fdh_rsa.ml
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3 changed files with 96 additions and 105 deletions
101
src/crypto.ml
101
src/crypto.ml
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@ -274,104 +274,3 @@ type rsa_priv = RsaPrivateKey.t
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type rsa_pub = RsaPublicKey.t
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type rsa_sig = RsaSignature.t
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type denom_hash = Hash.DenominationHash.t
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(* WIP *)
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module FDH_RSA = struct
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open Mirage_crypto_pk
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module Kdf = struct
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module XTR = Hkdf.Make (Digestif.SHA512)
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module PRF = Hkdf.Make (Digestif.SHA256)
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let kdf =
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fun ~xts ~ikm ~ctx ~len ->
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let prk = XTR.extract ~salt:xts ikm in
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let okm = PRF.expand ~prk ~info:ctx len in
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okm
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let kdf_mod_n ~n ~xts ~ikm ~ctx =
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let nbits = Z.numbits n in
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let len = ((nbits - 1) / 8) + 1 in
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assert (8 * len = nbits);
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let rec go ctr =
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(* cat ctx ctr_be *)
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let ctx =
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let ctx_len = String.length ctx in
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let b = Bytes.create (ctx_len + 2) in
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Bytes.blit_string ctx 0 b 0 ctx_len;
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Bytes.set_uint16_be b ctx_len ctr;
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Bytes.unsafe_to_string b
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in
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let okm = kdf ~xts ~ikm ~ctx ~len in
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assert (String.length okm = len);
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let r = Z_extra.of_octets_be okm in
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if Z.gt r n then go (succ ctr) else r
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in
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go 0
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end
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let gcd_validate r n =
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match Z.equal (Z.gcd r n) Z.one with
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| true -> ()
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| false -> Fmt.failwith "RSA key is malicious"
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let rsa_full_domain_hash pub msg =
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let xts = RsaPublicKey.to_octets pub in
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let ctx = "RSA-FDA FTpsW!" in
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let r = Kdf.kdf_mod_n ~n:pub.n ~xts ~ikm:msg ~ctx in
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gcd_validate r pub.n; r
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let rsa_blinding_key_derive (pub : RsaPublicKey.t) bks =
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let xts = "Blinding KDF extractor HMAC key" in
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let ctx = "Blinding KDF" in
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let r = Kdf.kdf_mod_n ~n:pub.n ~xts ~ikm:bks ~ctx in
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gcd_validate r pub.n; r
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let rsa_blind pub ~bks ~msg =
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let data = rsa_full_domain_hash pub msg in
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let bkey = rsa_blinding_key_derive pub bks in
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(* can we just use [powm] here instead? *)
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let r_e = Z.powm_sec bkey pub.e pub.n in
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let data_r_e = Z.rem (Z.mul data r_e) pub.n in
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Z_extra.to_octets_be data_r_e
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(* -- WIP crypto -- *)
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(* TODO crypto
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not sure about signature scheme used by taler
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libgnunetutil crypto_rsa.c use "(flags raw)" => no padding *)
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(* decrypt <=> sign *)
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let rsa_sign_z priv r =
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let data = Z_extra.to_octets_be r in
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Rsa.decrypt ~crt_hardening:true ~key:priv data
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(* TODO crypto
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look into mirage-crypto for this
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use Eqaf for constant time string compare *)
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let rsa_verify_z pub r sig_ =
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let data = Z_extra.to_octets_be r in
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let sig_' = Rsa.encrypt ~key:pub data in
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match String.equal sig_ sig_' with
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| false -> Fmt.error "RSA signature verification failed"
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| true -> Ok ()
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let rsa_sign_fdh priv msg =
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let pub = Rsa.pub_of_priv priv in
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let r = rsa_full_domain_hash pub msg in
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rsa_sign_z priv r
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let rsa_unblind pub ~bks ~sig_ =
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let bkey = rsa_blinding_key_derive pub bks in
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let r_inv =
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try Z.invert bkey pub.n
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with Division_by_zero ->
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(* => gcd(r,n) <> 1, should be already checked for *)
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assert false
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in
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let ubsig = Z.rem (Z.mul sig_ r_inv) pub.n in
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ubsig
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let rsa_verify pub ~msg ~sig_ =
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let r = rsa_full_domain_hash pub msg in
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rsa_verify_z pub r sig_
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end
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92
src/fdh_rsa.ml
Normal file
92
src/fdh_rsa.ml
Normal file
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@ -0,0 +1,92 @@
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(* WIP
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full-domain-hash RSA
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based on libgnunetutil crypto_rsa.c
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good explanation of taler crypto:
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https://www.taler.net/papers/cs-thesis.pdf *)
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module Z_extra = Mirage_crypto_pk.Z_extra
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open Crypto
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module Kdf = struct
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module XTR = Hkdf.Make (Digestif.SHA512)
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module PRF = Hkdf.Make (Digestif.SHA256)
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let kdf =
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fun ~xts ~ikm ~ctx ~len ->
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let prk = XTR.extract ~salt:xts ikm in
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let okm = PRF.expand ~prk ~info:ctx len in
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okm
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let kdf_mod_n ~n ~xts ~ikm ~ctx =
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let nbits = Z.numbits n in
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let len = ((nbits - 1) / 8) + 1 in
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assert (8 * len = nbits);
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let rec go ctr =
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(* cat ctx ctr_be *)
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let ctx =
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let ctx_len = String.length ctx in
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let b = Bytes.create (ctx_len + 2) in
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Bytes.blit_string ctx 0 b 0 ctx_len;
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Bytes.set_uint16_be b ctx_len ctr;
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Bytes.unsafe_to_string b
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in
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let okm = kdf ~xts ~ikm ~ctx ~len in
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assert (String.length okm = len);
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let r = Z_extra.of_octets_be okm in
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if Z.gt r n then go (succ ctr) else r
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in
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go 0
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end
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let gcd_validate r n =
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match Z.equal (Z.gcd r n) Z.one with
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| true -> ()
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| false -> Fmt.failwith "RSA key is malicious"
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let rsa_full_domain_hash pub msg =
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let xts = RsaPublicKey.to_octets pub in
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let ctx = "RSA-FDA FTpsW!" in
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let r = Kdf.kdf_mod_n ~n:pub.n ~xts ~ikm:msg ~ctx in
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gcd_validate r pub.n; r
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let rsa_blinding_key_derive (pub : RsaPublicKey.t) bks =
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let xts = "Blinding KDF extractor HMAC key" in
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let ctx = "Blinding KDF" in
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let r = Kdf.kdf_mod_n ~n:pub.n ~xts ~ikm:bks ~ctx in
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gcd_validate r pub.n; r
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let rsa_blind pub ~bks ~msg =
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let data = rsa_full_domain_hash pub msg in
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let bkey = rsa_blinding_key_derive pub bks in
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(* can we just use [powm] here instead? *)
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let r_e = Z.powm_sec bkey pub.e pub.n in
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let data_r_e = Z.rem (Z.mul data r_e) pub.n in
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Z_extra.to_octets_be data_r_e
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(* decrypt <=> sign *)
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let rsa_sign_blinded priv ~bmsg =
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Mirage_crypto_pk.Rsa.decrypt ~crt_hardening:true ~key:priv bmsg
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let rsa_unblind pub ~bks ~sig_ =
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let data = Z_extra.of_octets_be sig_ in
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let bkey = rsa_blinding_key_derive pub bks in
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let r_inv =
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try Z.invert bkey pub.n
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with Division_by_zero ->
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(* => gcd(r,n) <> 1, should be already checked for *)
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assert false
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in
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let data = Z.rem (Z.mul data r_inv) pub.n in
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Z_extra.to_octets_be data
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(* TODO crypto
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look into mirage-crypto for this
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at least use Eqaf for constant time string compare *)
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let rsa_verify pub ~msg ~sig_ =
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let msg_fdh = rsa_full_domain_hash pub msg in
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let s1 = Z_extra.to_octets_be msg_fdh in
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let s2 = Mirage_crypto_pk.Rsa.encrypt ~key:pub sig_ in
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match String.equal s1 s2 with
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| false -> Fmt.error "RSA signature verification failed"
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| true -> Ok ()
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@ -77,7 +77,7 @@ let () =
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let xts = salt |> decode in
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let ikm = ikm |> decode in
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let ctx = ctx |> decode in
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let okm = Crypto.FDH_RSA.Kdf.kdf ~xts ~ikm ~ctx ~len:out_len in
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let okm = Fdh_rsa.Kdf.kdf ~xts ~ikm ~ctx ~len:out_len in
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let okm = okm |> encode in
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assert (okm = out);
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@ -99,12 +99,12 @@ let () =
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"3KHKZJZ30ABB4E56MA2V0EQWGCWH0QQG9P2ZHYHR186C5HZXJMM4N9WXAQTKS94QSV9Y17GGNXN5MB1PZZFG7Q0FY88QPKKRG4MYCPSMTZK5W59R0MJVNJ4P4AQM96TDG5W7RV8GSNR1QQZ1GNHW3CX6D6ZRTMXB2NKB5SSYTDJS79F5ZFBRZ4HVED9JBBPWSR79KVV5QQ4APBGHBCKGMF9NJJS53A1BVYHDEVYAGFYF2SNEP827ZP50FKJ5GKGV8NQ15ESEZ69AT7GJG0T3TZVENY2YN9CVR98W3BKEZ53J7VTANARG8SJS8AMJQ7S23P5HRJ7XE9KTNRNXKH49MXV9JHHYE5535N7AGWEKR47SBCGNF44Z7XJ9RV5BQV12ZRJKN4HBZQHDNCMH3QKX9Z6G64"
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in
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let open Crypto in
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let msg = message_hash |> decode in
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let pub =
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rsa_public_key |> decode |> RsaPublicKey.of_octets |> Result.get_ok
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in
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let bks = blinding_key_secret |> decode in
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let s = FDH_RSA.rsa_blind pub ~bks ~msg |> encode in
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assert (s = blinded_message);
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let msg = decode message_hash in
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let bmsg = Fdh_rsa.rsa_blind pub ~bks ~msg in
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assert (encode bmsg = blinded_message);
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()
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