_FIAT_INLINE __inline__
#else
# define FIAT_25519_FIAT_EXTENSION
# define FIAT_25519_FIAT_INLINE
#endif
FIAT_25519_FIAT_EXTENSION typedef signed __int128 fiat_25519_int128;
FIAT_25519_FIAT_EXTENSION typedef unsigned __int128 fiat_25519_uint128;
/* The type fiat_25519_loose_field_element is a field element with loose bounds. */
/* Bounds: [[0x0 ~> 0x18000000000000], [0x0 ~> 0x18000000000000], [0x0 ~> 0x18000000000000], [0x0 ~> 0x18000000000000], [0x0 ~> 0x18000000000000]] */
typedef uint64_t fiat_25519_loose_field_element[5];
/* The type fiat_25519_tight_field_element is a field element with tight bounds. */
/* Bounds: [[0x0 ~> 0x8000000000000], [0x0 ~> 0x8000000000000], [0x0 ~> 0x8000000000000], [0x0 ~> 0x8000000000000], [0x0 ~> 0x8000000000000]] */
typedef uint64_t fiat_25519_tight_field_element[5];
#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif
#if !defined(FIAT_25519_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
static __inline__ uint64_t fiat_25519_value_barrier_u64(uint64_t a) {
__asm__("" : "+r"(a) : /* no inputs */);
return a;
}
#else
# define fiat_25519_value_barrier_u64(x) (x)
#endif
/*
* The function fiat_25519_addcarryx_u51 is an addition with carry.
*
* Postconditions:
* out1 = (arg1 + arg2 + arg3) mod 2^51
* out2 = (arg1 + arg2 + arg3) / 2^51
*
* Input Bounds:
* arg1: [0x0 ~> 0x1]
* arg2: [0x0 ~> 0x7ffffffffffff]
* arg3: [0x0 ~> 0x7ffffffffffff]
* Output Bounds:
* out1: [0x0 ~> 0x7ffffffffffff]
* out2: [0x0 ~> 0x1]
*/
static FIAT_25519_FIAT_INLINE void fiat_25519_addcarryx_u51(uint64_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint64_t arg2, uint64_t arg3) {
uint64_t x1;
uint64_t x2;
fiat_25519_uint1 x3;
x1 = ((arg1 + arg2) + arg3);
x2 = (x1 & UINT64_C(0x7ffffffffffff));
x3 = (fiat_25519_uint1)(x1 >> 51);
*out1 = x2;
*out2 = x3;
}
/*
* The function fiat_25519_subborrowx_u51 is a subtraction with borrow.
*
* Postconditions:
* out1 = (-arg1 + arg2 + -arg3) mod 2^51
* out2 = -(-arg1 + arg2 + -arg3) / 2^51
*
* Input Bounds:
* arg1: [0x0 ~> 0x1]
* arg2: [0x0 ~> 0x7ffffffffffff]
* arg3: [0x0 ~> 0x7ffffffffffff]
* Output Bounds:
* out1: [0x0 ~> 0x7ffffffffffff]
* out2: [0x0 ~> 0x1]
*/
static FIAT_25519_FIAT_INLINE void fiat_25519_subborrowx_u51(uint64_t* out1, fiat_25519_uint1* out2, fiat_25519_uint1 arg1, uint64_t arg2, uint64_t arg3) {
int64_t x1;
fiat_25519_int1 x2;
uint64_t x3;
x1 = ((int64_t)(arg2 - (int64_t)arg1) - (int64_t)arg3);
x2 = (fiat_25519_int1)(x1 >> 51);
x3 = (x1 & UINT64_C(0x7ffffffffffff));
*out1 = x3;
*out2 = (fiat_25519_uint1)(0x0 - x2);
}
/*
* The function fiat_25519_cmovznz_u64 is a single-word conditional move.
*
* Postconditions:
* out1 = (if arg1 = 0 then arg2 else arg3)
*
* Input Bounds:
* arg1: [0x0 ~> 0x1]
* arg2: [0x0 ~> 0xffffffffffffffff]
* arg3: [0x0 ~> 0xffffffffffffffff]
* Output Bounds:
* out1: [0x0 ~> 0xffffffffffffffff]
*/
static FIAT_25519_FIAT_INLINE void fiat_25519_cmovznz_u64(uint64_t* out1, fiat_25519_uint1 arg1, uint64_t arg2, uint64_t arg3) {
fiat_25519_uint1 x1;
uint64_t x2;
uint64_t x3;
x1 = (!(!arg1));
x2 = ((fiat_25519_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
x3 = ((fiat_25519_value_barrier_u64(x2) & arg3) | (fiat_25519_value_barrier_u64((~x2)) & arg2));
*out1 = x3;
}
/*
* The function fiat_25519_carry_mul multiplies two field elements and reduces the result.
*
* Postconditions:
* eval out1 mod m = (eval arg1 * eval arg2) mod m
*
*/
static void fiat_25519_carry_mul(fiat_25519_tight_field_element out1, const fiat_25519_loose_field_element arg1, const fiat_25519_loose_field_element arg2) {
fiat_25519_uint128 x1;
fiat_25519_uint128 x2;
fiat_25519_uint128 x3;
fiat_25519_uint128 x4;
fiat_25519_uint128 x5;
fiat_25519_uint128 x6;
fiat_25519_uint128 x7;
fiat_25519_uint128 x8;
fiat_25519_uint128 x9;
fiat_25519_uint128 x10;
fiat_25519_uint128 x11;
fiat_25519_uint128 x12;
fiat_25519_uint128 x13;
fiat_25519_uint128 x14;
fiat_25519_uint128 x15;
fiat_25519_uint128 x16;
fiat_25519_uint128 x17;
fiat_25519_uint128 x18;
fiat_25519_uint128 x19;
fiat_25519_uint128 x20;
fiat_25519_uint128 x21;
fiat_25519_uint128 x22;
fiat_25519_uint128 x23;
fiat_25519_uint128 x24;
fiat_25519_uint128 x25;
fiat_25519_uint128 x26;
uint64_t x27;
uint64_t x28;
fiat_25519_uint128 x29;
fiat_25519_uint128 x30;
fiat_25519_uint128 x31;
fiat_25519_uint128 x32;
fiat_25519_uint128 x33;
uint64_t x34;
uint64_t x35;
fiat_25519_uint128 x36;
uint64_t x37;
uint64_t x38;
fiat_25519_uint128 x39;
uint64_t x40;
uint64_t x41;
fiat_25519_uint128 x42;
uint64_t x43;
uint64_t x44;
uint64_t x45;
uint64_t x46;
uint64_t x47;
uint64_t x48;
uint64_t x49;
fiat_25519_uint1 x50;
uint64_t x51;
uint64_t x52;
x1 = ((fiat_25519_uint128)(arg1[4]) * ((arg2[4]) * UINT8_C(0x13)));
x2 = ((fiat_25519_uint128)(arg1[4]) * ((arg2[3]) * UINT8_C(0x13)));
x3 = ((fiat_25519_uint128)(arg1[4]) * ((arg2[2]) * UINT8_C(0x13)));
x4 = ((fiat_25519_uint128)(arg1[4]) * ((arg2[1]) * UINT8_C(0x13)));
x5 = ((fiat_25519_uint128)(arg1[3]) * ((arg2[4]) * UINT8_C(0x13)));
x6 = ((fiat_25519_uint128)(arg1[3]) * ((arg2[3]) * UINT8_C(0x13)));
x7 = ((fiat_25519_uint128)(arg1[3]) * ((arg2[2]) * UINT8_C(0x13)));
x8 = ((fiat_25519_uint128)(arg1[2]) * ((arg2[4]) * UINT8_C(0x13)));
x9 = ((fiat_25519_uint128)(arg1[2]) * ((arg2[3]) * UINT8_C(0x13)));
x10 = ((fiat_25519_uint128)(arg1[1]) * ((arg2[4]) * UINT8_C(0x13)));
x11 = ((fiat_25519_uint128)(arg1[4]) * (arg2[0]));
x12 = ((fiat_25519_uint128)(arg1[3]) * (arg2[1]));
x13 = ((fiat_25519_uint128)(arg1[3]) * (arg2[0]));
x14 = ((fiat_25519_uint128)(arg1[2]) * (arg2[2]));
x15 = ((fiat_25519_uint128)(arg1[2]) * (arg2[1]));
x16 = ((fiat_25519_uint128)(arg1[2]) * (arg2[0]));
x17 = ((fiat_25519_uint128)(arg1[1]) * (arg2[3]));
x18 = ((fiat_25519_uint128)(arg1[1]) * (arg2[2]));
x19 = ((fiat_25519_uint128)(arg1[1]) * (arg2[1]));
x20 = ((fiat_25519_uint128)(arg1[1]) * (arg2[0]));
x21 = ((fiat_25519_uint128)(arg1[0]) * (arg2[4]));
x22 = ((fiat_25519_uint128)(arg1[0]) * (arg2[3]));
x23 = ((fiat_25519_uint128)(arg1[0]) * (arg2[2]));
x24 = ((fiat_25519_uint128)(arg1[0]) * (arg2[1]));
x25 = ((fiat_25519_uint128)(arg1[0]) * (arg2[0]));
x26 = (x25 + (x10 + (x9 + (x7 + x4))));
x27 = (uint64_t)(x26 >> 51);
x28 = (uint64_t)(x26 & UINT64_C(0x7ffffffffffff));
x29 = (x21 + (x17 + (x14 + (x12 + x11))));
x30 = (x22 + (x18 + (x15 + (x13 + x1))));
x31 = (x23 + (x19 + (x16 + (x5 + x2))));
x32 = (x24 + (x20 + (x8 + (x6 + x3))));
x33 = (x27 + x32);
x34 = (uint64_t)(x33 >> 51);
x35 = (uint64_t)(x33 & UINT64_C(0x7ffffffffffff));
x36 = (x34 + x31);
x37 = (uint64_t)(x36 >> 51);
x38 = (uint64_t)(x36 & UINT64_C(0x7ffffffffffff));
x39 = (x37 + x30);
x40 = (uint64_t)(x39 >> 51);
x41 = (uint64_t)(x39 & UINT64_C(0x7ffffffffffff));
x42 = (x40 + x29);
x43 = (uint64_t)(x42 >> 51);
x44 = (uint64_t)(x42 & UINT64_C(0x7ffffffffffff));
x45 = (x43 * UINT8_C(0x13));
x46 = (x28 + x45);
x47 = (x46 >> 51);
x48 = (x46 & UINT64_C(0x7ffffffffffff));
x49 = (x47 + x35);
x50 = (fiat_25519_uint1)(x49 >> 51);
x51 = (x49 & UINT64_C(0x7ffffffffffff));
x52 = (x50 + x38);
out1[0] = x48;
out1[1] = x51;
out1[2] = x52;
out1[3] = x41;
out1[4] = x44;
}
/*
* The function fiat_25519_carry_square squares a field element and reduces the result.
*
* Postconditions:
* eval out1 mod m = (eval arg1 * eval arg1) mod m
*
*/
static void fiat_25519_carry_square(fiat_25519_tight_field_element out1, const fiat_25519_loose_field_element arg1) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
fiat_25519_uint128 x9;
fiat_25519_uint128 x10;
fiat_25519_uint128 x11;
fiat_25519_uint128 x12;
fiat_25519_uint128 x13;
fiat_25519_uint128 x14;
fiat_25519_uint128 x15;
fiat_25519_uint128 x16;
fiat_25519_uint128 x17;
fiat_25519_uint128 x18;
fiat_25519_uint128 x19;
fiat_25519_uint128 x20;
fiat_25519_uint128 x21;
fiat_25519_uint128 x22;
fiat_25519_uint128 x23;
fiat_25519_uint128 x24;
uint64_t x25;
uint64_t x26;
fiat_25519_uint128 x27;
fiat_25519_uint128 x28;
fiat_25519_uint128 x29;
fiat_25519_uint128 x30;
fiat_25519_uint128 x31;
uint64_t x32;
uint64_t x33;
fiat_25519_uint128 x34;
uint64_t x35;
uint64_t x36;
fiat_25519_uint128 x37;
uint64_t x38;
uint64_t x39;
fiat_25519_uint128 x40;
uint64_t x41;
uint64_t x42;
uint64_t x43;
uint64_t x44;
uint64_t x45;
uint64_t x46;
uint64_t x47;
fiat_25519_uint1 x48;
uint64_t x49;
uint64_t x50;
x1 = ((arg1[4]) * UINT8_C(0x13));
x2 = (x1 * 0x2);
x3 = ((arg1[4]) * 0x2);
x4 = ((arg1[3]) * UINT8_C(0x13));
x5 = (x4 * 0x2);
x6 = ((arg1[3]) * 0x2);
x7 = ((arg1[2]) * 0x2);
x8 = ((arg1[1]) * 0x2);
x9 = ((fiat_25519_uint128)(arg1[4]) * x1);
x10 = ((fiat_25519_uint128)(arg1[3]) * x2);
x11 = ((fiat_25519_uint128)(arg1[3]) * x4);
x12 = ((fiat_25519_uint128)(arg1[2]) * x2);
x13 = ((fiat_25519_uint128)(arg1[2]) * x5);
x14 = ((fiat_25519_uint128)(arg1[2]) * (arg1[2]));
x15 = ((fiat_25519_uint128)(arg1[1]) * x2);
x16 = ((fiat_25519_uint128)(arg1[1]) * x6);
x17 = ((fiat_25519_uint128)(arg1[1]) * x7);
x18 = ((fiat_25519_uint128)(arg1[1]) * (arg1[1]));
x19 = ((fiat_25519_uint128)(arg1[0]) * x3);
x20 = ((fiat_25519_uint128)(arg1[0]) * x6);
x21 = ((fiat_25519_uint128)(arg1[0]) * x7);
x22 = ((fiat_25519_uint128)(arg1[0]) * x8);
x23 = ((fiat_25519_uint128)(arg1[0]) * (arg1[0]));
x24 = (x23 + (x15 + x13));
x25 = (uint64_t)(x24 >> 51);
x26 = (uint64_t)(x24 & UINT64_C(0x7ffffffffffff));
x27 = (x19 + (x16 + x14));
x28 = (x20 + (x17 + x9));
x29 = (x21 + (x18 + x10));
x30 = (x22 + (x12 + x11));
x31 = (x25 + x30);
x32 = (uint64_t)(x31 >> 51);
x33 = (uint64_t)(x31 & UINT64_C(0x7ffffffffffff));
x34 = (x32 + x29);
x35 = (uint64_t)(x34 >> 51);
x36 = (uint64_t)(x34 & UINT64_C(0x7ffffffffffff));
x37 = (x35 + x28);
x38 = (uint64_t)(x37 >> 51);
x39 = (uint64_t)(x37 & UINT64_C(0x7ffffffffffff));
x40 = (x38 + x27);
x41 = (uint64_t)(x40 >> 51);
x42 = (uint64_t)(x40 & UINT64_C(0x7ffffffffffff));
x43 = (x41 * UINT8_C(0x13));
x44 = (x26 + x43);
x45 = (x44 >> 51);
x46 = (x44 & UINT64_C(0x7ffffffffffff));
x47 = (x45 + x33);
x48 = (fiat_25519_uint1)(x47 >> 51);
x49 = (x47 & UINT64_C(0x7ffffffffffff));
x50 = (x48 + x36);
out1[0] = x46;
out1[1] = x49;
out1[2] = x50;
out1[3] = x39;
out1[4] = x42;
}
/*
* The function fiat_25519_carry reduces a field element.
*
* Postconditions:
* eval out1 mod m = eval arg1 mod m
*
*/
static void fiat_25519_carry(fiat_25519_tight_field_element out1, const fiat_25519_loose_field_element arg1) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
x1 = (arg1[0]);
x2 = ((x1 >> 51) + (arg1[1]));
x3 = ((x2 >> 51) + (arg1[2]));
x4 = ((x3 >> 51) + (arg1[3]));
x5 = ((x4 >> 51) + (arg1[4]));
x6 = ((x1 & UINT64_C(0x7ffffffffffff)) + ((x5 >> 51) * UINT8_C(0x13)));
x7 = ((fiat_25519_uint1)(x6 >> 51) + (x2 & UINT64_C(0x7ffffffffffff)));
x8 = (x6 & UINT64_C(0x7ffffffffffff));
x9 = (x7 & UINT64_C(0x7ffffffffffff));
x10 = ((fiat_25519_uint1)(x7 >> 51) + (x3 & UINT64_C(0x7ffffffffffff)));
x11 = (x4 & UINT64_C(0x7ffffffffffff));
x12 = (x5 & UINT64_C(0x7ffffffffffff));
out1[0] = x8;
out1[1] = x9;
out1[2] = x10;
out1[3] = x11;
out1[4] = x12;
}
/*
* The function fiat_25519_add adds two field elements.
*
* Postconditions:
* eval out1 mod m = (eval arg1 + eval arg2) mod m
*
*/
static void fiat_25519_add(fiat_25519_loose_field_element out1, const fiat_25519_tight_field_element arg1, const fiat_25519_tight_field_element arg2) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
x1 = ((arg1[0]) + (arg2[0]));
x2 = ((arg1[1]) + (arg2[1]));
x3 = ((arg1[2]) + (arg2[2]));
x4 = ((arg1[3]) + (arg2[3]));
x5 = ((arg1[4]) + (arg2[4]));
out1[0] = x1;
out1[1] = x2;
out1[2] = x3;
out1[3] = x4;
out1[4] = x5;
}
/*
* The function fiat_25519_sub subtracts two field elements.
*
* Postconditions:
* eval out1 mod m = (eval arg1 - eval arg2) mod m
*
*/
static void fiat_25519_sub(fiat_25519_loose_field_element out1, const fiat_25519_tight_field_element arg1, const fiat_25519_tight_field_element arg2) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
x1 = ((UINT64_C(0xfffffffffffda) + (arg1[0])) - (arg2[0]));
x2 = ((UINT64_C(0xffffffffffffe) + (arg1[1])) - (arg2[1]));
x3 = ((UINT64_C(0xffffffffffffe) + (arg1[2])) - (arg2[2]));
x4 = ((UINT64_C(0xffffffffffffe) + (arg1[3])) - (arg2[3]));
x5 = ((UINT64_C(0xffffffffffffe) + (arg1[4])) - (arg2[4]));
out1[0] = x1;
out1[1] = x2;
out1[2] = x3;
out1[3] = x4;
out1[4] = x5;
}
/*
* The function fiat_25519_opp negates a field element.
*
* Postconditions:
* eval out1 mod m = -eval arg1 mod m
*
*/
static void fiat_25519_opp(fiat_25519_loose_field_element out1, const fiat_25519_tight_field_element arg1) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
x1 = (UINT64_C(0xfffffffffffda) - (arg1[0]));
x2 = (UINT64_C(0xffffffffffffe) - (arg1[1]));
x3 = (UINT64_C(0xffffffffffffe) - (arg1[2]));
x4 = (UINT64_C(0xffffffffffffe) - (arg1[3]));
x5 = (UINT64_C(0xffffffffffffe) - (arg1[4]));
out1[0] = x1;
out1[1] = x2;
out1[2] = x3;
out1[3] = x4;
out1[4] = x5;
}
/*
* The function fiat_25519_selectznz is a multi-limb conditional select.
*
* Postconditions:
* out1 = (if arg1 = 0 then arg2 else arg3)
*
* Input Bounds:
* arg1: [0x0 ~> 0x1]
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_25519_selectznz(uint64_t out1[5], fiat_25519_uint1 arg1, const uint64_t arg2[5], const uint64_t arg3[5]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
fiat_25519_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
fiat_25519_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
fiat_25519_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
fiat_25519_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
fiat_25519_cmovznz_u64(&x5, arg1, (arg2[4]), (arg3[4]));
out1[0] = x1;
out1[1] = x2;
out1[2] = x3;
out1[3] = x4;
out1[4] = x5;
}
/*
* The function fiat_25519_to_bytes serializes a field element to bytes in little-endian order.
*
* Postconditions:
* out1 = map (λ x, ((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)) [0..31]
*
* Output Bounds:
* out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
*/
static void fiat_25519_to_bytes(uint8_t out1[32], const fiat_25519_tight_field_element arg1) {
uint64_t x1;
fiat_25519_uint1 x2;
uint64_t x3;
fiat_25519_uint1 x4;
uint64_t x5;
fiat_25519_uint1 x6;
uint64_t x7;
fiat_25519_uint1 x8;
uint64_t x9;
fiat_25519_uint1 x10;
uint64_t x11;
uint64_t x12;
fiat_25519_uint1 x13;
uint64_t x14;
fiat_25519_uint1 x15;
uint64_t x16;
fiat_25519_uint1 x17;
uint64_t x18;
fiat_25519_uint1 x19;
uint64_t x20;
fiat_25519_uint1 x21;
uint64_t x22;
uint64_t x23;
uint64_t x24;
uint64_t x25;
uint8_t x26;
uint64_t x27;
uint8_t x28;
uint64_t x29;
uint8_t x30;
uint64_t x31;
uint8_t x32;
uint64_t x33;
uint8_t x34;
uint64_t x35;
uint8_t x36;
uint8_t x37;
uint64_t x38;
uint8_t x39;
uint64_t x40;
uint8_t x41;
uint64_t x42;
uint8_t x43;
uint64_t x44;
uint8_t x45;
uint64_t x46;
uint8_t x47;
uint64_t x48;
uint8_t x49;
uint8_t x50;
uint64_t x51;
uint8_t x52;
uint64_t x53;
uint8_t x54;
uint64_t x55;
uint8_t x56;
uint64_t x57;
uint8_t x58;
uint64_t x59;
uint8_t x60;
uint64_t x61;
uint8_t x62;
uint64_t x63;
uint8_t x64;
fiat_25519_uint1 x65;
uint64_t x66;
uint8_t x67;
uint64_t x68;
uint8_t x69;
uint64_t x70;
uint8_t x71;
uint64_t x72;
uint8_t x73;
uint64_t x74;
uint8_t x75;
uint64_t x76;
uint8_t x77;
uint8_t x78;
uint64_t x79;
uint8_t x80;
uint64_t x81;
uint8_t x82;
uint64_t x83;
uint8_t x84;
uint64_t x85;
uint8_t x86;
uint64_t x87;
uint8_t x88;
uint64_t x89;
uint8_t x90;
uint8_t x91;
fiat_25519_subborrowx_u51(&x1, &x2, 0x0, (arg1[0]), UINT64_C(0x7ffffffffffed));
fiat_25519_subborrowx_u51(&x3, &x4, x2, (arg1[1]), UINT64_C(0x7ffffffffffff));
fiat_25519_subborrowx_u51(&x5, &x6, x4, (arg1[2]), UINT64_C(0x7ffffffffffff));
fiat_25519_subborrowx_u51(&x7, &x8, x6, (arg1[3]), UINT64_C(0x7ffffffffffff));
fiat_25519_subborrowx_u51(&x9, &x10, x8, (arg1[4]), UINT64_C(0x7ffffffffffff));
fiat_25519_cmovznz_u64(&x11, x10, 0x0, UINT64_C(0xffffffffffffffff));
fiat_25519_addcarryx_u51(&x12, &x13, 0x0, x1, (x11 & UINT64_C(0x7ffffffffffed)));
fiat_25519_addcarryx_u51(&x14, &x15, x13, x3, (x11 & UINT64_C(0x7ffffffffffff)));
fiat_25519_addcarryx_u51(&x16, &x17, x15, x5, (x11 & UINT64_C(0x7ffffffffffff)));
fiat_25519_addcarryx_u51(&x18, &x19, x17, x7, (x11 & UINT64_C(0x7ffffffffffff)));
fiat_25519_addcarryx_u51(&x20, &x21, x19, x9, (x11 & UINT64_C(0x7ffffffffffff)));
x22 = (x20 << 4);
x23 = (x18 * (uint64_t)0x2);
x24 = (x16 << 6);
x25 = (x14 << 3);
x26 = (uint8_t)(x12 & UINT8_C(0xff));
x27 = (x12 >> 8);
x28 = (uint8_t)(x27 & UINT8_C(0xff));
x29 = (x27 >> 8);
x30 = (uint8_t)(x29 & UINT8_C(0xff));
x31 = (x29 >> 8);
x32 = (uint8_t)(x31 & UINT8_C(0xff));
x33 = (x31 >> 8);
x34 = (uint8_t)(x33 & UINT8_C(0xff));
x35 = (x33 >> 8);
x36 = (uint8_t)(x35 & UINT8_C(0xff));
x37 = (uint8_t)(x35 >> 8);
x38 = (x25 + (uint64_t)x37);
x39 = (uint8_t)(x38 & UINT8_C(0xff));
x40 = (x38 >> 8);
x41 = (uint8_t)(x40 & UINT8_C(0xff));
x42 = (x40 >> 8);
x43 = (uint8_t)(x42 & UINT8_C(0xff));
x44 = (x42 >> 8);
x45 = (uint8_t)(x44 & UINT8_C(0xff));
x46 = (x44 >> 8);
x47 = (uint8_t)(x46 & UINT8_C(0xff));
x48 = (x46 >> 8);
x49 = (uint8_t)(x48 & UINT8_C(0xff));
x50 = (uint8_t)(x48 >> 8);
x51 = (x24 + (uint64_t)x50);
x52 = (uint8_t)(x51 & UINT8_C(0xff));
x53 = (x51 >> 8);
x54 = (uint8_t)(x53 & UINT8_C(0xff));
x55 = (x53 >> 8);
x56 = (uint8_t)(x55 & UINT8_C(0xff));
x57 = (x55 >> 8);
x58 = (uint8_t)(x57 & UINT8_C(0xff));
x59 = (x57 >> 8);
x60 = (uint8_t)(x59 & UINT8_C(0xff));
x61 = (x59 >> 8);
x62 = (uint8_t)(x61 & UINT8_C(0xff));
x63 = (x61 >> 8);
x64 = (uint8_t)(x63 & UINT8_C(0xff));
x65 = (fiat_25519_uint1)(x63 >> 8);
x66 = (x23 + (uint64_t)x65);
x67 = (uint8_t)(x66 & UINT8_C(0xff));
x68 = (x66 >> 8);
x69 = (uint8_t)(x68 & UINT8_C(0xff));
x70 = (x68 >> 8);
x71 = (uint8_t)(x70 & UINT8_C(0xff));
x72 = (x70 >> 8);
x73 = (uint8_t)(x72 & UINT8_C(0xff));
x74 = (x72 >> 8);
x75 = (uint8_t)(x74 & UINT8_C(0xff));
x76 = (x74 >> 8);
x77 = (uint8_t)(x76 & UINT8_C(0xff));
x78 = (uint8_t)(x76 >> 8);
x79 = (x22 + (uint64_t)x78);
x80 = (uint8_t)(x79 & UINT8_C(0xff));
x81 = (x79 >> 8);
x82 = (uint8_t)(x81 & UINT8_C(0xff));
x83 = (x81 >> 8);
x84 = (uint8_t)(x83 & UINT8_C(0xff));
x85 = (x83 >> 8);
x86 = (uint8_t)(x85 & UINT8_C(0xff));
x87 = (x85 >> 8);
x88 = (uint8_t)(x87 & UINT8_C(0xff));
x89 = (x87 >> 8);
x90 = (uint8_t)(x89 & UINT8_C(0xff));
x91 = (uint8_t)(x89 >> 8);
out1[0] = x26;
out1[1] = x28;
out1[2] = x30;
out1[3] = x32;
out1[4] = x34;
out1[5] = x36;
out1[6] = x39;
out1[7] = x41;
out1[8] = x43;
out1[9] = x45;
out1[10] = x47;
out1[11] = x49;
out1[12] = x52;
out1[13] = x54;
out1[14] = x56;
out1[15] = x58;
out1[16] = x60;
out1[17] = x62;
out1[18] = x64;
out1[19] = x67;
out1[20] = x69;
out1[21] = x71;
out1[22] = x73;
out1[23] = x75;
out1[24] = x77;
out1[25] = x80;
out1[26] = x82;
out1[27] = x84;
out1[28] = x86;
out1[29] = x88;
out1[30] = x90;
out1[31] = x91;
}
/*
* The function fiat_25519_from_bytes deserializes a field element from bytes in little-endian order.
*
* Postconditions:
* eval out1 mod m = bytes_eval arg1 mod m
*
* Input Bounds:
* arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
*/
static void fiat_25519_from_bytes(fiat_25519_tight_field_element out1, const uint8_t arg1[32]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
uint64_t x13;
uint64_t x14;
uint64_t x15;
uint64_t x16;
uint64_t x17;
uint64_t x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
uint64_t x22;
uint64_t x23;
uint64_t x24;
uint64_t x25;
uint64_t x26;
uint64_t x27;
uint64_t x28;
uint64_t x29;
uint64_t x30;
uint64_t x31;
uint8_t x32;
uint64_t x33;
uint64_t x34;
uint64_t x35;
uint64_t x36;
uint64_t x37;
uint64_t x38;
uint64_t x39;
uint8_t x40;
uint64_t x41;
uint64_t x42;
uint64_t x43;
uint64_t x44;
uint64_t x45;
uint64_t x46;
uint64_t x47;
uint8_t x48;
uint64_t x49;
uint64_t x50;
uint64_t x51;
uint64_t x52;
uint64_t x53;
uint64_t x54;
uint64_t x55;
uint64_t x56;
uint8_t x57;
uint64_t x58;
uint64_t x59;
uint64_t x60;
uint64_t x61;
uint64_t x62;
uint64_t x63;
uint64_t x64;
uint8_t x65;
uint64_t x66;
uint64_t x67;
uint64_t x68;
uint64_t x69;
uint64_t x70;
uint64_t x71;
x1 = ((uint64_t)(arg1[31]) << 44);
x2 = ((uint64_t)(arg1[30]) << 36);
x3 = ((uint64_t)(arg1[29]) << 28);
x4 = ((uint64_t)(arg1[28]) << 20);
x5 = ((uint64_t)(arg1[27]) << 12);
x6 = ((uint64_t)(arg1[26]) << 4);
x7 = ((uint64_t)(arg1[25]) << 47);
x8 = ((uint64_t)(arg1[24]) << 39);
x9 = ((uint64_t)(arg1[23]) << 31);
x10 = ((uint64_t)(arg1[22]) << 23);
x11 = ((uint64_t)(arg1[21]) << 15);
x12 = ((uint64_t)(arg1[20]) << 7);
x13 = ((uint64_t)(arg1[19]) << 50);
x14 = ((uint64_t)(arg1[18]) << 42);
x15 = ((uint64_t)(arg1[17]) << 34);
x16 = ((uint64_t)(arg1[16]) << 26);
x17 = ((uint64_t)(arg1[15]) << 18);
x18 = ((uint64_t)(arg1[14]) << 10);
x19 = ((uint64_t)(arg1[13]) << 2);
x20 = ((uint64_t)(arg1[12]) << 45);
x21 = ((uint64_t)(arg1[11]) << 37);
x22 = ((uint64_t)(arg1[10]) << 29);
x23 = ((uint64_t)(arg1[9]) << 21);
x24 = ((uint64_t)(arg1[8]) << 13);
x25 = ((uint64_t)(arg1[7]) << 5);
x26 = ((uint64_t)(arg1[6]) << 48);
x27 = ((uint64_t)(arg1[5]) << 40);
x28 = ((uint64_t)(arg1[4]) << 32);
x29 = ((uint64_t)(arg1[3]) << 24);
x30 = ((uint64_t)(arg1[2]) << 16);
x31 = ((uint64_t)(arg1[1]) << 8);
x32 = (arg1[0]);
x33 = (x31 + (uint64_t)x32);
x34 = (x30 + x33);
x35 = (x29 + x34);
x36 = (x28 + x35);
x37 = (x27 + x36);
x38 = (x26 + x37);
x39 = (x38 & UINT64_C(0x7ffffffffffff));
x40 = (uint8_t)(x38 >> 51);
x41 = (x25 + (uint64_t)x40);
x42 = (x24 + x41);
x43 = (x23 + x42);
x44 = (x22 + x43);
x45 = (x21 + x44);
x46 = (x20 + x45);
x47 = (x46 & UINT64_C(0x7ffffffffffff));
x48 = (uint8_t)(x46 >> 51);
x49 = (x19 + (uint64_t)x48);
x50 = (x18 + x49);
x51 = (x17 + x50);
x52 = (x16 + x51);
x53 = (x15 + x52);
x54 = (x14 + x53);
x55 = (x13 + x54);
x56 = (x55 & UINT64_C(0x7ffffffffffff));
x57 = (uint8_t)(x55 >> 51);
x58 = (x12 + (uint64_t)x57);
x59 = (x11 + x58);
x60 = (x10 + x59);
x61 = (x9 + x60);
x62 = (x8 + x61);
x63 = (x7 + x62);
x64 = (x63 & UINT64_C(0x7ffffffffffff));
x65 = (uint8_t)(x63 >> 51);
x66 = (x6 + (uint64_t)x65);
x67 = (x5 + x66);
x68 = (x4 + x67);
x69 = (x3 + x68);
x70 = (x2 + x69);
x71 = (x1 + x70);
out1[0] = x39;
out1[1] = x47;
out1[2] = x56;
out1[3] = x64;
out1[4] = x71;
}
/*
* The function fiat_25519_carry_scmul_121666 multiplies a field element by 121666 and reduces the result.
*
* Postconditions:
* eval out1 mod m = (121666 * eval arg1) mod m
*
*/
static void fiat_25519_carry_scmul_121666(fiat_25519_tight_field_element out1, const fiat_25519_loose_field_element arg1) {
fiat_25519_uint128 x1;
fiat_25519_uint128 x2;
fiat_25519_uint128 x3;
fiat_25519_uint128 x4;
fiat_25519_uint128 x5;
uint64_t x6;
uint64_t x7;
fiat_25519_uint128 x8;
uint64_t x9;
uint64_t x10;
fiat_25519_uint128 x11;
uint64_t x12;
uint64_t x13;
fiat_25519_uint128 x14;
uint64_t x15;
uint64_t x16;
fiat_25519_uint128 x17;
uint64_t x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
fiat_25519_uint1 x22;
uint64_t x23;
uint64_t x24;
fiat_25519_uint1 x25;
uint64_t x26;
uint64_t x27;
x1 = ((fiat_25519_uint128)UINT32_C(0x1db42) * (arg1[4]));
x2 = ((fiat_25519_uint128)UINT32_C(0x1db42) * (arg1[3]));
x3 = ((fiat_25519_uint128)UINT32_C(0x1db42) * (arg1[2]));
x4 = ((fiat_25519_uint128)UINT32_C(0x1db42) * (arg1[1]));
x5 = ((fiat_25519_uint128)UINT32_C(0x1db42) * (arg1[0]));
x6 = (uint64_t)(x5 >> 51);
x7 = (uint64_t)(x5 & UINT64_C(0x7ffffffffffff));
x8 = (x6 + x4);
x9 = (uint64_t)(x8 >> 51);
x10 = (uint64_t)(x8 & UINT64_C(0x7ffffffffffff));
x11 = (x9 + x3);
x12 = (uint64_t)(x11 >> 51);
x13 = (uint64_t)(x11 & UINT64_C(0x7ffffffffffff));
x14 = (x12 + x2);
x15 = (uint64_t)(x14 >> 51);
x16 = (uint64_t)(x14 & UINT64_C(0x7ffffffffffff));
x17 = (x15 + x1);
x18 = (uint64_t)(x17 >> 51);
x19 = (uint64_t)(x17 & UINT64_C(0x7ffffffffffff));
x20 = (x18 * UINT8_C(0x13));
x21 = (x7 + x20);
x22 = (fiat_25519_uint1)(x21 >> 51);
x23 = (x21 & UINT64_C(0x7ffffffffffff));
x24 = (x22 + x10);
x25 = (fiat_25519_uint1)(x24 >> 51);
x26 = (x24 & UINT64_C(0x7ffffffffffff));
x27 = (x25 + x13);
out1[0] = x23;
out1[1] = x26;
out1[2] = x27;
out1[3] = x16;
out1[4] = x19;
}

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/* following code is from c47bfce06 of boringssl: crypto/curve25519 */
/* Copyright (c) 2020, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
// This file is generated from
// ./make_curve25519_tables.py > curve25519_tables.h
static const fe d = {{
#if defined(ARCH_64BIT)
929955233495203, 466365720129213, 1662059464998953, 2033849074728123,
1442794654840575
#else
56195235, 13857412, 51736253, 6949390, 114729, 24766616, 60832955, 30306712,
48412415, 21499315
#endif
}};
static const fe sqrtm1 = {{
#if defined(ARCH_64BIT)
1718705420411056, 234908883556509, 2233514472574048, 2117202627021982,
765476049583133
#else
34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654,
31548777, 326685, 11406482
#endif
}};
static const fe d2 = {{
#if defined(ARCH_64BIT)
1859910466990425, 932731440258426, 1072319116312658, 1815898335770999,
633789495995903
#else
45281625, 27714825, 36363642, 13898781, 229458, 15978800, 54557047,
27058993, 29715967, 9444199
#endif
}};
// This block of code replaces the standard base-point table with a much smaller
// one. The standard table is 30,720 bytes while this one is just 960.
//
// This table contains 15 pairs of group elements, (x, y), where each field
// element is serialised with |fe_tobytes|. If |i| is the index of the group
// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
// is the most significant bit). The value of the group element is then:
// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {
0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95,
0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e,
0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4,
0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62,
0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba,
0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd,
0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61,
0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c,
0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c,
0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5,
0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3,
0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18,
0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2,
0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95,
0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b,
0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90,
0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52,
0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb,
0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c,
0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e,
0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e,
0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a,
0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43,
0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53,
0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8,
0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89,
0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef,
0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60,
0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a,
0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8,
0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54,
0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b,
0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd,
0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb,
0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c,
0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b,
0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63,
0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a,
0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07,
0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa,
0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a,
0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84,
0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc,
0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42,
0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0,
0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0,
0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a,
0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5,
0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c,
0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27,
0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31,
0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c,
0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87,
0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0,
0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23,
0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2,
0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87,
0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d,
0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b,
0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d,
0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6,
0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84,
0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04,
0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19,
0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b,
0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a,
0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea,
0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30,
0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7,
0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa,
0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5,
0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71,
0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab,
0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb,
0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c,
0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25,
};
// Bi[i] = (2*i+1)*B
static const ge_precomp Bi[8] = {
{
{{
#if defined(ARCH_64BIT)
1288382639258501, 245678601348599, 269427782077623,
1462984067271730, 137412439391563
#else
25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
21800161, 61029707, 2047604
#endif
}},
{{
#if defined(ARCH_64BIT)
62697248952638, 204681361388450, 631292143396476, 338455783676468,
1213667448819585
#else
54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
5043384, 19500929, 18085054
#endif
}},
{{
#if defined(ARCH_64BIT)
301289933810280, 1259582250014073, 1422107436869536,
796239922652654, 1953934009299142
#else
58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
11864899, 42594502, 29115885
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
1601611775252272, 1720807796594148, 1132070835939856,
1260455018889551, 2147779492816911
#else
15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
18782243, 28944399, 32004408
#endif
}},
{{
#if defined(ARCH_64BIT)
316559037616741, 2177824224946892, 1459442586438991,
1461528397712656, 751590696113597
#else
16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
21778470, 7689661, 11199574
#endif
}},
{{
#if defined(ARCH_64BIT)
1850748884277385, 1200145853858453, 1068094770532492,
672251375690438, 1586055907191707
#else
30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
10017326, 49359771, 23634074
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
769950342298419, 132954430919746, 844085933195555, 974092374476333,
726076285546016
#else
10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
14515107, 51670560, 10819379
#endif
}},
{{
#if defined(ARCH_64BIT)
425251763115706, 608463272472562, 442562545713235, 837766094556764,
374555092627893
#else
4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
12483687, 54440373, 5581305
#endif
}},
{{
#if defined(ARCH_64BIT)
1086255230780037, 274979815921559, 1960002765731872,
929474102396301, 1190409889297339
#else
19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
13850243, 43430843, 17738489
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
665000864555967, 2065379846933859, 370231110385876, 350988370788628,
1233371373142985
#else
5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
5230134, 43156425, 18378665
#endif
}},
{{
#if defined(ARCH_64BIT)
2019367628972465, 676711900706637, 110710997811333,
1108646842542025, 517791959672113
#else
36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025,
16520125, 30598449, 7715701
#endif
}},
{{
#if defined(ARCH_64BIT)
965130719900578, 247011430587952, 526356006571389, 91986625355052,
2157223321444601
#else
28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
1370707, 29794553, 32145132
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
1802695059465007, 1664899123557221, 593559490740857,
2160434469266659, 927570450755031
#else
44589871, 26862249, 14201701, 24808930, 43598457, 8844725, 18474211,
32192982, 54046167, 13821876
#endif
}},
{{
#if defined(ARCH_64BIT)
1725674970513508, 1933645953859181, 1542344539275782,
1767788773573747, 1297447965928905
#else
60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027,
26342105, 18853321, 19333481
#endif
}},
{{
#if defined(ARCH_64BIT)
1381809363726107, 1430341051343062, 2061843536018959,
1551778050872521, 2036394857967624
#else
4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505,
23123294, 2207752, 30344648
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
1970894096313054, 528066325833207, 1619374932191227,
2207306624415883, 1169170329061080
#else
41954014, 29368610, 29681143, 7868801, 60254203, 24130566, 54671499,
32891431, 35997400, 17421995
#endif
}},
{{
#if defined(ARCH_64BIT)
2070390218572616, 1458919061857835, 624171843017421,
1055332792707765, 433987520732508
#else
25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789,
15725684, 171356, 6466918
#endif
}},
{{
#if defined(ARCH_64BIT)
893653801273833, 1168026499324677, 1242553501121234,
1306366254304474, 1086752658510815
#else
23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338,
19466374, 36393951, 16193876
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
213454002618221, 939771523987438, 1159882208056014, 317388369627517,
621213314200687
#else
33587053, 3180712, 64714734, 14003686, 50205390, 17283591, 17238397,
4729455, 49034351, 9256799
#endif
}},
{{
#if defined(ARCH_64BIT)
1971678598905747, 338026507889165, 762398079972271, 655096486107477,
42299032696322
#else
41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405,
9761698, 47281666, 630304
#endif
}},
{{
#if defined(ARCH_64BIT)
177130678690680, 1754759263300204, 1864311296286618,
1180675631479880, 1292726903152791
#else
53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312,
17593437, 64659607, 19263131
#endif
}},
},
{
{{
#if defined(ARCH_64BIT)
1913163449625248, 460779200291993, 2193883288642314,
1008900146920800, 1721983679009502
#else
63957664, 28508356, 9282713, 6866145, 35201802, 32691408, 48168288,
15033783, 25105118, 25659556
#endif
}},
{{
#if defined(ARCH_64BIT)
1070401523076875, 1272492007800961, 1910153608563310,
2075579521696771, 1191169788841221
#else
42782475, 15950225, 35307649, 18961608, 55446126, 28463506, 1573891,
30928545, 2198789, 17749813
#endif
}},
{{
#if defined(ARCH_64BIT)
692896803108118, 500174642072499, 2068223309439677,
1162190621851337, 1426986007309901
#else
64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841,
17317989, 34647629, 21263748
#endif
}},
},
};

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@ -0,0 +1,61 @@
#define MAKE_FN_NAME1(x,y) x ## y
#define MAKE_FN_NAME(x,y) MAKE_FN_NAME1(x,y)
#define PRECOMP MAKE_FN_NAME(CURVE_DESCRIPTION,_divstep_precomp)
#define MSAT MAKE_FN_NAME(CURVE_DESCRIPTION,_msat)
#define MONE MAKE_FN_NAME(CURVE_DESCRIPTION,_set_one)
#define DIVSTEP MAKE_FN_NAME(CURVE_DESCRIPTION,_divstep)
#define OPP MAKE_FN_NAME(CURVE_DESCRIPTION,_opp)
#define MUL MAKE_FN_NAME(CURVE_DESCRIPTION,_mul)
#define SZNZ MAKE_FN_NAME(CURVE_DESCRIPTION,_selectznz)
#if LEN_PRIME < 46
#define ITERATIONS (((49 * LEN_PRIME) + 80) / 17)
#else
#define ITERATIONS (((49 * LEN_PRIME) + 57) / 17)
#endif
#define SAT_LIMBS LIMBS + 1 /* we might need 2 more bits to represent m in twos complement */
#define BYTES 8 * (((LEN_PRIME - 1) / 64) + 1)
static void inverse(WORD out[LIMBS], WORD g[SAT_LIMBS]) {
WORD precomp[LIMBS];
PRECOMP(precomp);
WORD d = 1;
WORD f[SAT_LIMBS];
WORD v[LIMBS];
WORD r[LIMBS];
WORD out1;
WORD out2[SAT_LIMBS], out3[SAT_LIMBS], out4[LIMBS], out5[LIMBS];
MSAT(f);
MONE(r);
for (int j = 0; j < LIMBS; j++) v[j] = 0;
for (int i = 0; i < ITERATIONS - (ITERATIONS % 2); i+=2) {
DIVSTEP(&out1,out2,out3,out4,out5,d,f,g,v,r);
DIVSTEP(&d,f,g,v,r,out1,out2,out3,out4,out5);
}
if (ITERATIONS % 2) {
DIVSTEP(&out1,out2,out3,out4,out5,d,f,g,v,r);
for (int k = 0; k < LIMBS; k++) v[k] = out4[k];
for (int k = 0; k < SAT_LIMBS; k++) f[k] = out2[k];
}
WORD h[LIMBS];
OPP(h, v);
SZNZ(v, f[SAT_LIMBS -1 ] >> (WORDSIZE - 1), v, h);
MUL(out, v, precomp);
return;
}
static void inversion (WORD out[LIMBS], const WORD in[LIMBS]) {
WORD in_[SAT_LIMBS];
for (int i = 0; i < LIMBS; i++) in_[i] = in[i];
in_[LIMBS] = 0;
inverse(out, in_);
return;
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "np256_64.h"
#define LIMBS 4
#define WORD uint64_t
#define WORDSIZE 64
#else
#include "np256_32.h"
#define LIMBS 8
#define WORD uint32_t
#define WORDSIZE 32
#endif
#define LEN_PRIME 256
#define CURVE_DESCRIPTION fiat_np256
#include "inversion_template.h"
#include <caml/memory.h>
CAMLprim value mc_np256_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np256_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np256_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_one(value out)
{
CAMLparam1(out);
fiat_np256_set_one((WORD*)Bytes_val(out));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np256_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np256_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np256_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np256_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np256_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "np384_64.h"
#define LIMBS 6
#define WORD uint64_t
#define WORDSIZE 64
#else
#include "np384_32.h"
#define LIMBS 12
#define WORD uint32_t
#define WORDSIZE 32
#endif
#define LEN_PRIME 384
#define CURVE_DESCRIPTION fiat_np384
#include "inversion_template.h"
#include <caml/memory.h>
CAMLprim value mc_np384_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np384_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np384_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_one(value out)
{
CAMLparam1(out);
fiat_np384_set_one((WORD*)Bytes_val(out));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np384_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np384_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np384_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np384_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np384_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "np521_64.h"
#define LIMBS 9
#define WORD uint64_t
#define WORDSIZE 64
#else
#include "np521_32.h"
#define LIMBS 17
#define WORD uint32_t
#define WORDSIZE 32
#endif
#define LEN_PRIME 521
#define CURVE_DESCRIPTION fiat_np521
#include "inversion_template.h"
#include <caml/memory.h>
CAMLprim value mc_np521_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np521_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_np521_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_one(value out)
{
CAMLparam1(out);
fiat_np521_set_one((WORD*)Bytes_val(out));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np521_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_np521_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np521_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_np521_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_np521_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "p256_64.h"
#define LIMBS 4
#define WORD uint64_t
#define WORDSIZE 64
#include "p256_tables_64.h"
#else
#include "p256_32.h"
#define LIMBS 8
#define WORD uint32_t
#define WORDSIZE 32
#include "p256_tables_32.h"
#endif
#define LEN_PRIME 256
#define CURVE_DESCRIPTION fiat_p256
#include "inversion_template.h"
#include "point_operations.h"
#include <caml/memory.h>
CAMLprim value mc_p256_sub(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p256_sub((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p256_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p256_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p256_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p256_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_sqr(value out, value in)
{
CAMLparam2(out, in);
fiat_p256_square((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p256_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p256_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_nz(value x)
{
CAMLparam1(x);
CAMLreturn(Val_bool(fe_nz((const WORD*)String_val(x))));
}
CAMLprim value mc_p256_set_one(value x)
{
CAMLparam1(x);
fiat_p256_set_one((WORD*)Bytes_val(x));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_point_double(value out, value in)
{
CAMLparam2(out, in);
point_double(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(in, 0)),
(const WORD*)String_val(Field(in, 1)),
(const WORD*)String_val(Field(in, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_point_add(value out, value p, value q)
{
CAMLparam3(out, p, q);
point_add(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(p, 0)),
(const WORD*)String_val(Field(p, 1)),
(const WORD*)String_val(Field(p, 2)),
0,
(const WORD*)String_val(Field(q, 0)),
(const WORD*)String_val(Field(q, 1)),
(const WORD*)String_val(Field(q, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_select(value out, value bit, value t, value f)
{
CAMLparam4(out, bit, t, f);
fe_cmovznz(
(WORD*)Bytes_val(out),
Bool_val(bit),
(const WORD*)String_val(f),
(const WORD*)String_val(t)
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p256_scalar_mult_base(value out, value s)
{
CAMLparam2(out, s);
scalar_mult_base(
(WORD *) Bytes_val(Field(out, 0)),
(WORD *) Bytes_val(Field(out, 1)),
(WORD *) Bytes_val(Field(out, 2)),
_st_uint8(s),
caml_string_length(s)
);
CAMLreturn(Val_unit);
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "p384_64.h"
#define LIMBS 6
#define WORD uint64_t
#define WORDSIZE 64
#include "p384_tables_64.h"
#else
#include "p384_32.h"
#define LIMBS 12
#define WORD uint32_t
#define WORDSIZE 32
#include "p384_tables_32.h"
#endif
#define LEN_PRIME 384
#define CURVE_DESCRIPTION fiat_p384
#include "inversion_template.h"
#include "point_operations.h"
#include <caml/memory.h>
CAMLprim value mc_p384_sub(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p384_sub((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p384_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p384_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p384_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p384_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_sqr(value out, value in)
{
CAMLparam2(out, in);
fiat_p384_square((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p384_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p384_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_nz(value x)
{
CAMLparam1(x);
CAMLreturn(Val_bool(fe_nz((const WORD*)String_val(x))));
}
CAMLprim value mc_p384_set_one(value x)
{
CAMLparam1(x);
fiat_p384_set_one((WORD*)Bytes_val(x));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_point_double(value out, value in)
{
CAMLparam2(out, in);
point_double(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(in, 0)),
(const WORD*)String_val(Field(in, 1)),
(const WORD*)String_val(Field(in, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_point_add(value out, value p, value q)
{
CAMLparam3(out, p, q);
point_add(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(p, 0)),
(const WORD*)String_val(Field(p, 1)),
(const WORD*)String_val(Field(p, 2)),
0,
(const WORD*)String_val(Field(q, 0)),
(const WORD*)String_val(Field(q, 1)),
(const WORD*)String_val(Field(q, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_select(value out, value bit, value t, value f)
{
CAMLparam4(out, bit, t, f);
fe_cmovznz(
(WORD*)Bytes_val(out),
Bool_val(bit),
(const WORD*)String_val(f),
(const WORD*)String_val(t)
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p384_scalar_mult_base(value out, value s)
{
CAMLparam2(out, s);
scalar_mult_base(
(WORD *) Bytes_val(Field(out, 0)),
(WORD *) Bytes_val(Field(out, 1)),
(WORD *) Bytes_val(Field(out, 2)),
_st_uint8(s),
caml_string_length(s)
);
CAMLreturn(Val_unit);
}

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#include "mirage_crypto.h"
/* Microsoft compiler does not support 128-bit integers. Drop down to
* 32-bit for MSVC.
*/
#if defined(ARCH_64BIT) && !defined(_MSC_VER)
#include "p521_64.h"
#define LIMBS 9
#define WORD uint64_t
#define WORDSIZE 64
#include "p521_tables_64.h"
#else
#include "p521_32.h"
#define LIMBS 17
#define WORD uint32_t
#define WORDSIZE 32
#include "p521_tables_32.h"
#endif
#define LEN_PRIME 521
#define CURVE_DESCRIPTION fiat_p521
#include "inversion_template.h"
#include "point_operations.h"
#include <caml/memory.h>
CAMLprim value mc_p521_sub(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p521_sub((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_add(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p521_add((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_mul(value out, value a, value b)
{
CAMLparam3(out, a, b);
fiat_p521_mul((WORD*)Bytes_val(out), (const WORD*)String_val(a), (const WORD*)String_val(b));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_from_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p521_from_bytes((WORD*)Bytes_val(out), _st_uint8(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_to_bytes(value out, value in)
{
CAMLparam2(out, in);
fiat_p521_to_bytes(Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_sqr(value out, value in)
{
CAMLparam2(out, in);
fiat_p521_square((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_from_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p521_from_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_to_montgomery(value out, value in)
{
CAMLparam2(out, in);
fiat_p521_to_montgomery((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_nz(value x)
{
CAMLparam1(x);
CAMLreturn(Val_bool(fe_nz((const WORD*)String_val(x))));
}
CAMLprim value mc_p521_set_one(value x)
{
CAMLparam1(x);
fiat_p521_set_one((WORD*)Bytes_val(x));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_inv(value out, value in)
{
CAMLparam2(out, in);
inversion((WORD*)Bytes_val(out), (const WORD*)String_val(in));
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_point_double(value out, value in)
{
CAMLparam2(out, in);
point_double(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(in, 0)),
(const WORD*)String_val(Field(in, 1)),
(const WORD*)String_val(Field(in, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_point_add(value out, value p, value q)
{
CAMLparam3(out, p, q);
point_add(
(WORD*)Bytes_val(Field(out, 0)),
(WORD*)Bytes_val(Field(out, 1)),
(WORD*)Bytes_val(Field(out, 2)),
(const WORD*)String_val(Field(p, 0)),
(const WORD*)String_val(Field(p, 1)),
(const WORD*)String_val(Field(p, 2)),
0,
(const WORD*)String_val(Field(q, 0)),
(const WORD*)String_val(Field(q, 1)),
(const WORD*)String_val(Field(q, 2))
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_select(value out, value bit, value t, value f)
{
CAMLparam4(out, bit, t, f);
fe_cmovznz(
(WORD*)Bytes_val(out),
Bool_val(bit),
(const WORD*)String_val(f),
(const WORD*)String_val(t)
);
CAMLreturn(Val_unit);
}
CAMLprim value mc_p521_scalar_mult_base(value out, value s)
{
CAMLparam2(out, s);
scalar_mult_base(
(WORD *) Bytes_val(Field(out, 0)),
(WORD *) Bytes_val(Field(out, 1)),
(WORD *) Bytes_val(Field(out, 2)),
_st_uint8(s),
caml_string_length(s)
);
CAMLreturn(Val_unit);
}

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#define MAKE_FN_NAME1(x,y) x ## y
#define MAKE_FN_NAME(x,y) MAKE_FN_NAME1(x,y)
#define fe_one MAKE_FN_NAME(CURVE_DESCRIPTION,_set_one)
#define fe_add MAKE_FN_NAME(CURVE_DESCRIPTION,_add)
#define fe_sub MAKE_FN_NAME(CURVE_DESCRIPTION,_sub)
#define fe_mul MAKE_FN_NAME(CURVE_DESCRIPTION,_mul)
#define fe_sqr MAKE_FN_NAME(CURVE_DESCRIPTION,_square)
#define fe_nonzero MAKE_FN_NAME(CURVE_DESCRIPTION,_nonzero)
#define fe_selectznz MAKE_FN_NAME(CURVE_DESCRIPTION,_selectznz)
#define fe_from_bytes MAKE_FN_NAME(CURVE_DESCRIPTION,_from_bytes)
#define fe_to_mont MAKE_FN_NAME(CURVE_DESCRIPTION,_to_montgomery)
typedef WORD fe[LIMBS];
static WORD fe_nz(const WORD in1[LIMBS]) {
WORD ret;
fe_nonzero(&ret, in1);
return ret;
}
static void fe_copy(WORD out[LIMBS], const WORD in1[LIMBS]) {
for (int i = 0; i < LIMBS; i++) {
out[i] = in1[i];
}
}
static void fe_cmovznz(WORD out[LIMBS], WORD t, const WORD z[LIMBS],
const WORD nz[LIMBS]) {
fe_selectznz(out, !!t, z, nz);
}
// Group operations
// ----------------
//
// Building on top of the field operations we have the operations on the
// elliptic curve group itself. Points on the curve are represented in Jacobian
// coordinates.
//
// Both operations were transcribed to Coq and proven to correspond to naive
// implementations using Affine coordinates, for all suitable fields. In the
// Coq proofs, issues of constant-time execution and memory layout (aliasing)
// conventions were not considered. Specification of affine coordinates:
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Spec/WeierstrassCurve.v#L28>
// As a sanity check, a proof that these points form a commutative group:
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/AffineProofs.v#L33>
// point_double calculates 2*(x_in, y_in, z_in)
//
// The method is taken from:
// http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
//
// Coq transcription and correctness proof:
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L93>
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L201>
//
// Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
// while x_out == y_in is not (maybe this works, but it's not tested).
static void point_double(fe x_out, fe y_out, fe z_out,
const fe x_in, const fe y_in, const fe z_in) {
fe delta, gamma, beta, ftmp, ftmp2, tmptmp, alpha, fourbeta;
// delta = z^2
fe_sqr(delta, z_in);
// gamma = y^2
fe_sqr(gamma, y_in);
// beta = x*gamma
fe_mul(beta, x_in, gamma);
// alpha = 3*(x-delta)*(x+delta)
fe_sub(ftmp, x_in, delta);
fe_add(ftmp2, x_in, delta);
fe_add(tmptmp, ftmp2, ftmp2);
fe_add(ftmp2, ftmp2, tmptmp);
fe_mul(alpha, ftmp, ftmp2);
// x' = alpha^2 - 8*beta
fe_sqr(x_out, alpha);
fe_add(fourbeta, beta, beta);
fe_add(fourbeta, fourbeta, fourbeta);
fe_add(tmptmp, fourbeta, fourbeta);
fe_sub(x_out, x_out, tmptmp);
// z' = (y + z)^2 - gamma - delta
fe_add(delta, gamma, delta);
fe_add(ftmp, y_in, z_in);
fe_sqr(z_out, ftmp);
fe_sub(z_out, z_out, delta);
// y' = alpha*(4*beta - x') - 8*gamma^2
fe_sub(y_out, fourbeta, x_out);
fe_add(gamma, gamma, gamma);
fe_sqr(gamma, gamma);
fe_mul(y_out, alpha, y_out);
fe_add(gamma, gamma, gamma);
fe_sub(y_out, y_out, gamma);
}
// point_add calculates (x1, y1, z1) + (x2, y2, z2)
//
// The method is taken from:
// http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
// adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
//
// Coq transcription and correctness proof:
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L135>
// <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L205>
//
// This function includes a branch for checking whether the two input points
// are equal, (while not equal to the point at infinity). This case never
// happens during single point multiplication, so there is no timing leak for
// ECDH or ECDSA signing.
static void point_add(fe x3, fe y3, fe z3, const fe x1,
const fe y1, const fe z1, const int mixed,
const fe x2, const fe y2, const fe z2) {
fe x_out, y_out, z_out;
WORD z1nz = fe_nz(z1);
WORD z2nz = fe_nz(z2);
// z1z1 = z1z1 = z1**2
fe z1z1; fe_sqr(z1z1, z1);
fe u1, s1, two_z1z2;
if (!mixed) {
// z2z2 = z2**2
fe z2z2; fe_sqr(z2z2, z2);
// u1 = x1*z2z2
fe_mul(u1, x1, z2z2);
// two_z1z2 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2
fe_add(two_z1z2, z1, z2);
fe_sqr(two_z1z2, two_z1z2);
fe_sub(two_z1z2, two_z1z2, z1z1);
fe_sub(two_z1z2, two_z1z2, z2z2);
// s1 = y1 * z2**3
fe_mul(s1, z2, z2z2);
fe_mul(s1, s1, y1);
} else {
// We'll assume z2 = 1 (special case z2 = 0 is handled later).
// u1 = x1*z2z2
fe_copy(u1, x1);
// two_z1z2 = 2z1z2
fe_add(two_z1z2, z1, z1);
// s1 = y1 * z2**3
fe_copy(s1, y1);
}
// u2 = x2*z1z1
fe u2; fe_mul(u2, x2, z1z1);
// h = u2 - u1
fe h; fe_sub(h, u2, u1);
WORD xneq = fe_nz(h);
// z_out = two_z1z2 * h
fe_mul(z_out, h, two_z1z2);
// z1z1z1 = z1 * z1z1
fe z1z1z1; fe_mul(z1z1z1, z1, z1z1);
// s2 = y2 * z1**3
fe s2; fe_mul(s2, y2, z1z1z1);
// r = (s2 - s1)*2
fe r;
fe_sub(r, s2, s1);
fe_add(r, r, r);
WORD yneq = fe_nz(r);
if (!xneq && !yneq && z1nz && z2nz) {
point_double(x3, y3, z3, x1, y1, z1);
return;
}
// I = (2h)**2
fe i;
fe_add(i, h, h);
fe_sqr(i, i);
// J = h * I
fe j; fe_mul(j, h, i);
// V = U1 * I
fe v; fe_mul(v, u1, i);
// x_out = r**2 - J - 2V
fe_sqr(x_out, r);
fe_sub(x_out, x_out, j);
fe_sub(x_out, x_out, v);
fe_sub(x_out, x_out, v);
// y_out = r(V-x_out) - 2 * s1 * J
fe_sub(y_out, v, x_out);
fe_mul(y_out, y_out, r);
fe s1j;
fe_mul(s1j, s1, j);
fe_sub(y_out, y_out, s1j);
fe_sub(y_out, y_out, s1j);
fe_cmovznz(x_out, z1nz, x2, x_out);
fe_cmovznz(x3, z2nz, x1, x_out);
fe_cmovznz(y_out, z1nz, y2, y_out);
fe_cmovznz(y3, z2nz, y1, y_out);
fe_cmovznz(z_out, z1nz, z2, z_out);
fe_cmovznz(z3, z2nz, z1, z_out);
}
/* Use a sliding window optimization method for scalar multiplication
Hard-coded window size = 4
Implementation inspired from Go's crypto library
https://github.com/golang/go/blob/a5cd894318677359f6d07ee74f9004d28b4d164c/src/crypto/internal/nistec/p256.go#L317
*/
/* Select the n-th element of the table
without leaking information about [n] */
static void table_select(fe out_x, fe out_y, fe out_z, size_t index, uint8_t n) {
fe x, y, z = {0};
fe_one(x); fe_one(y);
for(uint8_t i = 1 ; i < 16 ; ++i) {
WORD cond = i ^ n;
fe_cmovznz(x, cond, generator_table[index][n - 1][0], x);
fe_cmovznz(y, cond, generator_table[index][n - 1][1], y);
fe_cmovznz(z, cond, generator_table[index][n - 1][2], z);
}
fe_copy(out_x, x);
fe_copy(out_y, y);
fe_copy(out_z, z);
}
/* Returns [kG] by decomposing [k] in binary form, and adding
[2^0G * k_0 + 2^1G * k_1 + ...] in constant time using
pre-computed values of 2^iG */
static void scalar_mult_base(fe x2, fe y2, fe z2,
const uint8_t* scalar, size_t len) {
// P = 0
fe p_x, p_y, p_z = {0};
fe_one(p_x);
fe_one(p_y);
size_t index = 0;
for(size_t i = 0 ; i < len ; ++i) {
fe s_x, s_y, s_z;
uint8_t window = scalar[i] & 0xf;
table_select(s_x, s_y, s_z, index, window);
point_add(p_x, p_y, p_z, p_x, p_y, p_z, 0, s_x, s_y, s_z);
index++;
window = scalar[i] >> 4;
table_select(s_x, s_y, s_z, index, window);
point_add(p_x, p_y, p_z, p_x, p_y, p_z, 0, s_x, s_y, s_z);
index++;
}
fe_copy(x2, p_x);
fe_copy(y2, p_y);
fe_copy(z2, p_z);
}