Secp256k1.hs (47306B)
1 {-# OPTIONS_HADDOCK prune #-} 2 {-# LANGUAGE BangPatterns #-} 3 {-# LANGUAGE CPP #-} 4 {-# LANGUAGE DeriveGeneric #-} 5 {-# LANGUAGE DerivingStrategies #-} 6 {-# LANGUAGE LambdaCase #-} 7 {-# LANGUAGE MagicHash #-} 8 {-# LANGUAGE OverloadedStrings #-} 9 {-# LANGUAGE PatternSynonyms #-} 10 {-# LANGUAGE RecordWildCards #-} 11 {-# LANGUAGE UnboxedTuples #-} 12 {-# LANGUAGE ViewPatterns #-} 13 14 #include "MachDeps.h" 15 #if WORD_SIZE_IN_BITS != 64 16 #error "ppad-secp256k1 requires a 64-bit architecture" 17 #endif 18 19 -- | 20 -- Module: Crypto.Curve.Secp256k1 21 -- Copyright: (c) 2024 Jared Tobin 22 -- License: MIT 23 -- Maintainer: Jared Tobin <jared@ppad.tech> 24 -- 25 -- Pure [BIP0340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki) 26 -- Schnorr signatures, deterministic 27 -- [RFC6979](https://www.rfc-editor.org/rfc/rfc6979) ECDSA (with 28 -- [BIP0146](https://github.com/bitcoin/bips/blob/master/bip-0146.mediawiki)-style 29 -- "low-S" signatures), and ECDH shared secret computation 30 -- on the elliptic curve secp256k1. 31 32 module Crypto.Curve.Secp256k1 ( 33 -- * Parsing 34 parse_int256 35 , parse_point 36 , parse_sig 37 38 -- * Serializing 39 , serialize_point 40 41 -- * secp256k1 points 42 , Pub 43 , derive_pub 44 , derive_pub' 45 , _CURVE_G 46 , _CURVE_ZERO 47 , ge 48 , fe 49 50 -- * ECDH 51 , ecdh 52 53 -- * BIP0340 Schnorr signatures 54 , sign_schnorr 55 , verify_schnorr 56 57 -- * RFC6979 ECDSA 58 , ECDSA(..) 59 , SigType(..) 60 , sign_ecdsa 61 , sign_ecdsa_unrestricted 62 , verify_ecdsa 63 , verify_ecdsa_unrestricted 64 65 -- * Fast variants 66 , Context 67 , precompute 68 , sign_schnorr' 69 , verify_schnorr' 70 , sign_ecdsa' 71 , sign_ecdsa_unrestricted' 72 , verify_ecdsa' 73 , verify_ecdsa_unrestricted' 74 75 -- Elliptic curve group operations 76 , neg 77 , add 78 , add_mixed 79 , add_proj 80 , double 81 , mul 82 , mul_vartime 83 , mul_wnaf 84 85 -- * Field and group parameters 86 , _CURVE_Q 87 , _CURVE_P 88 89 -- Coordinate systems and transformations 90 , Affine(..) 91 , Projective(..) 92 , affine 93 , projective 94 , valid 95 96 -- for testing/benchmarking 97 , _precompute 98 , _sign_ecdsa_no_hash 99 , _sign_ecdsa_no_hash' 100 , _verify_ecdsa_no_hash 101 , _verify_ecdsa_no_hash' 102 , roll32 103 , unsafe_roll32 104 , unroll32 105 , select_proj 106 ) where 107 108 import Control.Monad (guard) 109 import Control.Monad.ST 110 import qualified Crypto.DRBG.HMAC.SHA256 as DRBG 111 import qualified Crypto.Hash.SHA256 as SHA256 112 import qualified Data.Bits as B 113 import Data.Bits ((.<<.)) 114 import qualified Data.ByteString as BS 115 import qualified Data.ByteString.Internal as BI 116 import qualified Data.ByteString.Unsafe as BU 117 import qualified Data.Choice as CT 118 import qualified Data.Maybe as M 119 import Data.Primitive.ByteArray (ByteArray(..), MutableByteArray(..)) 120 import qualified Data.Primitive.ByteArray as BA 121 import Data.Word (Word8) 122 import Data.Word.Limb (Limb(..)) 123 import qualified Data.Word.Limb as L 124 import Data.Word.Wider (Wider(..)) 125 import qualified Data.Word.Wider as W 126 import qualified Foreign.Storable as Storable (pokeByteOff) 127 import qualified GHC.Exts as Exts 128 import GHC.Generics 129 import qualified GHC.Word (Word(..), Word8(..)) 130 import qualified Numeric.Montgomery.Secp256k1.Curve as C 131 import qualified Numeric.Montgomery.Secp256k1.Scalar as S 132 import Prelude hiding (sqrt) 133 134 -- convenience synonyms ------------------------------------------------------- 135 136 -- Unboxed Wider/Montgomery synonym. 137 type Limb4 = (# Limb, Limb, Limb, Limb #) 138 139 -- Unboxed Projective synonym. 140 type Proj = (# Limb4, Limb4, Limb4 #) 141 142 pattern Z :: Limb4 143 pattern Z = (# Limb 0##, Limb 0##, Limb 0##, Limb 0## #) 144 145 pattern P :: Limb4 -> Limb4 -> Limb4 -> Projective 146 pattern P x y z = Projective (C.Montgomery x) (C.Montgomery y) (C.Montgomery z) 147 {-# COMPLETE P #-} 148 149 -- utilities ------------------------------------------------------------------ 150 151 fi :: (Integral a, Num b) => a -> b 152 fi = fromIntegral 153 {-# INLINE fi #-} 154 155 -- convert a Word8 to a Limb 156 limb :: Word8 -> Limb 157 limb (GHC.Word.W8# (Exts.word8ToWord# -> w)) = Limb w 158 {-# INLINABLE limb #-} 159 160 -- convert a Limb to a Word8 161 word8 :: Limb -> Word8 162 word8 (Limb w) = GHC.Word.W8# (Exts.wordToWord8# w) 163 {-# INLINABLE word8 #-} 164 165 -- convert a Limb to a Word8 after right-shifting 166 word8s :: Limb -> Exts.Int# -> Word8 167 word8s l s = 168 let !(Limb w) = L.shr# l s 169 in GHC.Word.W8# (Exts.wordToWord8# w) 170 {-# INLINABLE word8s #-} 171 172 -- convert a Word8 to a Wider 173 word8_to_wider :: Word8 -> Wider 174 word8_to_wider w = Wider (# limb w, Limb 0##, Limb 0##, Limb 0## #) 175 {-# INLINABLE word8_to_wider #-} 176 177 -- unsafely extract the first 64-bit word from a big-endian-encoded bytestring 178 unsafe_word0 :: BS.ByteString -> Limb 179 unsafe_word0 bs = 180 (limb (BU.unsafeIndex bs 00) `L.shl#` 56#) 181 `L.or#` (limb (BU.unsafeIndex bs 01) `L.shl#` 48#) 182 `L.or#` (limb (BU.unsafeIndex bs 02) `L.shl#` 40#) 183 `L.or#` (limb (BU.unsafeIndex bs 03) `L.shl#` 32#) 184 `L.or#` (limb (BU.unsafeIndex bs 04) `L.shl#` 24#) 185 `L.or#` (limb (BU.unsafeIndex bs 05) `L.shl#` 16#) 186 `L.or#` (limb (BU.unsafeIndex bs 06) `L.shl#` 08#) 187 `L.or#` (limb (BU.unsafeIndex bs 07)) 188 {-# INLINABLE unsafe_word0 #-} 189 190 -- unsafely extract the second 64-bit word from a big-endian-encoded bytestring 191 unsafe_word1 :: BS.ByteString -> Limb 192 unsafe_word1 bs = 193 (limb (BU.unsafeIndex bs 08) `L.shl#` 56#) 194 `L.or#` (limb (BU.unsafeIndex bs 09) `L.shl#` 48#) 195 `L.or#` (limb (BU.unsafeIndex bs 10) `L.shl#` 40#) 196 `L.or#` (limb (BU.unsafeIndex bs 11) `L.shl#` 32#) 197 `L.or#` (limb (BU.unsafeIndex bs 12) `L.shl#` 24#) 198 `L.or#` (limb (BU.unsafeIndex bs 13) `L.shl#` 16#) 199 `L.or#` (limb (BU.unsafeIndex bs 14) `L.shl#` 08#) 200 `L.or#` (limb (BU.unsafeIndex bs 15)) 201 {-# INLINABLE unsafe_word1 #-} 202 203 -- unsafely extract the third 64-bit word from a big-endian-encoded bytestring 204 unsafe_word2 :: BS.ByteString -> Limb 205 unsafe_word2 bs = 206 (limb (BU.unsafeIndex bs 16) `L.shl#` 56#) 207 `L.or#` (limb (BU.unsafeIndex bs 17) `L.shl#` 48#) 208 `L.or#` (limb (BU.unsafeIndex bs 18) `L.shl#` 40#) 209 `L.or#` (limb (BU.unsafeIndex bs 19) `L.shl#` 32#) 210 `L.or#` (limb (BU.unsafeIndex bs 20) `L.shl#` 24#) 211 `L.or#` (limb (BU.unsafeIndex bs 21) `L.shl#` 16#) 212 `L.or#` (limb (BU.unsafeIndex bs 22) `L.shl#` 08#) 213 `L.or#` (limb (BU.unsafeIndex bs 23)) 214 {-# INLINABLE unsafe_word2 #-} 215 216 -- unsafely extract the fourth 64-bit word from a big-endian-encoded bytestring 217 unsafe_word3 :: BS.ByteString -> Limb 218 unsafe_word3 bs = 219 (limb (BU.unsafeIndex bs 24) `L.shl#` 56#) 220 `L.or#` (limb (BU.unsafeIndex bs 25) `L.shl#` 48#) 221 `L.or#` (limb (BU.unsafeIndex bs 26) `L.shl#` 40#) 222 `L.or#` (limb (BU.unsafeIndex bs 27) `L.shl#` 32#) 223 `L.or#` (limb (BU.unsafeIndex bs 28) `L.shl#` 24#) 224 `L.or#` (limb (BU.unsafeIndex bs 29) `L.shl#` 16#) 225 `L.or#` (limb (BU.unsafeIndex bs 30) `L.shl#` 08#) 226 `L.or#` (limb (BU.unsafeIndex bs 31)) 227 {-# INLINABLE unsafe_word3 #-} 228 229 -- 256-bit big-endian bytestring decoding. the input size is not checked! 230 unsafe_roll32 :: BS.ByteString -> Wider 231 unsafe_roll32 bs = 232 let !w0 = unsafe_word0 bs 233 !w1 = unsafe_word1 bs 234 !w2 = unsafe_word2 bs 235 !w3 = unsafe_word3 bs 236 in Wider (# w3, w2, w1, w0 #) 237 {-# INLINABLE unsafe_roll32 #-} 238 239 -- arbitrary-size big-endian bytestring decoding 240 roll32 :: BS.ByteString -> Maybe Wider 241 roll32 bs 242 | BS.length stripped > 32 = Nothing 243 | otherwise = Just $! BS.foldl' alg 0 stripped 244 where 245 stripped = BS.dropWhile (== 0) bs 246 alg !a (word8_to_wider -> !b) = (a `W.shl_limb` 8) `W.or` b 247 {-# INLINABLE roll32 #-} 248 249 -- 256-bit big-endian bytestring encoding 250 unroll32 :: Wider -> BS.ByteString 251 unroll32 (Wider (# w0, w1, w2, w3 #)) = 252 BI.unsafeCreate 32 $ \ptr -> do 253 -- w0 254 Storable.pokeByteOff ptr 00 (word8s w3 56#) 255 Storable.pokeByteOff ptr 01 (word8s w3 48#) 256 Storable.pokeByteOff ptr 02 (word8s w3 40#) 257 Storable.pokeByteOff ptr 03 (word8s w3 32#) 258 Storable.pokeByteOff ptr 04 (word8s w3 24#) 259 Storable.pokeByteOff ptr 05 (word8s w3 16#) 260 Storable.pokeByteOff ptr 06 (word8s w3 08#) 261 Storable.pokeByteOff ptr 07 (word8 w3) 262 -- w1 263 Storable.pokeByteOff ptr 08 (word8s w2 56#) 264 Storable.pokeByteOff ptr 09 (word8s w2 48#) 265 Storable.pokeByteOff ptr 10 (word8s w2 40#) 266 Storable.pokeByteOff ptr 11 (word8s w2 32#) 267 Storable.pokeByteOff ptr 12 (word8s w2 24#) 268 Storable.pokeByteOff ptr 13 (word8s w2 16#) 269 Storable.pokeByteOff ptr 14 (word8s w2 08#) 270 Storable.pokeByteOff ptr 15 (word8 w2) 271 -- w2 272 Storable.pokeByteOff ptr 16 (word8s w1 56#) 273 Storable.pokeByteOff ptr 17 (word8s w1 48#) 274 Storable.pokeByteOff ptr 18 (word8s w1 40#) 275 Storable.pokeByteOff ptr 19 (word8s w1 32#) 276 Storable.pokeByteOff ptr 20 (word8s w1 24#) 277 Storable.pokeByteOff ptr 21 (word8s w1 16#) 278 Storable.pokeByteOff ptr 22 (word8s w1 08#) 279 Storable.pokeByteOff ptr 23 (word8 w1) 280 -- w3 281 Storable.pokeByteOff ptr 24 (word8s w0 56#) 282 Storable.pokeByteOff ptr 25 (word8s w0 48#) 283 Storable.pokeByteOff ptr 26 (word8s w0 40#) 284 Storable.pokeByteOff ptr 27 (word8s w0 32#) 285 Storable.pokeByteOff ptr 28 (word8s w0 24#) 286 Storable.pokeByteOff ptr 29 (word8s w0 16#) 287 Storable.pokeByteOff ptr 30 (word8s w0 08#) 288 Storable.pokeByteOff ptr 31 (word8 w0) 289 {-# INLINABLE unroll32 #-} 290 291 -- modQ via conditional subtraction 292 modQ :: Wider -> Wider 293 modQ x = W.select x (x - _CURVE_Q) (CT.not (W.lt x _CURVE_Q)) 294 {-# INLINABLE modQ #-} 295 296 -- bytewise xor 297 xor :: BS.ByteString -> BS.ByteString -> BS.ByteString 298 xor = BS.packZipWith B.xor 299 {-# INLINABLE xor #-} 300 301 -- constants ------------------------------------------------------------------ 302 303 -- | secp256k1 field prime. 304 -- 305 -- >>> _CURVE_P 306 -- 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 307 _CURVE_P :: Wider 308 _CURVE_P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 309 310 -- | secp256k1 group order. 311 -- 312 -- >>> _CURVE_Q 313 -- 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 314 _CURVE_Q :: Wider 315 _CURVE_Q = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 316 317 -- | half of the secp256k1 group order. 318 _CURVE_QH :: Wider 319 _CURVE_QH = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0 320 321 -- bitlength of group order 322 -- 323 -- = smallest integer such that _CURVE_Q < 2 ^ _CURVE_Q_BITS 324 _CURVE_Q_BITS :: Int 325 _CURVE_Q_BITS = 256 326 327 -- bytelength of _CURVE_Q 328 -- 329 -- = _CURVE_Q_BITS / 8 330 _CURVE_Q_BYTES :: Int 331 _CURVE_Q_BYTES = 32 332 333 -- secp256k1 weierstrass form, /b/ coefficient 334 _CURVE_B :: Wider 335 _CURVE_B = 7 336 337 -- secp256k1 weierstrass form, /b/ coefficient, montgomery form 338 _CURVE_Bm :: C.Montgomery 339 _CURVE_Bm = 7 340 341 -- _CURVE_Bm * 3 342 _CURVE_Bm3 :: C.Montgomery 343 _CURVE_Bm3 = 21 344 345 -- Is field element? 346 fe :: Wider -> Bool 347 fe n = case W.cmp_vartime n 0 of 348 GT -> case W.cmp_vartime n _CURVE_P of 349 LT -> True 350 _ -> False 351 _ -> False 352 {-# INLINE fe #-} 353 354 -- Is group element? 355 ge :: Wider -> Bool 356 ge (Wider n) = CT.decide (ge# n) 357 {-# INLINE ge #-} 358 359 -- curve points --------------------------------------------------------------- 360 361 -- curve point, affine coordinates 362 data Affine = Affine !C.Montgomery !C.Montgomery 363 deriving stock (Show, Generic) 364 365 -- curve point, projective coordinates 366 data Projective = Projective { 367 px :: !C.Montgomery 368 , py :: !C.Montgomery 369 , pz :: !C.Montgomery 370 } 371 deriving stock (Show, Generic) 372 373 instance Eq Projective where 374 Projective ax ay az == Projective bx by bz = 375 let !x1z2 = ax * bz 376 !x2z1 = bx * az 377 !y1z2 = ay * bz 378 !y2z1 = by * az 379 in CT.decide (CT.and (C.eq x1z2 x2z1) (C.eq y1z2 y2z1)) 380 381 -- | A public key, i.e. secp256k1 point. 382 type Pub = Projective 383 384 -- Convert to affine coordinates. 385 affine :: Projective -> Affine 386 affine (Projective x y z) = 387 let !iz = C.inv z 388 in Affine (x * iz) (y * iz) 389 {-# INLINABLE affine #-} 390 391 -- Convert to projective coordinates. 392 projective :: Affine -> Projective 393 projective (Affine x y) 394 | C.eq_vartime x 0 || C.eq_vartime y 0 = _CURVE_ZERO 395 | otherwise = Projective x y 1 396 397 -- | secp256k1 generator point. 398 _CURVE_G :: Projective 399 _CURVE_G = Projective x y z where 400 !x = C.Montgomery 401 (# Limb 15507633332195041431##, Limb 2530505477788034779## 402 , Limb 10925531211367256732##, Limb 11061375339145502536## #) 403 !y = C.Montgomery 404 (# Limb 12780836216951778274##, Limb 10231155108014310989## 405 , Limb 8121878653926228278##, Limb 14933801261141951190## #) 406 !z = C.Montgomery 407 (# Limb 0x1000003D1##, Limb 0##, Limb 0##, Limb 0## #) 408 409 -- | secp256k1 zero point, point at infinity, or monoidal identity. 410 _CURVE_ZERO :: Projective 411 _CURVE_ZERO = Projective 0 1 0 412 413 -- secp256k1 zero point, point at infinity, or monoidal identity 414 _ZERO :: Projective 415 _ZERO = Projective 0 1 0 416 {-# DEPRECATED _ZERO "use _CURVE_ZERO instead" #-} 417 418 -- secp256k1 in short weierstrass form (y ^ 2 = x ^ 3 + 7) 419 weierstrass :: C.Montgomery -> C.Montgomery 420 weierstrass x = C.sqr x * x + _CURVE_Bm 421 {-# INLINE weierstrass #-} 422 423 -- Point is valid 424 valid :: Projective -> Bool 425 valid (affine -> Affine x y) = C.eq_vartime (C.sqr y) (weierstrass x) 426 427 -- (bip0340) return point with x coordinate == x and with even y coordinate 428 -- 429 -- conceptually: 430 -- y ^ 2 = x ^ 3 + 7 431 -- y = "+-" sqrt (x ^ 3 + 7) 432 -- (n.b. for solution y, p - y is also a solution) 433 -- y + (p - y) = p (odd) 434 -- (n.b. sum is odd, so one of y and p - y must be odd, and the other even) 435 -- if y even, return (x, y) 436 -- else, return (x, p - y) 437 lift_vartime :: C.Montgomery -> Maybe Affine 438 lift_vartime x = do 439 let !c = weierstrass x 440 !y <- C.sqrt_vartime c 441 let !y_e | C.odd_vartime y = negate y 442 | otherwise = y 443 pure $! Affine x y_e 444 445 even_y_vartime :: Projective -> Projective 446 even_y_vartime p = case affine p of 447 Affine _ (C.retr -> y) 448 | CT.decide (W.odd y) -> neg p 449 | otherwise -> p 450 451 -- Constant-time selection of Projective points. 452 select_proj :: Projective -> Projective -> CT.Choice -> Projective 453 select_proj (Projective ax ay az) (Projective bx by bz) c = 454 Projective (C.select ax bx c) (C.select ay by c) (C.select az bz c) 455 {-# INLINE select_proj #-} 456 457 -- unboxed internals ---------------------------------------------------------- 458 459 -- algo 7, renes et al, 2015 460 add_proj# :: Proj -> Proj -> Proj 461 add_proj# (# x1, y1, z1 #) (# x2, y2, z2 #) = 462 let !(C.Montgomery b3) = _CURVE_Bm3 463 !t0a = C.mul# x1 x2 464 !t1a = C.mul# y1 y2 465 !t2a = C.mul# z1 z2 466 !t3a = C.add# x1 y1 467 !t4a = C.add# x2 y2 468 !t3b = C.mul# t3a t4a 469 !t4b = C.add# t0a t1a 470 !t3c = C.sub# t3b t4b 471 !t4c = C.add# y1 z1 472 !x3a = C.add# y2 z2 473 !t4d = C.mul# t4c x3a 474 !x3b = C.add# t1a t2a 475 !t4e = C.sub# t4d x3b 476 !x3c = C.add# x1 z1 477 !y3a = C.add# x2 z2 478 !x3d = C.mul# x3c y3a 479 !y3b = C.add# t0a t2a 480 !y3c = C.sub# x3d y3b 481 !x3e = C.add# t0a t0a 482 !t0b = C.add# x3e t0a 483 !t2b = C.mul# b3 t2a 484 !z3a = C.add# t1a t2b 485 !t1b = C.sub# t1a t2b 486 !y3d = C.mul# b3 y3c 487 !x3f = C.mul# t4e y3d 488 !t2c = C.mul# t3c t1b 489 !x3g = C.sub# t2c x3f 490 !y3e = C.mul# y3d t0b 491 !t1c = C.mul# t1b z3a 492 !y3f = C.add# t1c y3e 493 !t0c = C.mul# t0b t3c 494 !z3b = C.mul# z3a t4e 495 !z3c = C.add# z3b t0c 496 in (# x3g, y3f, z3c #) 497 {-# INLINE add_proj# #-} 498 499 -- algo 8, renes et al, 2015 500 add_mixed# :: Proj -> Proj -> Proj 501 add_mixed# (# x1, y1, z1 #) (# x2, y2, _z2 #) = 502 let !(C.Montgomery b3) = _CURVE_Bm3 503 !t0a = C.mul# x1 x2 504 !t1a = C.mul# y1 y2 505 !t3a = C.add# x2 y2 506 !t4a = C.add# x1 y1 507 !t3b = C.mul# t3a t4a 508 !t4b = C.add# t0a t1a 509 !t3c = C.sub# t3b t4b 510 !t4c = C.mul# y2 z1 511 !t4d = C.add# t4c y1 512 !y3a = C.mul# x2 z1 513 !y3b = C.add# y3a x1 514 !x3a = C.add# t0a t0a 515 !t0b = C.add# x3a t0a 516 !t2a = C.mul# b3 z1 517 !z3a = C.add# t1a t2a 518 !t1b = C.sub# t1a t2a 519 !y3c = C.mul# b3 y3b 520 !x3b = C.mul# t4d y3c 521 !t2b = C.mul# t3c t1b 522 !x3c = C.sub# t2b x3b 523 !y3d = C.mul# y3c t0b 524 !t1c = C.mul# t1b z3a 525 !y3e = C.add# t1c y3d 526 !t0c = C.mul# t0b t3c 527 !z3b = C.mul# z3a t4d 528 !z3c = C.add# z3b t0c 529 in (# x3c, y3e, z3c #) 530 {-# INLINE add_mixed# #-} 531 532 -- algo 9, renes et al, 2015 533 double# :: Proj -> Proj 534 double# (# x, y, z #) = 535 let !(C.Montgomery b3) = _CURVE_Bm3 536 !t0 = C.sqr# y 537 !z3a = C.add# t0 t0 538 !z3b = C.add# z3a z3a 539 !z3c = C.add# z3b z3b 540 !t1 = C.mul# y z 541 !t2a = C.sqr# z 542 !t2b = C.mul# b3 t2a 543 !x3a = C.mul# t2b z3c 544 !y3a = C.add# t0 t2b 545 !z3d = C.mul# t1 z3c 546 !t1b = C.add# t2b t2b 547 !t2c = C.add# t1b t2b 548 !t0b = C.sub# t0 t2c 549 !y3b = C.mul# t0b y3a 550 !y3c = C.add# x3a y3b 551 !t1c = C.mul# x y 552 !x3b = C.mul# t0b t1c 553 !x3c = C.add# x3b x3b 554 in (# x3c, y3c, z3d #) 555 {-# INLINE double# #-} 556 557 select_proj# :: Proj -> Proj -> CT.Choice -> Proj 558 select_proj# (# ax, ay, az #) (# bx, by, bz #) c = 559 (# W.select# ax bx c, W.select# ay by c, W.select# az bz c #) 560 {-# INLINE select_proj# #-} 561 562 neg# :: Proj -> Proj 563 neg# (# x, y, z #) = (# x, C.neg# y, z #) 564 {-# INLINE neg# #-} 565 566 mul# :: Proj -> Limb4 -> (# () | Proj #) 567 mul# (# px, py, pz #) s 568 | CT.decide (CT.not (ge# s)) = (# () | #) 569 | otherwise = 570 let !(C.Montgomery o) = C.one 571 in loop (0 :: Int) (# Z, o, Z #) (# px, py, pz #) s 572 where 573 loop !j !a !d !_SECRET 574 | j == _CURVE_Q_BITS = (# | a #) 575 | otherwise = 576 let !nd = double# d 577 !(# nm, lsb_set #) = W.shr1_c# _SECRET 578 !nacc = select_proj# a (add_proj# a d) lsb_set 579 in loop (succ j) nacc nd nm 580 {-# INLINE mul# #-} 581 582 mul_vartime# :: Proj -> Limb4 -> (# () | Proj #) 583 mul_vartime# (# px, py, pz #) s 584 | zero# s = 585 let !(P zx zy zz) = _CURVE_ZERO 586 in (# | (# zx, zy, zz #) #) 587 | CT.decide (CT.not (ge# s)) = (# () | #) 588 | otherwise = 589 let !(P zx zy zz) = _CURVE_ZERO 590 in (# | loop (# zx, zy, zz #) (# px, py, pz #) s #) 591 where 592 zero# (# Limb a, Limb b, Limb c, Limb d #) = Exts.isTrue# 593 ((a `Exts.or#` b `Exts.or#` c `Exts.or#` d) `Exts.eqWord#` 0##) 594 595 loop !r !d !m 596 | zero# m = r 597 | otherwise = 598 let !nd = double# d 599 !(# nm, lsb_set #) = W.shr1_c# m 600 !nr = if CT.decide lsb_set then add_proj# r d else r 601 in loop nr nd nm 602 {-# INLINE mul_vartime# #-} 603 604 ge# :: Limb4 -> CT.Choice 605 ge# n = 606 let !(Wider q) = _CURVE_Q 607 in CT.and (W.gt# n Z) (W.lt# n q) 608 {-# INLINE ge# #-} 609 610 mul_wnaf# :: ByteArray -> Int -> Limb4 -> (# () | Proj #) 611 mul_wnaf# ctxArray ctxW ls 612 | CT.decide (CT.not (ge# ls)) = (# () | #) 613 | otherwise = 614 let !(P zx zy zz) = _CURVE_ZERO 615 in (# | loop 0 (# zx, zy, zz #) ls #) 616 where 617 !one = (# Limb 1##, Limb 0##, Limb 0##, Limb 0## #) 618 !wins = fi (256 `quot` ctxW + 1) 619 !size@(GHC.Word.W# s) = 1 .<<. (ctxW - 1) 620 !(GHC.Word.W# mask) = 1 .<<. ctxW - 1 621 !(GHC.Word.W# texW) = fi ctxW 622 !(GHC.Word.W# mnum) = 1 .<<. ctxW 623 624 loop !j !acc !n@(# Limb lo, _, _, _ #) 625 | j == wins = acc 626 | otherwise = 627 let !(GHC.Word.W# off0) = j * size 628 !b0 = Exts.and# lo mask 629 !bor = CT.from_word_gt# b0 s 630 631 !(# n0, _ #) = W.shr_limb# n (Exts.word2Int# texW) 632 !n0_plus_1 = W.add_w# n0 one 633 !n1 = W.select# n0 n0_plus_1 bor 634 635 !abs_b = CT.select_word# b0 (Exts.minusWord# mnum b0) bor 636 !is_zero = CT.from_word_eq# b0 0## 637 !off_nz = Exts.minusWord# (Exts.plusWord# off0 abs_b) 1## 638 !off = CT.select_word# off0 off_nz (CT.not is_zero) 639 640 !pr = ct_index_proj# ctxArray off0 s off 641 !neg_pr = neg# pr 642 !pt_nonzero = select_proj# pr neg_pr bor 643 644 !acc_added = add_proj# acc pt_nonzero 645 !nacc = select_proj# acc_added acc is_zero 646 in loop (succ j) nacc n1 647 {-# INLINE mul_wnaf# #-} 648 649 -- retrieve a point (as an unboxed tuple) from a context array 650 index_proj# :: ByteArray -> Exts.Int# -> Proj 651 index_proj# (ByteArray arr#) i# = 652 let !base# = i# Exts.*# 12# 653 !x = (# Limb (Exts.indexWordArray# arr# base#) 654 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 01#)) 655 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 02#)) 656 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 03#)) #) 657 !y = (# Limb (Exts.indexWordArray# arr# (base# Exts.+# 04#)) 658 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 05#)) 659 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 06#)) 660 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 07#)) #) 661 !z = (# Limb (Exts.indexWordArray# arr# (base# Exts.+# 08#)) 662 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 09#)) 663 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 10#)) 664 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 11#)) #) 665 in (# x, y, z #) 666 {-# INLINE index_proj# #-} 667 668 -- Constant-time table lookup within a window. 669 -- 670 -- Unconditionally scans all entries from 'base' to 'base + size - 1', 671 -- selecting the one where 'index' equals 'target'. 672 ct_index_proj# 673 :: ByteArray 674 -> Exts.Word# -- ^ base index 675 -> Exts.Word# -- ^ size of window 676 -> Exts.Word# -- ^ target index 677 -> Proj 678 ct_index_proj# arr base size target = loop 0## (# Z, Z, Z #) where 679 loop i acc 680 | Exts.isTrue# (i `Exts.geWord#` size) = acc 681 | otherwise = 682 let !idx = Exts.plusWord# base i 683 !pt = index_proj# arr (Exts.word2Int# idx) 684 !eq = CT.from_word_eq# idx target 685 !nacc = select_proj# acc pt eq 686 in loop (Exts.plusWord# i 1##) nacc 687 {-# INLINE ct_index_proj# #-} 688 689 -- ec arithmetic -------------------------------------------------------------- 690 691 -- Negate secp256k1 point. 692 neg :: Projective -> Projective 693 neg (P x y z) = 694 let !(# px, py, pz #) = neg# (# x, y, z #) 695 in P px py pz 696 {-# INLINABLE neg #-} 697 698 -- Elliptic curve addition on secp256k1. 699 add :: Projective -> Projective -> Projective 700 add p q = add_proj p q 701 {-# INLINABLE add #-} 702 703 -- algo 7, "complete addition formulas for prime order elliptic curves," 704 -- renes et al, 2015 705 -- 706 -- https://eprint.iacr.org/2015/1060.pdf 707 add_proj :: Projective -> Projective -> Projective 708 add_proj (P ax ay az) (P bx by bz) = 709 let !(# x, y, z #) = add_proj# (# ax, ay, az #) (# bx, by, bz #) 710 in P x y z 711 {-# INLINABLE add_proj #-} 712 713 -- algo 8, renes et al, 2015 714 add_mixed :: Projective -> Projective -> Projective 715 add_mixed (P ax ay az) (P bx by bz) = 716 let !(# x, y, z #) = add_mixed# (# ax, ay, az #) (# bx, by, bz #) 717 in P x y z 718 {-# INLINABLE add_mixed #-} 719 720 -- algo 9, renes et al, 2015 721 double :: Projective -> Projective 722 double (Projective (C.Montgomery ax) (C.Montgomery ay) (C.Montgomery az)) = 723 let !(# x, y, z #) = double# (# ax, ay, az #) 724 in P x y z 725 {-# INLINABLE double #-} 726 727 -- Timing-safe scalar multiplication of secp256k1 points. 728 mul :: Projective -> Wider -> Maybe Projective 729 mul (P x y z) (Wider s) = case mul# (# x, y, z #) s of 730 (# () | #) -> Nothing 731 (# | (# px, py, pz #) #) -> Just $! P px py pz 732 {-# INLINABLE mul #-} 733 734 -- Timing-unsafe scalar multiplication of secp256k1 points. 735 -- 736 -- Don't use this function if the scalar could potentially be a secret. 737 mul_vartime :: Projective -> Wider -> Maybe Projective 738 mul_vartime (P x y z) (Wider s) = case mul_vartime# (# x, y, z #) s of 739 (# () | #) -> Nothing 740 (# | (# px, py, pz #) #) -> Just $! P px py pz 741 742 -- | Precomputed multiples of the secp256k1 base or generator point. 743 data Context = Context { 744 ctxW :: {-# UNPACK #-} !Int 745 , ctxArray :: {-# UNPACK #-} !ByteArray 746 } deriving Generic 747 748 instance Show Context where 749 show Context {} = "<secp256k1 context>" 750 751 -- | Create a secp256k1 context by precomputing multiples of the curve's 752 -- generator point. 753 -- 754 -- This should be used once to create a 'Context' to be reused 755 -- repeatedly afterwards. 756 -- 757 -- >>> let !tex = precompute 758 -- >>> sign_ecdsa' tex sec msg 759 -- >>> sign_schnorr' tex sec msg aux 760 precompute :: Context 761 precompute = _precompute 4 762 763 -- This is a highly-optimized version of a function originally 764 -- translated from noble-secp256k1's "precompute". Points are stored in 765 -- a ByteArray by arranging each limb into slices of 12 consecutive 766 -- slots (each Projective point consists of three Montgomery values, 767 -- each of which consists of four limbs, summing to twelve limbs in 768 -- total). 769 -- 770 -- Each point takes 96 bytes to store in this fashion, so the total size of 771 -- the ByteArray is (size * 96) bytes. 772 _precompute :: Int -> Context 773 _precompute ctxW = Context {..} where 774 capJ = (1 :: Int) .<<. (ctxW - 1) 775 ws = 256 `quot` ctxW + 1 776 size = ws * capJ 777 778 -- construct the context array 779 ctxArray = runST $ do 780 marr <- BA.newByteArray (size * 96) 781 loop_w marr _CURVE_G 0 782 BA.unsafeFreezeByteArray marr 783 784 -- write a point into the i^th 12-slot slice in the array 785 write :: MutableByteArray s -> Int -> Projective -> ST s () 786 write marr i 787 (P (# Limb x0, Limb x1, Limb x2, Limb x3 #) 788 (# Limb y0, Limb y1, Limb y2, Limb y3 #) 789 (# Limb z0, Limb z1, Limb z2, Limb z3 #)) = do 790 let !base = i * 12 791 BA.writeByteArray marr (base + 00) (GHC.Word.W# x0) 792 BA.writeByteArray marr (base + 01) (GHC.Word.W# x1) 793 BA.writeByteArray marr (base + 02) (GHC.Word.W# x2) 794 BA.writeByteArray marr (base + 03) (GHC.Word.W# x3) 795 BA.writeByteArray marr (base + 04) (GHC.Word.W# y0) 796 BA.writeByteArray marr (base + 05) (GHC.Word.W# y1) 797 BA.writeByteArray marr (base + 06) (GHC.Word.W# y2) 798 BA.writeByteArray marr (base + 07) (GHC.Word.W# y3) 799 BA.writeByteArray marr (base + 08) (GHC.Word.W# z0) 800 BA.writeByteArray marr (base + 09) (GHC.Word.W# z1) 801 BA.writeByteArray marr (base + 10) (GHC.Word.W# z2) 802 BA.writeByteArray marr (base + 11) (GHC.Word.W# z3) 803 804 -- loop over windows 805 loop_w :: MutableByteArray s -> Projective -> Int -> ST s () 806 loop_w !marr !p !w 807 | w == ws = pure () 808 | otherwise = do 809 nb <- loop_j marr p p (w * capJ) 0 810 let np = double nb 811 loop_w marr np (succ w) 812 813 -- loop within windows 814 loop_j 815 :: MutableByteArray s 816 -> Projective 817 -> Projective 818 -> Int 819 -> Int 820 -> ST s Projective 821 loop_j !marr !p !b !idx !j = do 822 write marr idx b 823 if j == capJ - 1 824 then pure b 825 else do 826 let !nb = add b p 827 loop_j marr p nb (succ idx) (succ j) 828 829 -- Timing-safe wNAF (w-ary non-adjacent form) scalar multiplication of 830 -- secp256k1 points. 831 mul_wnaf :: Context -> Wider -> Maybe Projective 832 mul_wnaf Context {..} (Wider s) = case mul_wnaf# ctxArray ctxW s of 833 (# () | #) -> Nothing 834 (# | (# px, py, pz #) #) -> Just $! P px py pz 835 {-# INLINABLE mul_wnaf #-} 836 837 -- | Derive a public key (i.e., a secp256k1 point) from the provided 838 -- secret. 839 -- 840 -- >>> import qualified System.Entropy as E 841 -- >>> sk <- fmap parse_int256 (E.getEntropy 32) 842 -- >>> derive_pub sk 843 -- Just "<secp256k1 point>" 844 derive_pub :: Wider -> Maybe Pub 845 derive_pub = mul _CURVE_G 846 {-# NOINLINE derive_pub #-} 847 848 -- | The same as 'derive_pub', except uses a 'Context' to optimise 849 -- internal calculations. 850 -- 851 -- >>> import qualified System.Entropy as E 852 -- >>> sk <- fmap parse_int256 (E.getEntropy 32) 853 -- >>> let !tex = precompute 854 -- >>> derive_pub' tex sk 855 -- Just "<secp256k1 point>" 856 derive_pub' :: Context -> Wider -> Maybe Pub 857 derive_pub' = mul_wnaf 858 {-# NOINLINE derive_pub' #-} 859 860 -- parsing -------------------------------------------------------------------- 861 862 -- | Parse a 'Wider', /e.g./ a Schnorr or ECDSA secret key. 863 -- 864 -- >>> import qualified Data.ByteString as BS 865 -- >>> parse_int256 (BS.replicate 32 0xFF) 866 -- Just <2^256 - 1> 867 parse_int256 :: BS.ByteString -> Maybe Wider 868 parse_int256 bs = do 869 guard (BS.length bs == 32) 870 pure $! unsafe_roll32 bs 871 {-# INLINABLE parse_int256 #-} 872 873 -- | Parse compressed secp256k1 point (33 bytes), uncompressed point (65 874 -- bytes), or BIP0340-style point (32 bytes). 875 -- 876 -- >>> parse_point <33-byte compressed point> 877 -- Just <Pub> 878 -- >>> parse_point <65-byte uncompressed point> 879 -- Just <Pub> 880 -- >>> parse_point <32-byte bip0340 public key> 881 -- Just <Pub> 882 -- >>> parse_point <anything else> 883 -- Nothing 884 parse_point :: BS.ByteString -> Maybe Projective 885 parse_point bs 886 | len == 32 = _parse_bip0340 bs 887 | len == 33 = _parse_compressed h t 888 | len == 65 = _parse_uncompressed h t 889 | otherwise = Nothing 890 where 891 len = BS.length bs 892 h = BU.unsafeIndex bs 0 -- lazy 893 t = BS.drop 1 bs 894 895 -- input is guaranteed to be 32B in length 896 _parse_bip0340 :: BS.ByteString -> Maybe Projective 897 _parse_bip0340 = fmap projective . lift_vartime . C.to . unsafe_roll32 898 899 -- bytestring input is guaranteed to be 32B in length 900 _parse_compressed :: Word8 -> BS.ByteString -> Maybe Projective 901 _parse_compressed h (unsafe_roll32 -> x) 902 | h /= 0x02 && h /= 0x03 = Nothing 903 | not (fe x) = Nothing 904 | otherwise = do 905 let !mx = C.to x 906 !my <- C.sqrt_vartime (weierstrass mx) 907 let !yodd = CT.decide (W.odd (C.retr my)) 908 !hodd = B.testBit h 0 909 pure $! 910 if hodd /= yodd 911 then Projective mx (negate my) 1 912 else Projective mx my 1 913 914 -- bytestring input is guaranteed to be 64B in length 915 _parse_uncompressed :: Word8 -> BS.ByteString -> Maybe Projective 916 _parse_uncompressed h bs = do 917 let (unsafe_roll32 -> x, unsafe_roll32 -> y) = BS.splitAt _CURVE_Q_BYTES bs 918 guard (h == 0x04) 919 let !p = Projective (C.to x) (C.to y) 1 920 guard (valid p) 921 pure $! p 922 923 -- | Parse an ECDSA signature encoded in 64-byte "compact" form. 924 -- 925 -- >>> parse_sig <64-byte compact signature> 926 -- Just "<ecdsa signature>" 927 parse_sig :: BS.ByteString -> Maybe ECDSA 928 parse_sig bs = do 929 guard (BS.length bs == 64) 930 let (r0, s0) = BS.splitAt 32 bs 931 r <- roll32 r0 932 s <- roll32 s0 933 pure $! ECDSA r s 934 935 -- serializing ---------------------------------------------------------------- 936 937 -- | Serialize a secp256k1 point in 33-byte compressed form. 938 -- 939 -- >>> serialize_point pub 940 -- "<33-byte compressed point>" 941 serialize_point :: Projective -> BS.ByteString 942 serialize_point (affine -> Affine (C.from -> x) (C.from -> y)) = 943 let !(Wider (# Limb w, _, _, _ #)) = y 944 !b | B.testBit (GHC.Word.W# w) 0 = 0x03 945 | otherwise = 0x02 946 in BS.cons b (unroll32 x) 947 948 -- ecdh ----------------------------------------------------------------------- 949 950 -- SEC1-v2 3.3.1, plus SHA256 hash 951 952 -- | Compute a shared secret, given a secret key and public secp256k1 point, 953 -- via Elliptic Curve Diffie-Hellman (ECDH). 954 -- 955 -- The shared secret is the SHA256 hash of the x-coordinate of the 956 -- point obtained by scalar multiplication. 957 -- 958 -- >>> let sec_alice = 0x03 959 -- >>> let sec_bob = 2 ^ 128 - 1 960 -- >>> let Just pub_alice = derive_pub sec_alice 961 -- >>> let Just pub_bob = derive_pub sec_bob 962 -- >>> let secret_as_computed_by_alice = ecdh pub_bob sec_alice 963 -- >>> let secret_as_computed_by_bob = ecdh pub_alice sec_bob 964 -- >>> secret_as_computed_by_alice == secret_as_computed_by_bob 965 -- True 966 ecdh 967 :: Projective -- ^ public key 968 -> Wider -- ^ secret key 969 -> Maybe BS.ByteString -- ^ shared secret 970 ecdh pub _SECRET = do 971 pt@(P _ _ (C.Montgomery -> z)) <- mul pub _SECRET 972 let !(Affine (C.retr -> x) _) = affine pt 973 !result = SHA256.hash (unroll32 x) 974 if CT.decide (C.eq z 0) then Nothing else Just result 975 976 -- schnorr -------------------------------------------------------------------- 977 -- see https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki 978 979 -- | Create a 64-byte Schnorr signature for the provided message, using 980 -- the provided secret key. 981 -- 982 -- BIP0340 recommends that 32 bytes of fresh auxiliary entropy be 983 -- generated and added at signing time as additional protection 984 -- against side-channel attacks (namely, to thwart so-called "fault 985 -- injection" attacks). This entropy is /supplemental/ to security, 986 -- and the cryptographic security of the signature scheme itself does 987 -- not rely on it, so it is not strictly required; 32 zero bytes can 988 -- be used in its stead (and can be supplied via 'mempty'). 989 -- 990 -- >>> import qualified System.Entropy as E 991 -- >>> aux <- E.getEntropy 32 992 -- >>> sign_schnorr sec msg aux 993 -- Just "<64-byte schnorr signature>" 994 sign_schnorr 995 :: Wider -- ^ secret key 996 -> BS.ByteString -- ^ message 997 -> BS.ByteString -- ^ 32 bytes of auxilliary random data 998 -> Maybe BS.ByteString -- ^ 64-byte Schnorr signature 999 sign_schnorr = _sign_schnorr (mul _CURVE_G) 1000 1001 -- | The same as 'sign_schnorr', except uses a 'Context' to optimise 1002 -- internal calculations. 1003 -- 1004 -- You can expect about a 2x performance increase when using this 1005 -- function, compared to 'sign_schnorr'. 1006 -- 1007 -- >>> import qualified System.Entropy as E 1008 -- >>> aux <- E.getEntropy 32 1009 -- >>> let !tex = precompute 1010 -- >>> sign_schnorr' tex sec msg aux 1011 -- Just "<64-byte schnorr signature>" 1012 sign_schnorr' 1013 :: Context -- ^ secp256k1 context 1014 -> Wider -- ^ secret key 1015 -> BS.ByteString -- ^ message 1016 -> BS.ByteString -- ^ 32 bytes of auxilliary random data 1017 -> Maybe BS.ByteString -- ^ 64-byte Schnorr signature 1018 sign_schnorr' tex = _sign_schnorr (mul_wnaf tex) 1019 1020 _sign_schnorr 1021 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1022 -> Wider -- secret key 1023 -> BS.ByteString -- message 1024 -> BS.ByteString -- 32 bytes of auxilliary random data 1025 -> Maybe BS.ByteString 1026 _sign_schnorr _mul _SECRET m a = do 1027 p <- _mul _SECRET 1028 let Affine (C.retr -> x_p) (C.retr -> y_p) = affine p 1029 s = S.to _SECRET 1030 d = S.select s (negate s) (W.odd y_p) 1031 bytes_d = unroll32 (S.retr d) 1032 bytes_p = unroll32 x_p 1033 t = xor bytes_d (hash_aux a) 1034 rand = hash_nonce (t <> bytes_p <> m) 1035 k' = S.to (unsafe_roll32 rand) 1036 guard (not (S.eq_vartime k' 0)) -- negligible probability 1037 pt <- _mul (S.retr k') 1038 let Affine (C.retr -> x_r) (C.retr -> y_r) = affine pt 1039 k = S.select k' (negate k') (W.odd y_r) 1040 bytes_r = unroll32 x_r 1041 rand' = hash_challenge (bytes_r <> bytes_p <> m) 1042 e = S.to (unsafe_roll32 rand') 1043 bytes_ked = unroll32 (S.retr (k + e * d)) 1044 sig = bytes_r <> bytes_ked 1045 -- NB for benchmarking we morally want to remove the precautionary 1046 -- verification check here. 1047 -- 1048 -- guard (verify_schnorr m p sig) 1049 pure $! sig 1050 {-# INLINE _sign_schnorr #-} 1051 1052 -- | Verify a 64-byte Schnorr signature for the provided message with 1053 -- the supplied public key. 1054 -- 1055 -- >>> verify_schnorr msg pub <valid signature> 1056 -- True 1057 -- >>> verify_schnorr msg pub <invalid signature> 1058 -- False 1059 verify_schnorr 1060 :: BS.ByteString -- ^ message 1061 -> Pub -- ^ public key 1062 -> BS.ByteString -- ^ 64-byte Schnorr signature 1063 -> Bool 1064 verify_schnorr = _verify_schnorr (mul_vartime _CURVE_G) 1065 1066 -- | The same as 'verify_schnorr', except uses a 'Context' to optimise 1067 -- internal calculations. 1068 -- 1069 -- You can expect about a 1.5x performance increase when using this 1070 -- function, compared to 'verify_schnorr'. 1071 -- 1072 -- >>> let !tex = precompute 1073 -- >>> verify_schnorr' tex msg pub <valid signature> 1074 -- True 1075 -- >>> verify_schnorr' tex msg pub <invalid signature> 1076 -- False 1077 verify_schnorr' 1078 :: Context -- ^ secp256k1 context 1079 -> BS.ByteString -- ^ message 1080 -> Pub -- ^ public key 1081 -> BS.ByteString -- ^ 64-byte Schnorr signature 1082 -> Bool 1083 verify_schnorr' tex = _verify_schnorr (mul_wnaf tex) 1084 1085 _verify_schnorr 1086 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1087 -> BS.ByteString 1088 -> Pub 1089 -> BS.ByteString 1090 -> Bool 1091 _verify_schnorr _mul m p sig 1092 | BS.length sig /= 64 = False 1093 | otherwise = M.isJust $ do 1094 let capP = even_y_vartime p 1095 (unsafe_roll32 -> r, unsafe_roll32 -> s) = BS.splitAt 32 sig 1096 guard (fe r && ge s) 1097 let Affine (C.retr -> x_P) _ = affine capP 1098 e = modQ . unsafe_roll32 $ 1099 hash_challenge (unroll32 r <> unroll32 x_P <> m) 1100 pt0 <- _mul s 1101 pt1 <- mul_vartime capP e 1102 let dif = add pt0 (neg pt1) 1103 guard (dif /= _CURVE_ZERO) 1104 let Affine (C.from -> x_R) (C.from -> y_R) = affine dif 1105 guard $ not (CT.decide (W.odd y_R) || not (W.eq_vartime x_R r)) 1106 {-# INLINE _verify_schnorr #-} 1107 1108 -- hardcoded tag of BIP0340/aux 1109 -- 1110 -- \x -> let h = SHA256.hash "BIP0340/aux" 1111 -- in SHA256.hash (h <> h <> x) 1112 hash_aux :: BS.ByteString -> BS.ByteString 1113 hash_aux x = SHA256.hash $ 1114 "\241\239N^\192c\202\218m\148\202\250\157\152~\160i&X9\236\193\US\151-w\165.\216\193\204\144\241\239N^\192c\202\218m\148\202\250\157\152~\160i&X9\236\193\US\151-w\165.\216\193\204\144" <> x 1115 {-# INLINE hash_aux #-} 1116 1117 -- hardcoded tag of BIP0340/nonce 1118 hash_nonce :: BS.ByteString -> BS.ByteString 1119 hash_nonce x = SHA256.hash $ 1120 "\aIw4\167\155\203\&5[\155\140}\ETXO\DC2\FS\244\&4\215>\247-\218\EM\135\NULa\251R\191\235/\aIw4\167\155\203\&5[\155\140}\ETXO\DC2\FS\244\&4\215>\247-\218\EM\135\NULa\251R\191\235/" <> x 1121 {-# INLINE hash_nonce #-} 1122 1123 -- hardcoded tag of BIP0340/challenge 1124 hash_challenge :: BS.ByteString -> BS.ByteString 1125 hash_challenge x = SHA256.hash $ 1126 "{\181-z\159\239X2>\177\191z@}\179\130\210\243\242\216\ESC\177\"OI\254Q\143mH\211|{\181-z\159\239X2>\177\191z@}\179\130\210\243\242\216\ESC\177\"OI\254Q\143mH\211|" <> x 1127 {-# INLINE hash_challenge #-} 1128 1129 -- ecdsa ---------------------------------------------------------------------- 1130 -- see https://www.rfc-editor.org/rfc/rfc6979, https://secg.org/sec1-v2.pdf 1131 1132 -- RFC6979 2.3.2 1133 bits2int :: BS.ByteString -> Wider 1134 bits2int = unsafe_roll32 1135 {-# INLINABLE bits2int #-} 1136 1137 -- RFC6979 2.3.3 1138 int2octets :: Wider -> BS.ByteString 1139 int2octets = unroll32 1140 {-# INLINABLE int2octets #-} 1141 1142 -- RFC6979 2.3.4 1143 bits2octets :: BS.ByteString -> BS.ByteString 1144 bits2octets bs = 1145 let z1 = bits2int bs 1146 z2 = modQ z1 1147 in int2octets z2 1148 1149 -- | An ECDSA signature. 1150 data ECDSA = ECDSA { 1151 ecdsa_r :: !Wider 1152 , ecdsa_s :: !Wider 1153 } 1154 deriving (Generic) 1155 1156 instance Show ECDSA where 1157 show _ = "<ecdsa signature>" 1158 1159 -- ECDSA signature type. 1160 data SigType = 1161 LowS 1162 | Unrestricted 1163 deriving Show 1164 1165 -- Indicates whether to hash the message or assume it has already been 1166 -- hashed. 1167 data HashFlag = 1168 Hash 1169 | NoHash 1170 deriving Show 1171 1172 -- Convert an ECDSA signature to low-S form. 1173 low :: ECDSA -> ECDSA 1174 low (ECDSA r s) = ECDSA r (W.select s (_CURVE_Q - s) (W.gt s _CURVE_QH)) 1175 {-# INLINE low #-} 1176 1177 -- | Produce an ECDSA signature for the provided message, using the 1178 -- provided private key. 1179 -- 1180 -- 'sign_ecdsa' produces a "low-s" signature, as is commonly required 1181 -- in applications using secp256k1. If you need a generic ECDSA 1182 -- signature, use 'sign_ecdsa_unrestricted'. 1183 -- 1184 -- >>> sign_ecdsa sec msg 1185 -- Just "<ecdsa signature>" 1186 sign_ecdsa 1187 :: Wider -- ^ secret key 1188 -> BS.ByteString -- ^ message 1189 -> Maybe ECDSA 1190 sign_ecdsa = _sign_ecdsa (mul _CURVE_G) LowS Hash 1191 1192 -- | The same as 'sign_ecdsa', except uses a 'Context' to optimise internal 1193 -- calculations. 1194 -- 1195 -- You can expect about a 10x performance increase when using this 1196 -- function, compared to 'sign_ecdsa'. 1197 -- 1198 -- >>> let !tex = precompute 1199 -- >>> sign_ecdsa' tex sec msg 1200 -- Just "<ecdsa signature>" 1201 sign_ecdsa' 1202 :: Context -- ^ secp256k1 context 1203 -> Wider -- ^ secret key 1204 -> BS.ByteString -- ^ message 1205 -> Maybe ECDSA 1206 sign_ecdsa' tex = _sign_ecdsa (mul_wnaf tex) LowS Hash 1207 1208 -- | Produce an ECDSA signature for the provided message, using the 1209 -- provided private key. 1210 -- 1211 -- 'sign_ecdsa_unrestricted' produces an unrestricted ECDSA signature, 1212 -- which is less common in applications using secp256k1 due to the 1213 -- signature's inherent malleability. If you need a conventional 1214 -- "low-s" signature, use 'sign_ecdsa'. 1215 -- 1216 -- >>> sign_ecdsa_unrestricted sec msg 1217 -- Just "<ecdsa signature>" 1218 sign_ecdsa_unrestricted 1219 :: Wider -- ^ secret key 1220 -> BS.ByteString -- ^ message 1221 -> Maybe ECDSA 1222 sign_ecdsa_unrestricted = _sign_ecdsa (mul _CURVE_G) Unrestricted Hash 1223 1224 -- | The same as 'sign_ecdsa_unrestricted', except uses a 'Context' to 1225 -- optimise internal calculations. 1226 -- 1227 -- You can expect about a 10x performance increase when using this 1228 -- function, compared to 'sign_ecdsa_unrestricted'. 1229 -- 1230 -- >>> let !tex = precompute 1231 -- >>> sign_ecdsa_unrestricted' tex sec msg 1232 -- Just "<ecdsa signature>" 1233 sign_ecdsa_unrestricted' 1234 :: Context -- ^ secp256k1 context 1235 -> Wider -- ^ secret key 1236 -> BS.ByteString -- ^ message 1237 -> Maybe ECDSA 1238 sign_ecdsa_unrestricted' tex = _sign_ecdsa (mul_wnaf tex) Unrestricted Hash 1239 1240 -- Produce a "low-s" ECDSA signature for the provided message, using 1241 -- the provided private key. Assumes that the message has already been 1242 -- pre-hashed. 1243 -- 1244 -- (Useful for testing against noble-secp256k1's suite, in which messages 1245 -- in the test vectors have already been hashed.) 1246 _sign_ecdsa_no_hash 1247 :: Wider -- ^ secret key 1248 -> BS.ByteString -- ^ message digest 1249 -> Maybe ECDSA 1250 _sign_ecdsa_no_hash = _sign_ecdsa (mul _CURVE_G) LowS NoHash 1251 1252 _sign_ecdsa_no_hash' 1253 :: Context 1254 -> Wider 1255 -> BS.ByteString 1256 -> Maybe ECDSA 1257 _sign_ecdsa_no_hash' tex = _sign_ecdsa (mul_wnaf tex) LowS NoHash 1258 1259 _sign_ecdsa 1260 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1261 -> SigType 1262 -> HashFlag 1263 -> Wider 1264 -> BS.ByteString 1265 -> Maybe ECDSA 1266 _sign_ecdsa _mul ty hf _SECRET m = runST $ do 1267 -- RFC6979 sec 3.3a 1268 let entropy = int2octets _SECRET 1269 nonce = bits2octets h 1270 drbg <- DRBG.new entropy nonce mempty 1271 -- RFC6979 sec 2.4 1272 sign_loop drbg 1273 where 1274 d = S.to _SECRET 1275 hm = S.to (bits2int h) 1276 h = case hf of 1277 Hash -> SHA256.hash m 1278 NoHash -> m 1279 1280 sign_loop g = do 1281 k <- gen_k g 1282 let mpair = do 1283 kg <- _mul k 1284 let Affine (S.to . C.retr -> r) _ = affine kg 1285 ki = S.inv (S.to k) 1286 s = (hm + d * r) * ki 1287 pure $! (S.retr r, S.retr s) 1288 case mpair of 1289 Nothing -> do 1290 DRBG.wipe g 1291 pure Nothing 1292 Just (r, s) 1293 | W.eq_vartime r 0 -> sign_loop g -- negligible probability 1294 | otherwise -> do 1295 DRBG.wipe g 1296 let !sig = Just $! ECDSA r s 1297 pure $ case ty of 1298 Unrestricted -> sig 1299 LowS -> fmap low sig 1300 {-# INLINE _sign_ecdsa #-} 1301 1302 -- RFC6979 sec 3.3b 1303 gen_k :: DRBG.DRBG s -> ST s Wider 1304 gen_k g = loop g where 1305 loop drbg = do 1306 bytes <- DRBG.gen drbg mempty (fi _CURVE_Q_BYTES) 1307 case bytes of 1308 Left {} -> error "ppad-secp256k1: internal error (please report a bug!)" 1309 Right bs -> do 1310 let can = bits2int bs 1311 case W.cmp_vartime can _CURVE_Q of 1312 LT -> pure can 1313 _ -> loop drbg -- 2 ^ -128 probability 1314 {-# INLINE gen_k #-} 1315 1316 -- | Verify a "low-s" ECDSA signature for the provided message and 1317 -- public key, 1318 -- 1319 -- Fails to verify otherwise-valid "high-s" signatures. If you need to 1320 -- verify generic ECDSA signatures, use 'verify_ecdsa_unrestricted'. 1321 -- 1322 -- >>> verify_ecdsa msg pub valid_sig 1323 -- True 1324 -- >>> verify_ecdsa msg pub invalid_sig 1325 -- False 1326 verify_ecdsa 1327 :: BS.ByteString -- ^ message 1328 -> Pub -- ^ public key 1329 -> ECDSA -- ^ signature 1330 -> Bool 1331 verify_ecdsa m p sig@(ECDSA _ s) 1332 | CT.decide (W.gt s _CURVE_QH) = False 1333 | otherwise = verify_ecdsa_unrestricted m p sig 1334 1335 -- | The same as 'verify_ecdsa', except uses a 'Context' to optimise 1336 -- internal calculations. 1337 -- 1338 -- You can expect about a 2x performance increase when using this 1339 -- function, compared to 'verify_ecdsa'. 1340 -- 1341 -- >>> let !tex = precompute 1342 -- >>> verify_ecdsa' tex msg pub valid_sig 1343 -- True 1344 -- >>> verify_ecdsa' tex msg pub invalid_sig 1345 -- False 1346 verify_ecdsa' 1347 :: Context -- ^ secp256k1 context 1348 -> BS.ByteString -- ^ message 1349 -> Pub -- ^ public key 1350 -> ECDSA -- ^ signature 1351 -> Bool 1352 verify_ecdsa' tex m p sig@(ECDSA _ s) 1353 | CT.decide (W.gt s _CURVE_QH) = False 1354 | otherwise = verify_ecdsa_unrestricted' tex m p sig 1355 1356 -- | Verify an unrestricted ECDSA signature for the provided message and 1357 -- public key. 1358 -- 1359 -- >>> verify_ecdsa_unrestricted msg pub valid_sig 1360 -- True 1361 -- >>> verify_ecdsa_unrestricted msg pub invalid_sig 1362 -- False 1363 verify_ecdsa_unrestricted 1364 :: BS.ByteString -- ^ message 1365 -> Pub -- ^ public key 1366 -> ECDSA -- ^ signature 1367 -> Bool 1368 verify_ecdsa_unrestricted = 1369 _verify_ecdsa_unrestricted (mul_vartime _CURVE_G) Hash 1370 1371 -- | The same as 'verify_ecdsa_unrestricted', except uses a 'Context' to 1372 -- optimise internal calculations. 1373 -- 1374 -- You can expect about a 2x performance increase when using this 1375 -- function, compared to 'verify_ecdsa_unrestricted'. 1376 -- 1377 -- >>> let !tex = precompute 1378 -- >>> verify_ecdsa_unrestricted' tex msg pub valid_sig 1379 -- True 1380 -- >>> verify_ecdsa_unrestricted' tex msg pub invalid_sig 1381 -- False 1382 verify_ecdsa_unrestricted' 1383 :: Context -- ^ secp256k1 context 1384 -> BS.ByteString -- ^ message 1385 -> Pub -- ^ public key 1386 -> ECDSA -- ^ signature 1387 -> Bool 1388 verify_ecdsa_unrestricted' tex = 1389 _verify_ecdsa_unrestricted (mul_wnaf tex) Hash 1390 1391 _verify_ecdsa_unrestricted 1392 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1393 -> HashFlag 1394 -> BS.ByteString 1395 -> Pub 1396 -> ECDSA 1397 -> Bool 1398 _verify_ecdsa_unrestricted _mul hf m p (ECDSA r0 s0) = M.isJust $ do 1399 -- SEC1-v2 4.1.4 1400 let h = case hf of 1401 Hash -> SHA256.hash m 1402 NoHash -> m 1403 guard (ge r0 && ge s0) 1404 let r = S.to r0 1405 s = S.to s0 1406 e = S.to (bits2int h) 1407 si = S.inv s 1408 u1 = S.retr (e * si) 1409 u2 = S.retr (r * si) 1410 pt0 = case _mul u1 of 1411 Nothing -> _CURVE_ZERO 1412 Just pt -> pt 1413 pt1 <- mul_vartime p u2 1414 let capR = add pt0 pt1 1415 guard (capR /= _CURVE_ZERO) 1416 let Affine (S.to . C.retr -> v) _ = affine capR 1417 guard (S.eq_vartime v r) 1418 {-# INLINE _verify_ecdsa_unrestricted #-} 1419 1420 -- | Verify a "low-s" ECDSA signature for the provided message digest 1421 -- and public key. 1422 -- 1423 -- Mirrors 'verify_ecdsa', but skips the internal SHA256 step, 1424 -- treating the input as the message digest itself. 1425 -- 1426 -- >>> _verify_ecdsa_no_hash dig pub valid_sig 1427 -- True 1428 -- >>> _verify_ecdsa_no_hash dig pub invalid_sig 1429 -- False 1430 _verify_ecdsa_no_hash 1431 :: BS.ByteString -- ^ message digest 1432 -> Pub -- ^ public key 1433 -> ECDSA -- ^ signature 1434 -> Bool 1435 _verify_ecdsa_no_hash m p sig@(ECDSA _ s) 1436 | W.gt_vartime s _CURVE_QH = False 1437 | otherwise = 1438 _verify_ecdsa_unrestricted (mul_vartime _CURVE_G) NoHash m p sig 1439 1440 -- | The same as '_verify_ecdsa_no_hash', except uses a 'Context' to 1441 -- optimise internal calculations. 1442 -- 1443 -- You can expect about a 2x performance increase when using this 1444 -- function, compared to '_verify_ecdsa_no_hash'. 1445 -- 1446 -- >>> let !tex = precompute 1447 -- >>> _verify_ecdsa_no_hash' tex dig pub valid_sig 1448 -- True 1449 -- >>> _verify_ecdsa_no_hash' tex dig pub invalid_sig 1450 -- False 1451 _verify_ecdsa_no_hash' 1452 :: Context -- ^ secp256k1 context 1453 -> BS.ByteString -- ^ message digest 1454 -> Pub -- ^ public key 1455 -> ECDSA -- ^ signature 1456 -> Bool 1457 _verify_ecdsa_no_hash' tex m p sig@(ECDSA _ s) 1458 | W.gt_vartime s _CURVE_QH = False 1459 | otherwise = 1460 _verify_ecdsa_unrestricted (mul_wnaf tex) NoHash m p sig 1461