Secp256k1.hs (46107B)
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 , roll32 101 , unsafe_roll32 102 , unroll32 103 , select_proj 104 ) where 105 106 import Control.Monad (guard) 107 import Control.Monad.ST 108 import qualified Crypto.DRBG.HMAC.SHA256 as DRBG 109 import qualified Crypto.Hash.SHA256 as SHA256 110 import qualified Data.Bits as B 111 import qualified Data.ByteString as BS 112 import qualified Data.ByteString.Internal as BI 113 import qualified Data.ByteString.Unsafe as BU 114 import qualified Data.Choice as CT 115 import qualified Data.Maybe as M 116 import Data.Primitive.ByteArray (ByteArray(..), MutableByteArray(..)) 117 import qualified Data.Primitive.ByteArray as BA 118 import Data.Word (Word8) 119 import Data.Word.Limb (Limb(..)) 120 import qualified Data.Word.Limb as L 121 import Data.Word.Wider (Wider(..)) 122 import qualified Data.Word.Wider as W 123 import qualified Foreign.Storable as Storable (pokeByteOff) 124 import qualified GHC.Exts as Exts 125 import GHC.Generics 126 import qualified GHC.Word (Word(..), Word8(..)) 127 import qualified Numeric.Montgomery.Secp256k1.Curve as C 128 import qualified Numeric.Montgomery.Secp256k1.Scalar as S 129 import Prelude hiding (sqrt) 130 131 -- convenience synonyms ------------------------------------------------------- 132 133 -- Unboxed Wider/Montgomery synonym. 134 type Limb4 = (# Limb, Limb, Limb, Limb #) 135 136 -- Unboxed Projective synonym. 137 type Proj = (# Limb4, Limb4, Limb4 #) 138 139 pattern Z :: Limb4 140 pattern Z = (# Limb 0##, Limb 0##, Limb 0##, Limb 0## #) 141 142 pattern P :: Limb4 -> Limb4 -> Limb4 -> Projective 143 pattern P x y z = Projective (C.Montgomery x) (C.Montgomery y) (C.Montgomery z) 144 {-# COMPLETE P #-} 145 146 -- utilities ------------------------------------------------------------------ 147 148 fi :: (Integral a, Num b) => a -> b 149 fi = fromIntegral 150 {-# INLINE fi #-} 151 152 -- convert a Word8 to a Limb 153 limb :: Word8 -> Limb 154 limb (GHC.Word.W8# (Exts.word8ToWord# -> w)) = Limb w 155 {-# INLINABLE limb #-} 156 157 -- convert a Limb to a Word8 158 word8 :: Limb -> Word8 159 word8 (Limb w) = GHC.Word.W8# (Exts.wordToWord8# w) 160 {-# INLINABLE word8 #-} 161 162 -- convert a Limb to a Word8 after right-shifting 163 word8s :: Limb -> Exts.Int# -> Word8 164 word8s l s = 165 let !(Limb w) = L.shr# l s 166 in GHC.Word.W8# (Exts.wordToWord8# w) 167 {-# INLINABLE word8s #-} 168 169 -- convert a Word8 to a Wider 170 word8_to_wider :: Word8 -> Wider 171 word8_to_wider w = Wider (# limb w, Limb 0##, Limb 0##, Limb 0## #) 172 {-# INLINABLE word8_to_wider #-} 173 174 -- unsafely extract the first 64-bit word from a big-endian-encoded bytestring 175 unsafe_word0 :: BS.ByteString -> Limb 176 unsafe_word0 bs = 177 (limb (BU.unsafeIndex bs 00) `L.shl#` 56#) 178 `L.or#` (limb (BU.unsafeIndex bs 01) `L.shl#` 48#) 179 `L.or#` (limb (BU.unsafeIndex bs 02) `L.shl#` 40#) 180 `L.or#` (limb (BU.unsafeIndex bs 03) `L.shl#` 32#) 181 `L.or#` (limb (BU.unsafeIndex bs 04) `L.shl#` 24#) 182 `L.or#` (limb (BU.unsafeIndex bs 05) `L.shl#` 16#) 183 `L.or#` (limb (BU.unsafeIndex bs 06) `L.shl#` 08#) 184 `L.or#` (limb (BU.unsafeIndex bs 07)) 185 {-# INLINABLE unsafe_word0 #-} 186 187 -- unsafely extract the second 64-bit word from a big-endian-encoded bytestring 188 unsafe_word1 :: BS.ByteString -> Limb 189 unsafe_word1 bs = 190 (limb (BU.unsafeIndex bs 08) `L.shl#` 56#) 191 `L.or#` (limb (BU.unsafeIndex bs 09) `L.shl#` 48#) 192 `L.or#` (limb (BU.unsafeIndex bs 10) `L.shl#` 40#) 193 `L.or#` (limb (BU.unsafeIndex bs 11) `L.shl#` 32#) 194 `L.or#` (limb (BU.unsafeIndex bs 12) `L.shl#` 24#) 195 `L.or#` (limb (BU.unsafeIndex bs 13) `L.shl#` 16#) 196 `L.or#` (limb (BU.unsafeIndex bs 14) `L.shl#` 08#) 197 `L.or#` (limb (BU.unsafeIndex bs 15)) 198 {-# INLINABLE unsafe_word1 #-} 199 200 -- unsafely extract the third 64-bit word from a big-endian-encoded bytestring 201 unsafe_word2 :: BS.ByteString -> Limb 202 unsafe_word2 bs = 203 (limb (BU.unsafeIndex bs 16) `L.shl#` 56#) 204 `L.or#` (limb (BU.unsafeIndex bs 17) `L.shl#` 48#) 205 `L.or#` (limb (BU.unsafeIndex bs 18) `L.shl#` 40#) 206 `L.or#` (limb (BU.unsafeIndex bs 19) `L.shl#` 32#) 207 `L.or#` (limb (BU.unsafeIndex bs 20) `L.shl#` 24#) 208 `L.or#` (limb (BU.unsafeIndex bs 21) `L.shl#` 16#) 209 `L.or#` (limb (BU.unsafeIndex bs 22) `L.shl#` 08#) 210 `L.or#` (limb (BU.unsafeIndex bs 23)) 211 {-# INLINABLE unsafe_word2 #-} 212 213 -- unsafely extract the fourth 64-bit word from a big-endian-encoded bytestring 214 unsafe_word3 :: BS.ByteString -> Limb 215 unsafe_word3 bs = 216 (limb (BU.unsafeIndex bs 24) `L.shl#` 56#) 217 `L.or#` (limb (BU.unsafeIndex bs 25) `L.shl#` 48#) 218 `L.or#` (limb (BU.unsafeIndex bs 26) `L.shl#` 40#) 219 `L.or#` (limb (BU.unsafeIndex bs 27) `L.shl#` 32#) 220 `L.or#` (limb (BU.unsafeIndex bs 28) `L.shl#` 24#) 221 `L.or#` (limb (BU.unsafeIndex bs 29) `L.shl#` 16#) 222 `L.or#` (limb (BU.unsafeIndex bs 30) `L.shl#` 08#) 223 `L.or#` (limb (BU.unsafeIndex bs 31)) 224 {-# INLINABLE unsafe_word3 #-} 225 226 -- 256-bit big-endian bytestring decoding. the input size is not checked! 227 unsafe_roll32 :: BS.ByteString -> Wider 228 unsafe_roll32 bs = 229 let !w0 = unsafe_word0 bs 230 !w1 = unsafe_word1 bs 231 !w2 = unsafe_word2 bs 232 !w3 = unsafe_word3 bs 233 in Wider (# w3, w2, w1, w0 #) 234 {-# INLINABLE unsafe_roll32 #-} 235 236 -- arbitrary-size big-endian bytestring decoding 237 roll32 :: BS.ByteString -> Maybe Wider 238 roll32 bs 239 | BS.length stripped > 32 = Nothing 240 | otherwise = Just $! BS.foldl' alg 0 stripped 241 where 242 stripped = BS.dropWhile (== 0) bs 243 alg !a (word8_to_wider -> !b) = (a `W.shl_limb` 8) `W.or` b 244 {-# INLINABLE roll32 #-} 245 246 -- 256-bit big-endian bytestring encoding 247 unroll32 :: Wider -> BS.ByteString 248 unroll32 (Wider (# w0, w1, w2, w3 #)) = 249 BI.unsafeCreate 32 $ \ptr -> do 250 -- w0 251 Storable.pokeByteOff ptr 00 (word8s w3 56#) 252 Storable.pokeByteOff ptr 01 (word8s w3 48#) 253 Storable.pokeByteOff ptr 02 (word8s w3 40#) 254 Storable.pokeByteOff ptr 03 (word8s w3 32#) 255 Storable.pokeByteOff ptr 04 (word8s w3 24#) 256 Storable.pokeByteOff ptr 05 (word8s w3 16#) 257 Storable.pokeByteOff ptr 06 (word8s w3 08#) 258 Storable.pokeByteOff ptr 07 (word8 w3) 259 -- w1 260 Storable.pokeByteOff ptr 08 (word8s w2 56#) 261 Storable.pokeByteOff ptr 09 (word8s w2 48#) 262 Storable.pokeByteOff ptr 10 (word8s w2 40#) 263 Storable.pokeByteOff ptr 11 (word8s w2 32#) 264 Storable.pokeByteOff ptr 12 (word8s w2 24#) 265 Storable.pokeByteOff ptr 13 (word8s w2 16#) 266 Storable.pokeByteOff ptr 14 (word8s w2 08#) 267 Storable.pokeByteOff ptr 15 (word8 w2) 268 -- w2 269 Storable.pokeByteOff ptr 16 (word8s w1 56#) 270 Storable.pokeByteOff ptr 17 (word8s w1 48#) 271 Storable.pokeByteOff ptr 18 (word8s w1 40#) 272 Storable.pokeByteOff ptr 19 (word8s w1 32#) 273 Storable.pokeByteOff ptr 20 (word8s w1 24#) 274 Storable.pokeByteOff ptr 21 (word8s w1 16#) 275 Storable.pokeByteOff ptr 22 (word8s w1 08#) 276 Storable.pokeByteOff ptr 23 (word8 w1) 277 -- w3 278 Storable.pokeByteOff ptr 24 (word8s w0 56#) 279 Storable.pokeByteOff ptr 25 (word8s w0 48#) 280 Storable.pokeByteOff ptr 26 (word8s w0 40#) 281 Storable.pokeByteOff ptr 27 (word8s w0 32#) 282 Storable.pokeByteOff ptr 28 (word8s w0 24#) 283 Storable.pokeByteOff ptr 29 (word8s w0 16#) 284 Storable.pokeByteOff ptr 30 (word8s w0 08#) 285 Storable.pokeByteOff ptr 31 (word8 w0) 286 {-# INLINABLE unroll32 #-} 287 288 -- modQ via conditional subtraction 289 modQ :: Wider -> Wider 290 modQ x = W.select x (x - _CURVE_Q) (CT.not (W.lt x _CURVE_Q)) 291 {-# INLINABLE modQ #-} 292 293 -- bytewise xor 294 xor :: BS.ByteString -> BS.ByteString -> BS.ByteString 295 xor = BS.packZipWith B.xor 296 {-# INLINABLE xor #-} 297 298 -- constants ------------------------------------------------------------------ 299 300 -- | secp256k1 field prime. 301 -- 302 -- >>> _CURVE_P 303 -- 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 304 _CURVE_P :: Wider 305 _CURVE_P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 306 307 -- | secp256k1 group order. 308 -- 309 -- >>> _CURVE_Q 310 -- 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 311 _CURVE_Q :: Wider 312 _CURVE_Q = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 313 314 -- | half of the secp256k1 group order. 315 _CURVE_QH :: Wider 316 _CURVE_QH = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0 317 318 -- bitlength of group order 319 -- 320 -- = smallest integer such that _CURVE_Q < 2 ^ _CURVE_Q_BITS 321 _CURVE_Q_BITS :: Int 322 _CURVE_Q_BITS = 256 323 324 -- bytelength of _CURVE_Q 325 -- 326 -- = _CURVE_Q_BITS / 8 327 _CURVE_Q_BYTES :: Int 328 _CURVE_Q_BYTES = 32 329 330 -- secp256k1 weierstrass form, /b/ coefficient 331 _CURVE_B :: Wider 332 _CURVE_B = 7 333 334 -- secp256k1 weierstrass form, /b/ coefficient, montgomery form 335 _CURVE_Bm :: C.Montgomery 336 _CURVE_Bm = 7 337 338 -- _CURVE_Bm * 3 339 _CURVE_Bm3 :: C.Montgomery 340 _CURVE_Bm3 = 21 341 342 -- Is field element? 343 fe :: Wider -> Bool 344 fe n = case W.cmp_vartime n 0 of 345 GT -> case W.cmp_vartime n _CURVE_P of 346 LT -> True 347 _ -> False 348 _ -> False 349 {-# INLINE fe #-} 350 351 -- Is group element? 352 ge :: Wider -> Bool 353 ge (Wider n) = CT.decide (ge# n) 354 {-# INLINE ge #-} 355 356 -- curve points --------------------------------------------------------------- 357 358 -- curve point, affine coordinates 359 data Affine = Affine !C.Montgomery !C.Montgomery 360 deriving stock (Show, Generic) 361 362 -- curve point, projective coordinates 363 data Projective = Projective { 364 px :: !C.Montgomery 365 , py :: !C.Montgomery 366 , pz :: !C.Montgomery 367 } 368 deriving stock (Show, Generic) 369 370 instance Eq Projective where 371 Projective ax ay az == Projective bx by bz = 372 let !x1z2 = ax * bz 373 !x2z1 = bx * az 374 !y1z2 = ay * bz 375 !y2z1 = by * az 376 in CT.decide (CT.and (C.eq x1z2 x2z1) (C.eq y1z2 y2z1)) 377 378 -- | A public key, i.e. secp256k1 point. 379 type Pub = Projective 380 381 -- Convert to affine coordinates. 382 affine :: Projective -> Affine 383 affine (Projective x y z) = 384 let !iz = C.inv z 385 in Affine (x * iz) (y * iz) 386 {-# INLINABLE affine #-} 387 388 -- Convert to projective coordinates. 389 projective :: Affine -> Projective 390 projective (Affine x y) 391 | C.eq_vartime x 0 || C.eq_vartime y 0 = _CURVE_ZERO 392 | otherwise = Projective x y 1 393 394 -- | secp256k1 generator point. 395 _CURVE_G :: Projective 396 _CURVE_G = Projective x y z where 397 !x = C.Montgomery 398 (# Limb 15507633332195041431##, Limb 2530505477788034779## 399 , Limb 10925531211367256732##, Limb 11061375339145502536## #) 400 !y = C.Montgomery 401 (# Limb 12780836216951778274##, Limb 10231155108014310989## 402 , Limb 8121878653926228278##, Limb 14933801261141951190## #) 403 !z = C.Montgomery 404 (# Limb 0x1000003D1##, Limb 0##, Limb 0##, Limb 0## #) 405 406 -- | secp256k1 zero point, point at infinity, or monoidal identity. 407 _CURVE_ZERO :: Projective 408 _CURVE_ZERO = Projective 0 1 0 409 410 -- secp256k1 zero point, point at infinity, or monoidal identity 411 _ZERO :: Projective 412 _ZERO = Projective 0 1 0 413 {-# DEPRECATED _ZERO "use _CURVE_ZERO instead" #-} 414 415 -- secp256k1 in short weierstrass form (y ^ 2 = x ^ 3 + 7) 416 weierstrass :: C.Montgomery -> C.Montgomery 417 weierstrass x = C.sqr x * x + _CURVE_Bm 418 {-# INLINE weierstrass #-} 419 420 -- Point is valid 421 valid :: Projective -> Bool 422 valid (affine -> Affine x y) = C.eq_vartime (C.sqr y) (weierstrass x) 423 424 -- (bip0340) return point with x coordinate == x and with even y coordinate 425 -- 426 -- conceptually: 427 -- y ^ 2 = x ^ 3 + 7 428 -- y = "+-" sqrt (x ^ 3 + 7) 429 -- (n.b. for solution y, p - y is also a solution) 430 -- y + (p - y) = p (odd) 431 -- (n.b. sum is odd, so one of y and p - y must be odd, and the other even) 432 -- if y even, return (x, y) 433 -- else, return (x, p - y) 434 lift_vartime :: C.Montgomery -> Maybe Affine 435 lift_vartime x = do 436 let !c = weierstrass x 437 !y <- C.sqrt_vartime c 438 let !y_e | C.odd_vartime y = negate y 439 | otherwise = y 440 pure $! Affine x y_e 441 442 even_y_vartime :: Projective -> Projective 443 even_y_vartime p = case affine p of 444 Affine _ (C.retr -> y) 445 | CT.decide (W.odd y) -> neg p 446 | otherwise -> p 447 448 -- Constant-time selection of Projective points. 449 select_proj :: Projective -> Projective -> CT.Choice -> Projective 450 select_proj (Projective ax ay az) (Projective bx by bz) c = 451 Projective (C.select ax bx c) (C.select ay by c) (C.select az bz c) 452 {-# INLINE select_proj #-} 453 454 -- unboxed internals ---------------------------------------------------------- 455 456 -- algo 7, renes et al, 2015 457 add_proj# :: Proj -> Proj -> Proj 458 add_proj# (# x1, y1, z1 #) (# x2, y2, z2 #) = 459 let !(C.Montgomery b3) = _CURVE_Bm3 460 !t0a = C.mul# x1 x2 461 !t1a = C.mul# y1 y2 462 !t2a = C.mul# z1 z2 463 !t3a = C.add# x1 y1 464 !t4a = C.add# x2 y2 465 !t3b = C.mul# t3a t4a 466 !t4b = C.add# t0a t1a 467 !t3c = C.sub# t3b t4b 468 !t4c = C.add# y1 z1 469 !x3a = C.add# y2 z2 470 !t4d = C.mul# t4c x3a 471 !x3b = C.add# t1a t2a 472 !t4e = C.sub# t4d x3b 473 !x3c = C.add# x1 z1 474 !y3a = C.add# x2 z2 475 !x3d = C.mul# x3c y3a 476 !y3b = C.add# t0a t2a 477 !y3c = C.sub# x3d y3b 478 !x3e = C.add# t0a t0a 479 !t0b = C.add# x3e t0a 480 !t2b = C.mul# b3 t2a 481 !z3a = C.add# t1a t2b 482 !t1b = C.sub# t1a t2b 483 !y3d = C.mul# b3 y3c 484 !x3f = C.mul# t4e y3d 485 !t2c = C.mul# t3c t1b 486 !x3g = C.sub# t2c x3f 487 !y3e = C.mul# y3d t0b 488 !t1c = C.mul# t1b z3a 489 !y3f = C.add# t1c y3e 490 !t0c = C.mul# t0b t3c 491 !z3b = C.mul# z3a t4e 492 !z3c = C.add# z3b t0c 493 in (# x3g, y3f, z3c #) 494 {-# INLINE add_proj# #-} 495 496 -- algo 8, renes et al, 2015 497 add_mixed# :: Proj -> Proj -> Proj 498 add_mixed# (# x1, y1, z1 #) (# x2, y2, _z2 #) = 499 let !(C.Montgomery b3) = _CURVE_Bm3 500 !t0a = C.mul# x1 x2 501 !t1a = C.mul# y1 y2 502 !t3a = C.add# x2 y2 503 !t4a = C.add# x1 y1 504 !t3b = C.mul# t3a t4a 505 !t4b = C.add# t0a t1a 506 !t3c = C.sub# t3b t4b 507 !t4c = C.mul# y2 z1 508 !t4d = C.add# t4c y1 509 !y3a = C.mul# x2 z1 510 !y3b = C.add# y3a x1 511 !x3a = C.add# t0a t0a 512 !t0b = C.add# x3a t0a 513 !t2a = C.mul# b3 z1 514 !z3a = C.add# t1a t2a 515 !t1b = C.sub# t1a t2a 516 !y3c = C.mul# b3 y3b 517 !x3b = C.mul# t4d y3c 518 !t2b = C.mul# t3c t1b 519 !x3c = C.sub# t2b x3b 520 !y3d = C.mul# y3c t0b 521 !t1c = C.mul# t1b z3a 522 !y3e = C.add# t1c y3d 523 !t0c = C.mul# t0b t3c 524 !z3b = C.mul# z3a t4d 525 !z3c = C.add# z3b t0c 526 in (# x3c, y3e, z3c #) 527 {-# INLINE add_mixed# #-} 528 529 -- algo 9, renes et al, 2015 530 double# :: Proj -> Proj 531 double# (# x, y, z #) = 532 let !(C.Montgomery b3) = _CURVE_Bm3 533 !t0 = C.sqr# y 534 !z3a = C.add# t0 t0 535 !z3b = C.add# z3a z3a 536 !z3c = C.add# z3b z3b 537 !t1 = C.mul# y z 538 !t2a = C.sqr# z 539 !t2b = C.mul# b3 t2a 540 !x3a = C.mul# t2b z3c 541 !y3a = C.add# t0 t2b 542 !z3d = C.mul# t1 z3c 543 !t1b = C.add# t2b t2b 544 !t2c = C.add# t1b t2b 545 !t0b = C.sub# t0 t2c 546 !y3b = C.mul# t0b y3a 547 !y3c = C.add# x3a y3b 548 !t1c = C.mul# x y 549 !x3b = C.mul# t0b t1c 550 !x3c = C.add# x3b x3b 551 in (# x3c, y3c, z3d #) 552 {-# INLINE double# #-} 553 554 select_proj# :: Proj -> Proj -> CT.Choice -> Proj 555 select_proj# (# ax, ay, az #) (# bx, by, bz #) c = 556 (# W.select# ax bx c, W.select# ay by c, W.select# az bz c #) 557 {-# INLINE select_proj# #-} 558 559 neg# :: Proj -> Proj 560 neg# (# x, y, z #) = (# x, C.neg# y, z #) 561 {-# INLINE neg# #-} 562 563 mul# :: Proj -> Limb4 -> (# () | Proj #) 564 mul# (# px, py, pz #) s 565 | CT.decide (CT.not (ge# s)) = (# () | #) 566 | otherwise = 567 let !(P gx gy gz) = _CURVE_G 568 !(C.Montgomery o) = C.one 569 in loop (0 :: Int) (# Z, o, Z #) (# gx, gy, gz #) (# px, py, pz #) s 570 where 571 loop !j !a !f !d !_SECRET 572 | j == _CURVE_Q_BITS = (# | a #) 573 | otherwise = 574 let !nd = double# d 575 !(# nm, lsb_set #) = W.shr1_c# _SECRET 576 !nacc = select_proj# a (add_proj# a d) lsb_set 577 !nf = select_proj# (add_proj# f d) f lsb_set 578 in loop (succ j) nacc nf nd nm 579 {-# INLINE mul# #-} 580 581 mul_vartime# :: Proj -> Limb4 -> (# () | Proj #) 582 mul_vartime# (# px, py, pz #) s 583 | zero# s = 584 let !(P zx zy zz) = _CURVE_ZERO 585 in (# | (# zx, zy, zz #) #) 586 | CT.decide (CT.not (ge# s)) = (# () | #) 587 | otherwise = 588 let !(P zx zy zz) = _CURVE_ZERO 589 in (# | loop (# zx, zy, zz #) (# px, py, pz #) s #) 590 where 591 zero# (# Limb a, Limb b, Limb c, Limb d #) = Exts.isTrue# 592 ((a `Exts.or#` b `Exts.or#` c `Exts.or#` d) `Exts.eqWord#` 0##) 593 594 loop !r !d !m 595 | zero# m = r 596 | otherwise = 597 let !nd = double# d 598 !(# nm, lsb_set #) = W.shr1_c# m 599 !nr = if CT.decide lsb_set then add_proj# r d else r 600 in loop nr nd nm 601 {-# INLINE mul_vartime# #-} 602 603 ge# :: Limb4 -> CT.Choice 604 ge# n = 605 let !(Wider q) = _CURVE_Q 606 in CT.and (W.gt# n Z) (W.lt# n q) 607 {-# INLINE ge# #-} 608 609 mul_wnaf# :: ByteArray -> Int -> Limb4 -> (# () | Proj #) 610 mul_wnaf# ctxArray ctxW ls 611 | CT.decide (CT.not (ge# ls)) = (# () | #) 612 | otherwise = 613 let !(P zx zy zz) = _CURVE_ZERO 614 !(P gx gy gz) = _CURVE_G 615 in (# | loop 0 (# zx, zy, zz #) (# gx, gy, gz #) 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) = 2 ^ (ctxW - 1) 620 !(GHC.Word.W# mask) = 2 ^ ctxW - 1 621 !(GHC.Word.W# texW) = fi ctxW 622 !(GHC.Word.W# mnum) = 2 ^ ctxW 623 624 loop !j@(GHC.Word.W# w) !acc !f !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 !c0 = CT.from_bit# (Exts.and# w 1##) 638 !off_nz = Exts.minusWord# (Exts.plusWord# off0 abs_b) 1## 639 !off = CT.select_word# off0 off_nz (CT.not is_zero) 640 641 !pr = ct_index_proj# ctxArray off0 s off 642 !neg_pr = neg# pr 643 !pt_zero = select_proj# pr neg_pr c0 644 !pt_nonzero = select_proj# pr neg_pr bor 645 646 !f_added = add_proj# f pt_zero 647 !acc_added = add_proj# acc pt_nonzero 648 !nacc = select_proj# acc_added acc is_zero 649 !nf = select_proj# f f_added is_zero 650 in loop (succ j) nacc nf n1 651 {-# INLINE mul_wnaf# #-} 652 653 -- retrieve a point (as an unboxed tuple) from a context array 654 index_proj# :: ByteArray -> Exts.Int# -> Proj 655 index_proj# (ByteArray arr#) i# = 656 let !base# = i# Exts.*# 12# 657 !x = (# Limb (Exts.indexWordArray# arr# base#) 658 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 01#)) 659 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 02#)) 660 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 03#)) #) 661 !y = (# Limb (Exts.indexWordArray# arr# (base# Exts.+# 04#)) 662 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 05#)) 663 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 06#)) 664 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 07#)) #) 665 !z = (# Limb (Exts.indexWordArray# arr# (base# Exts.+# 08#)) 666 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 09#)) 667 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 10#)) 668 , Limb (Exts.indexWordArray# arr# (base# Exts.+# 11#)) #) 669 in (# x, y, z #) 670 {-# INLINE index_proj# #-} 671 672 -- Constant-time table lookup within a window. 673 -- 674 -- Unconditionally scans all entries from 'base' to 'base + size - 1', 675 -- selecting the one where 'index' equals 'target'. 676 ct_index_proj# 677 :: ByteArray 678 -> Exts.Word# -- ^ base index 679 -> Exts.Word# -- ^ size of window 680 -> Exts.Word# -- ^ target index 681 -> Proj 682 ct_index_proj# arr base size target = loop 0## (# Z, Z, Z #) where 683 loop i acc 684 | Exts.isTrue# (i `Exts.geWord#` size) = acc 685 | otherwise = 686 let !idx = Exts.plusWord# base i 687 !pt = index_proj# arr (Exts.word2Int# idx) 688 !eq = CT.from_word_eq# idx target 689 !nacc = select_proj# acc pt eq 690 in loop (Exts.plusWord# i 1##) nacc 691 {-# INLINE ct_index_proj# #-} 692 693 -- ec arithmetic -------------------------------------------------------------- 694 695 -- Negate secp256k1 point. 696 neg :: Projective -> Projective 697 neg (P x y z) = 698 let !(# px, py, pz #) = neg# (# x, y, z #) 699 in P px py pz 700 {-# INLINABLE neg #-} 701 702 -- Elliptic curve addition on secp256k1. 703 add :: Projective -> Projective -> Projective 704 add p q = add_proj p q 705 {-# INLINABLE add #-} 706 707 -- algo 7, "complete addition formulas for prime order elliptic curves," 708 -- renes et al, 2015 709 -- 710 -- https://eprint.iacr.org/2015/1060.pdf 711 add_proj :: Projective -> Projective -> Projective 712 add_proj (P ax ay az) (P bx by bz) = 713 let !(# x, y, z #) = add_proj# (# ax, ay, az #) (# bx, by, bz #) 714 in P x y z 715 {-# INLINABLE add_proj #-} 716 717 -- algo 8, renes et al, 2015 718 add_mixed :: Projective -> Projective -> Projective 719 add_mixed (P ax ay az) (P bx by bz) = 720 let !(# x, y, z #) = add_mixed# (# ax, ay, az #) (# bx, by, bz #) 721 in P x y z 722 {-# INLINABLE add_mixed #-} 723 724 -- algo 9, renes et al, 2015 725 double :: Projective -> Projective 726 double (Projective (C.Montgomery ax) (C.Montgomery ay) (C.Montgomery az)) = 727 let !(# x, y, z #) = double# (# ax, ay, az #) 728 in P x y z 729 {-# INLINABLE double #-} 730 731 -- Timing-safe scalar multiplication of secp256k1 points. 732 mul :: Projective -> Wider -> Maybe Projective 733 mul (P x y z) (Wider s) = case mul# (# x, y, z #) s of 734 (# () | #) -> Nothing 735 (# | (# px, py, pz #) #) -> Just $! P px py pz 736 {-# INLINABLE mul #-} 737 738 -- Timing-unsafe scalar multiplication of secp256k1 points. 739 -- 740 -- Don't use this function if the scalar could potentially be a secret. 741 mul_vartime :: Projective -> Wider -> Maybe Projective 742 mul_vartime (P x y z) (Wider s) = case mul_vartime# (# x, y, z #) s of 743 (# () | #) -> Nothing 744 (# | (# px, py, pz #) #) -> Just $! P px py pz 745 746 -- | Precomputed multiples of the secp256k1 base or generator point. 747 data Context = Context { 748 ctxW :: {-# UNPACK #-} !Int 749 , ctxArray :: {-# UNPACK #-} !ByteArray 750 } deriving Generic 751 752 instance Show Context where 753 show Context {} = "<secp256k1 context>" 754 755 -- | Create a secp256k1 context by precomputing multiples of the curve's 756 -- generator point. 757 -- 758 -- This should be used once to create a 'Context' to be reused 759 -- repeatedly afterwards. 760 -- 761 -- >>> let !tex = precompute 762 -- >>> sign_ecdsa' tex sec msg 763 -- >>> sign_schnorr' tex sec msg aux 764 precompute :: Context 765 precompute = _precompute 4 766 767 -- This is a highly-optimized version of a function originally 768 -- translated from noble-secp256k1's "precompute". Points are stored in 769 -- a ByteArray by arranging each limb into slices of 12 consecutive 770 -- slots (each Projective point consists of three Montgomery values, 771 -- each of which consists of four limbs, summing to twelve limbs in 772 -- total). 773 -- 774 -- Each point takes 96 bytes to store in this fashion, so the total size of 775 -- the ByteArray is (size * 96) bytes. 776 _precompute :: Int -> Context 777 _precompute ctxW = Context {..} where 778 capJ = (2 :: Int) ^ (ctxW - 1) 779 ws = 256 `quot` ctxW + 1 780 size = ws * capJ 781 782 -- construct the context array 783 ctxArray = runST $ do 784 marr <- BA.newByteArray (size * 96) 785 loop_w marr _CURVE_G 0 786 BA.unsafeFreezeByteArray marr 787 788 -- write a point into the i^th 12-slot slice in the array 789 write :: MutableByteArray s -> Int -> Projective -> ST s () 790 write marr i 791 (P (# Limb x0, Limb x1, Limb x2, Limb x3 #) 792 (# Limb y0, Limb y1, Limb y2, Limb y3 #) 793 (# Limb z0, Limb z1, Limb z2, Limb z3 #)) = do 794 let !base = i * 12 795 BA.writeByteArray marr (base + 00) (GHC.Word.W# x0) 796 BA.writeByteArray marr (base + 01) (GHC.Word.W# x1) 797 BA.writeByteArray marr (base + 02) (GHC.Word.W# x2) 798 BA.writeByteArray marr (base + 03) (GHC.Word.W# x3) 799 BA.writeByteArray marr (base + 04) (GHC.Word.W# y0) 800 BA.writeByteArray marr (base + 05) (GHC.Word.W# y1) 801 BA.writeByteArray marr (base + 06) (GHC.Word.W# y2) 802 BA.writeByteArray marr (base + 07) (GHC.Word.W# y3) 803 BA.writeByteArray marr (base + 08) (GHC.Word.W# z0) 804 BA.writeByteArray marr (base + 09) (GHC.Word.W# z1) 805 BA.writeByteArray marr (base + 10) (GHC.Word.W# z2) 806 BA.writeByteArray marr (base + 11) (GHC.Word.W# z3) 807 808 -- loop over windows 809 loop_w :: MutableByteArray s -> Projective -> Int -> ST s () 810 loop_w !marr !p !w 811 | w == ws = pure () 812 | otherwise = do 813 nb <- loop_j marr p p (w * capJ) 0 814 let np = double nb 815 loop_w marr np (succ w) 816 817 -- loop within windows 818 loop_j 819 :: MutableByteArray s 820 -> Projective 821 -> Projective 822 -> Int 823 -> Int 824 -> ST s Projective 825 loop_j !marr !p !b !idx !j = do 826 write marr idx b 827 if j == capJ - 1 828 then pure b 829 else do 830 let !nb = add b p 831 loop_j marr p nb (succ idx) (succ j) 832 833 -- Timing-safe wNAF (w-ary non-adjacent form) scalar multiplication of 834 -- secp256k1 points. 835 mul_wnaf :: Context -> Wider -> Maybe Projective 836 mul_wnaf Context {..} (Wider s) = case mul_wnaf# ctxArray ctxW s of 837 (# () | #) -> Nothing 838 (# | (# px, py, pz #) #) -> Just $! P px py pz 839 {-# INLINABLE mul_wnaf #-} 840 841 -- | Derive a public key (i.e., a secp256k1 point) from the provided 842 -- secret. 843 -- 844 -- >>> import qualified System.Entropy as E 845 -- >>> sk <- fmap parse_int256 (E.getEntropy 32) 846 -- >>> derive_pub sk 847 -- Just "<secp256k1 point>" 848 derive_pub :: Wider -> Maybe Pub 849 derive_pub = mul _CURVE_G 850 {-# NOINLINE derive_pub #-} 851 852 -- | The same as 'derive_pub', except uses a 'Context' to optimise 853 -- internal calculations. 854 -- 855 -- >>> import qualified System.Entropy as E 856 -- >>> sk <- fmap parse_int256 (E.getEntropy 32) 857 -- >>> let !tex = precompute 858 -- >>> derive_pub' tex sk 859 -- Just "<secp256k1 point>" 860 derive_pub' :: Context -> Wider -> Maybe Pub 861 derive_pub' = mul_wnaf 862 {-# NOINLINE derive_pub' #-} 863 864 -- parsing -------------------------------------------------------------------- 865 866 -- | Parse a 'Wider', /e.g./ a Schnorr or ECDSA secret key. 867 -- 868 -- >>> import qualified Data.ByteString as BS 869 -- >>> parse_int256 (BS.replicate 32 0xFF) 870 -- Just <2^256 - 1> 871 parse_int256 :: BS.ByteString -> Maybe Wider 872 parse_int256 bs = do 873 guard (BS.length bs == 32) 874 pure $! unsafe_roll32 bs 875 {-# INLINABLE parse_int256 #-} 876 877 -- | Parse compressed secp256k1 point (33 bytes), uncompressed point (65 878 -- bytes), or BIP0340-style point (32 bytes). 879 -- 880 -- >>> parse_point <33-byte compressed point> 881 -- Just <Pub> 882 -- >>> parse_point <65-byte uncompressed point> 883 -- Just <Pub> 884 -- >>> parse_point <32-byte bip0340 public key> 885 -- Just <Pub> 886 -- >>> parse_point <anything else> 887 -- Nothing 888 parse_point :: BS.ByteString -> Maybe Projective 889 parse_point bs 890 | len == 32 = _parse_bip0340 bs 891 | len == 33 = _parse_compressed h t 892 | len == 65 = _parse_uncompressed h t 893 | otherwise = Nothing 894 where 895 len = BS.length bs 896 h = BU.unsafeIndex bs 0 -- lazy 897 t = BS.drop 1 bs 898 899 -- input is guaranteed to be 32B in length 900 _parse_bip0340 :: BS.ByteString -> Maybe Projective 901 _parse_bip0340 = fmap projective . lift_vartime . C.to . unsafe_roll32 902 903 -- bytestring input is guaranteed to be 32B in length 904 _parse_compressed :: Word8 -> BS.ByteString -> Maybe Projective 905 _parse_compressed h (unsafe_roll32 -> x) 906 | h /= 0x02 && h /= 0x03 = Nothing 907 | not (fe x) = Nothing 908 | otherwise = do 909 let !mx = C.to x 910 !my <- C.sqrt_vartime (weierstrass mx) 911 let !yodd = CT.decide (W.odd (C.retr my)) 912 !hodd = B.testBit h 0 913 pure $! 914 if hodd /= yodd 915 then Projective mx (negate my) 1 916 else Projective mx my 1 917 918 -- bytestring input is guaranteed to be 64B in length 919 _parse_uncompressed :: Word8 -> BS.ByteString -> Maybe Projective 920 _parse_uncompressed h bs = do 921 let (unsafe_roll32 -> x, unsafe_roll32 -> y) = BS.splitAt _CURVE_Q_BYTES bs 922 guard (h == 0x04) 923 let !p = Projective (C.to x) (C.to y) 1 924 guard (valid p) 925 pure $! p 926 927 -- | Parse an ECDSA signature encoded in 64-byte "compact" form. 928 -- 929 -- >>> parse_sig <64-byte compact signature> 930 -- Just "<ecdsa signature>" 931 parse_sig :: BS.ByteString -> Maybe ECDSA 932 parse_sig bs = do 933 guard (BS.length bs == 64) 934 let (r0, s0) = BS.splitAt 32 bs 935 r <- roll32 r0 936 s <- roll32 s0 937 pure $! ECDSA r s 938 939 -- serializing ---------------------------------------------------------------- 940 941 -- | Serialize a secp256k1 point in 33-byte compressed form. 942 -- 943 -- >>> serialize_point pub 944 -- "<33-byte compressed point>" 945 serialize_point :: Projective -> BS.ByteString 946 serialize_point (affine -> Affine (C.from -> x) (C.from -> y)) = 947 let !(Wider (# Limb w, _, _, _ #)) = y 948 !b | B.testBit (GHC.Word.W# w) 0 = 0x03 949 | otherwise = 0x02 950 in BS.cons b (unroll32 x) 951 952 -- ecdh ----------------------------------------------------------------------- 953 954 -- SEC1-v2 3.3.1, plus SHA256 hash 955 956 -- | Compute a shared secret, given a secret key and public secp256k1 point, 957 -- via Elliptic Curve Diffie-Hellman (ECDH). 958 -- 959 -- The shared secret is the SHA256 hash of the x-coordinate of the 960 -- point obtained by scalar multiplication. 961 -- 962 -- >>> let sec_alice = 0x03 963 -- >>> let sec_bob = 2 ^ 128 - 1 964 -- >>> let Just pub_alice = derive_pub sec_alice 965 -- >>> let Just pub_bob = derive_pub sec_bob 966 -- >>> let secret_as_computed_by_alice = ecdh pub_bob sec_alice 967 -- >>> let secret_as_computed_by_bob = ecdh pub_alice sec_bob 968 -- >>> secret_as_computed_by_alice == secret_as_computed_by_bob 969 -- True 970 ecdh 971 :: Projective -- ^ public key 972 -> Wider -- ^ secret key 973 -> Maybe BS.ByteString -- ^ shared secret 974 ecdh pub _SECRET = do 975 pt@(P _ _ (C.Montgomery -> z)) <- mul pub _SECRET 976 let !(Affine (C.retr -> x) _) = affine pt 977 !result = SHA256.hash (unroll32 x) 978 if CT.decide (C.eq z 0) then Nothing else Just result 979 980 -- schnorr -------------------------------------------------------------------- 981 -- see https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki 982 983 -- | Create a 64-byte Schnorr signature for the provided message, using 984 -- the provided secret key. 985 -- 986 -- BIP0340 recommends that 32 bytes of fresh auxiliary entropy be 987 -- generated and added at signing time as additional protection 988 -- against side-channel attacks (namely, to thwart so-called "fault 989 -- injection" attacks). This entropy is /supplemental/ to security, 990 -- and the cryptographic security of the signature scheme itself does 991 -- not rely on it, so it is not strictly required; 32 zero bytes can 992 -- be used in its stead (and can be supplied via 'mempty'). 993 -- 994 -- >>> import qualified System.Entropy as E 995 -- >>> aux <- E.getEntropy 32 996 -- >>> sign_schnorr sec msg aux 997 -- Just "<64-byte schnorr signature>" 998 sign_schnorr 999 :: Wider -- ^ secret key 1000 -> BS.ByteString -- ^ message 1001 -> BS.ByteString -- ^ 32 bytes of auxilliary random data 1002 -> Maybe BS.ByteString -- ^ 64-byte Schnorr signature 1003 sign_schnorr = _sign_schnorr (mul _CURVE_G) 1004 1005 -- | The same as 'sign_schnorr', except uses a 'Context' to optimise 1006 -- internal calculations. 1007 -- 1008 -- You can expect about a 2x performance increase when using this 1009 -- function, compared to 'sign_schnorr'. 1010 -- 1011 -- >>> import qualified System.Entropy as E 1012 -- >>> aux <- E.getEntropy 32 1013 -- >>> let !tex = precompute 1014 -- >>> sign_schnorr' tex sec msg aux 1015 -- Just "<64-byte schnorr signature>" 1016 sign_schnorr' 1017 :: Context -- ^ secp256k1 context 1018 -> Wider -- ^ secret key 1019 -> BS.ByteString -- ^ message 1020 -> BS.ByteString -- ^ 32 bytes of auxilliary random data 1021 -> Maybe BS.ByteString -- ^ 64-byte Schnorr signature 1022 sign_schnorr' tex = _sign_schnorr (mul_wnaf tex) 1023 1024 _sign_schnorr 1025 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1026 -> Wider -- secret key 1027 -> BS.ByteString -- message 1028 -> BS.ByteString -- 32 bytes of auxilliary random data 1029 -> Maybe BS.ByteString 1030 _sign_schnorr _mul _SECRET m a = do 1031 p <- _mul _SECRET 1032 let Affine (C.retr -> x_p) (C.retr -> y_p) = affine p 1033 s = S.to _SECRET 1034 d = S.select s (negate s) (W.odd y_p) 1035 bytes_d = unroll32 (S.retr d) 1036 bytes_p = unroll32 x_p 1037 t = xor bytes_d (hash_aux a) 1038 rand = hash_nonce (t <> bytes_p <> m) 1039 k' = S.to (unsafe_roll32 rand) 1040 guard (not (S.eq_vartime k' 0)) -- negligible probability 1041 pt <- _mul (S.retr k') 1042 let Affine (C.retr -> x_r) (C.retr -> y_r) = affine pt 1043 k = S.select k' (negate k') (W.odd y_r) 1044 bytes_r = unroll32 x_r 1045 rand' = hash_challenge (bytes_r <> bytes_p <> m) 1046 e = S.to (unsafe_roll32 rand') 1047 bytes_ked = unroll32 (S.retr (k + e * d)) 1048 sig = bytes_r <> bytes_ked 1049 -- NB for benchmarking we morally want to remove the precautionary 1050 -- verification check here. 1051 -- 1052 -- guard (verify_schnorr m p sig) 1053 pure $! sig 1054 {-# INLINE _sign_schnorr #-} 1055 1056 -- | Verify a 64-byte Schnorr signature for the provided message with 1057 -- the supplied public key. 1058 -- 1059 -- >>> verify_schnorr msg pub <valid signature> 1060 -- True 1061 -- >>> verify_schnorr msg pub <invalid signature> 1062 -- False 1063 verify_schnorr 1064 :: BS.ByteString -- ^ message 1065 -> Pub -- ^ public key 1066 -> BS.ByteString -- ^ 64-byte Schnorr signature 1067 -> Bool 1068 verify_schnorr = _verify_schnorr (mul_vartime _CURVE_G) 1069 1070 -- | The same as 'verify_schnorr', except uses a 'Context' to optimise 1071 -- internal calculations. 1072 -- 1073 -- You can expect about a 1.5x performance increase when using this 1074 -- function, compared to 'verify_schnorr'. 1075 -- 1076 -- >>> let !tex = precompute 1077 -- >>> verify_schnorr' tex msg pub <valid signature> 1078 -- True 1079 -- >>> verify_schnorr' tex msg pub <invalid signature> 1080 -- False 1081 verify_schnorr' 1082 :: Context -- ^ secp256k1 context 1083 -> BS.ByteString -- ^ message 1084 -> Pub -- ^ public key 1085 -> BS.ByteString -- ^ 64-byte Schnorr signature 1086 -> Bool 1087 verify_schnorr' tex = _verify_schnorr (mul_wnaf tex) 1088 1089 _verify_schnorr 1090 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1091 -> BS.ByteString 1092 -> Pub 1093 -> BS.ByteString 1094 -> Bool 1095 _verify_schnorr _mul m p sig 1096 | BS.length sig /= 64 = False 1097 | otherwise = M.isJust $ do 1098 let capP = even_y_vartime p 1099 (unsafe_roll32 -> r, unsafe_roll32 -> s) = BS.splitAt 32 sig 1100 guard (fe r && ge s) 1101 let Affine (C.retr -> x_P) _ = affine capP 1102 e = modQ . unsafe_roll32 $ 1103 hash_challenge (unroll32 r <> unroll32 x_P <> m) 1104 pt0 <- _mul s 1105 pt1 <- mul_vartime capP e 1106 let dif = add pt0 (neg pt1) 1107 guard (dif /= _CURVE_ZERO) 1108 let Affine (C.from -> x_R) (C.from -> y_R) = affine dif 1109 guard $ not (CT.decide (W.odd y_R) || not (W.eq_vartime x_R r)) 1110 {-# INLINE _verify_schnorr #-} 1111 1112 -- hardcoded tag of BIP0340/aux 1113 -- 1114 -- \x -> let h = SHA256.hash "BIP0340/aux" 1115 -- in SHA256.hash (h <> h <> x) 1116 hash_aux :: BS.ByteString -> BS.ByteString 1117 hash_aux x = SHA256.hash $ 1118 "\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 1119 {-# INLINE hash_aux #-} 1120 1121 -- hardcoded tag of BIP0340/nonce 1122 hash_nonce :: BS.ByteString -> BS.ByteString 1123 hash_nonce x = SHA256.hash $ 1124 "\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 1125 {-# INLINE hash_nonce #-} 1126 1127 -- hardcoded tag of BIP0340/challenge 1128 hash_challenge :: BS.ByteString -> BS.ByteString 1129 hash_challenge x = SHA256.hash $ 1130 "{\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 1131 {-# INLINE hash_challenge #-} 1132 1133 -- ecdsa ---------------------------------------------------------------------- 1134 -- see https://www.rfc-editor.org/rfc/rfc6979, https://secg.org/sec1-v2.pdf 1135 1136 -- RFC6979 2.3.2 1137 bits2int :: BS.ByteString -> Wider 1138 bits2int = unsafe_roll32 1139 {-# INLINABLE bits2int #-} 1140 1141 -- RFC6979 2.3.3 1142 int2octets :: Wider -> BS.ByteString 1143 int2octets = unroll32 1144 {-# INLINABLE int2octets #-} 1145 1146 -- RFC6979 2.3.4 1147 bits2octets :: BS.ByteString -> BS.ByteString 1148 bits2octets bs = 1149 let z1 = bits2int bs 1150 z2 = modQ z1 1151 in int2octets z2 1152 1153 -- | An ECDSA signature. 1154 data ECDSA = ECDSA { 1155 ecdsa_r :: !Wider 1156 , ecdsa_s :: !Wider 1157 } 1158 deriving (Generic) 1159 1160 instance Show ECDSA where 1161 show _ = "<ecdsa signature>" 1162 1163 -- ECDSA signature type. 1164 data SigType = 1165 LowS 1166 | Unrestricted 1167 deriving Show 1168 1169 -- Indicates whether to hash the message or assume it has already been 1170 -- hashed. 1171 data HashFlag = 1172 Hash 1173 | NoHash 1174 deriving Show 1175 1176 -- Convert an ECDSA signature to low-S form. 1177 low :: ECDSA -> ECDSA 1178 low (ECDSA r s) = ECDSA r (W.select s (_CURVE_Q - s) (W.gt s _CURVE_QH)) 1179 {-# INLINE low #-} 1180 1181 -- | Produce an ECDSA signature for the provided message, using the 1182 -- provided private key. 1183 -- 1184 -- 'sign_ecdsa' produces a "low-s" signature, as is commonly required 1185 -- in applications using secp256k1. If you need a generic ECDSA 1186 -- signature, use 'sign_ecdsa_unrestricted'. 1187 -- 1188 -- >>> sign_ecdsa sec msg 1189 -- Just "<ecdsa signature>" 1190 sign_ecdsa 1191 :: Wider -- ^ secret key 1192 -> BS.ByteString -- ^ message 1193 -> Maybe ECDSA 1194 sign_ecdsa = _sign_ecdsa (mul _CURVE_G) LowS Hash 1195 1196 -- | The same as 'sign_ecdsa', except uses a 'Context' to optimise internal 1197 -- calculations. 1198 -- 1199 -- You can expect about a 10x performance increase when using this 1200 -- function, compared to 'sign_ecdsa'. 1201 -- 1202 -- >>> let !tex = precompute 1203 -- >>> sign_ecdsa' tex sec msg 1204 -- Just "<ecdsa signature>" 1205 sign_ecdsa' 1206 :: Context -- ^ secp256k1 context 1207 -> Wider -- ^ secret key 1208 -> BS.ByteString -- ^ message 1209 -> Maybe ECDSA 1210 sign_ecdsa' tex = _sign_ecdsa (mul_wnaf tex) LowS Hash 1211 1212 -- | Produce an ECDSA signature for the provided message, using the 1213 -- provided private key. 1214 -- 1215 -- 'sign_ecdsa_unrestricted' produces an unrestricted ECDSA signature, 1216 -- which is less common in applications using secp256k1 due to the 1217 -- signature's inherent malleability. If you need a conventional 1218 -- "low-s" signature, use 'sign_ecdsa'. 1219 -- 1220 -- >>> sign_ecdsa_unrestricted sec msg 1221 -- Just "<ecdsa signature>" 1222 sign_ecdsa_unrestricted 1223 :: Wider -- ^ secret key 1224 -> BS.ByteString -- ^ message 1225 -> Maybe ECDSA 1226 sign_ecdsa_unrestricted = _sign_ecdsa (mul _CURVE_G) Unrestricted Hash 1227 1228 -- | The same as 'sign_ecdsa_unrestricted', except uses a 'Context' to 1229 -- optimise internal calculations. 1230 -- 1231 -- You can expect about a 10x performance increase when using this 1232 -- function, compared to 'sign_ecdsa_unrestricted'. 1233 -- 1234 -- >>> let !tex = precompute 1235 -- >>> sign_ecdsa_unrestricted' tex sec msg 1236 -- Just "<ecdsa signature>" 1237 sign_ecdsa_unrestricted' 1238 :: Context -- ^ secp256k1 context 1239 -> Wider -- ^ secret key 1240 -> BS.ByteString -- ^ message 1241 -> Maybe ECDSA 1242 sign_ecdsa_unrestricted' tex = _sign_ecdsa (mul_wnaf tex) Unrestricted Hash 1243 1244 -- Produce a "low-s" ECDSA signature for the provided message, using 1245 -- the provided private key. Assumes that the message has already been 1246 -- pre-hashed. 1247 -- 1248 -- (Useful for testing against noble-secp256k1's suite, in which messages 1249 -- in the test vectors have already been hashed.) 1250 _sign_ecdsa_no_hash 1251 :: Wider -- ^ secret key 1252 -> BS.ByteString -- ^ message digest 1253 -> Maybe ECDSA 1254 _sign_ecdsa_no_hash = _sign_ecdsa (mul _CURVE_G) LowS NoHash 1255 1256 _sign_ecdsa_no_hash' 1257 :: Context 1258 -> Wider 1259 -> BS.ByteString 1260 -> Maybe ECDSA 1261 _sign_ecdsa_no_hash' tex = _sign_ecdsa (mul_wnaf tex) LowS NoHash 1262 1263 _sign_ecdsa 1264 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1265 -> SigType 1266 -> HashFlag 1267 -> Wider 1268 -> BS.ByteString 1269 -> Maybe ECDSA 1270 _sign_ecdsa _mul ty hf _SECRET m = runST $ do 1271 -- RFC6979 sec 3.3a 1272 let entropy = int2octets _SECRET 1273 nonce = bits2octets h 1274 drbg <- DRBG.new entropy nonce mempty 1275 -- RFC6979 sec 2.4 1276 sign_loop drbg 1277 where 1278 d = S.to _SECRET 1279 hm = S.to (bits2int h) 1280 h = case hf of 1281 Hash -> SHA256.hash m 1282 NoHash -> m 1283 1284 sign_loop g = do 1285 k <- gen_k g 1286 let mpair = do 1287 kg <- _mul k 1288 let Affine (S.to . C.retr -> r) _ = affine kg 1289 ki = S.inv (S.to k) 1290 s = (hm + d * r) * ki 1291 pure $! (S.retr r, S.retr s) 1292 case mpair of 1293 Nothing -> do 1294 DRBG.wipe g 1295 pure Nothing 1296 Just (r, s) 1297 | W.eq_vartime r 0 -> sign_loop g -- negligible probability 1298 | otherwise -> do 1299 DRBG.wipe g 1300 let !sig = Just $! ECDSA r s 1301 pure $ case ty of 1302 Unrestricted -> sig 1303 LowS -> fmap low sig 1304 {-# INLINE _sign_ecdsa #-} 1305 1306 -- RFC6979 sec 3.3b 1307 gen_k :: DRBG.DRBG s -> ST s Wider 1308 gen_k g = loop g where 1309 loop drbg = do 1310 bytes <- DRBG.gen drbg mempty (fi _CURVE_Q_BYTES) 1311 case bytes of 1312 Left {} -> error "ppad-secp256k1: internal error (please report a bug!)" 1313 Right bs -> do 1314 let can = bits2int bs 1315 case W.cmp_vartime can _CURVE_Q of 1316 LT -> pure can 1317 _ -> loop drbg -- 2 ^ -128 probability 1318 {-# INLINE gen_k #-} 1319 1320 -- | Verify a "low-s" ECDSA signature for the provided message and 1321 -- public key, 1322 -- 1323 -- Fails to verify otherwise-valid "high-s" signatures. If you need to 1324 -- verify generic ECDSA signatures, use 'verify_ecdsa_unrestricted'. 1325 -- 1326 -- >>> verify_ecdsa msg pub valid_sig 1327 -- True 1328 -- >>> verify_ecdsa msg pub invalid_sig 1329 -- False 1330 verify_ecdsa 1331 :: BS.ByteString -- ^ message 1332 -> Pub -- ^ public key 1333 -> ECDSA -- ^ signature 1334 -> Bool 1335 verify_ecdsa m p sig@(ECDSA _ s) 1336 | CT.decide (W.gt s _CURVE_QH) = False 1337 | otherwise = verify_ecdsa_unrestricted m p sig 1338 1339 -- | The same as 'verify_ecdsa', except uses a 'Context' to optimise 1340 -- internal calculations. 1341 -- 1342 -- You can expect about a 2x performance increase when using this 1343 -- function, compared to 'verify_ecdsa'. 1344 -- 1345 -- >>> let !tex = precompute 1346 -- >>> verify_ecdsa' tex msg pub valid_sig 1347 -- True 1348 -- >>> verify_ecdsa' tex msg pub invalid_sig 1349 -- False 1350 verify_ecdsa' 1351 :: Context -- ^ secp256k1 context 1352 -> BS.ByteString -- ^ message 1353 -> Pub -- ^ public key 1354 -> ECDSA -- ^ signature 1355 -> Bool 1356 verify_ecdsa' tex m p sig@(ECDSA _ s) 1357 | CT.decide (W.gt s _CURVE_QH) = False 1358 | otherwise = verify_ecdsa_unrestricted' tex m p sig 1359 1360 -- | Verify an unrestricted ECDSA signature for the provided message and 1361 -- public key. 1362 -- 1363 -- >>> verify_ecdsa_unrestricted msg pub valid_sig 1364 -- True 1365 -- >>> verify_ecdsa_unrestricted msg pub invalid_sig 1366 -- False 1367 verify_ecdsa_unrestricted 1368 :: BS.ByteString -- ^ message 1369 -> Pub -- ^ public key 1370 -> ECDSA -- ^ signature 1371 -> Bool 1372 verify_ecdsa_unrestricted = _verify_ecdsa_unrestricted (mul_vartime _CURVE_G) 1373 1374 -- | The same as 'verify_ecdsa_unrestricted', except uses a 'Context' to 1375 -- optimise internal calculations. 1376 -- 1377 -- You can expect about a 2x performance increase when using this 1378 -- function, compared to 'verify_ecdsa_unrestricted'. 1379 -- 1380 -- >>> let !tex = precompute 1381 -- >>> verify_ecdsa_unrestricted' tex msg pub valid_sig 1382 -- True 1383 -- >>> verify_ecdsa_unrestricted' tex msg pub invalid_sig 1384 -- False 1385 verify_ecdsa_unrestricted' 1386 :: Context -- ^ secp256k1 context 1387 -> BS.ByteString -- ^ message 1388 -> Pub -- ^ public key 1389 -> ECDSA -- ^ signature 1390 -> Bool 1391 verify_ecdsa_unrestricted' tex = _verify_ecdsa_unrestricted (mul_wnaf tex) 1392 1393 _verify_ecdsa_unrestricted 1394 :: (Wider -> Maybe Projective) -- partially-applied multiplication function 1395 -> BS.ByteString 1396 -> Pub 1397 -> ECDSA 1398 -> Bool 1399 _verify_ecdsa_unrestricted _mul m p (ECDSA r0 s0) = M.isJust $ do 1400 -- SEC1-v2 4.1.4 1401 let h = SHA256.hash m 1402 guard (ge r0 && ge s0) 1403 let r = S.to r0 1404 s = S.to s0 1405 e = S.to (bits2int h) 1406 si = S.inv s 1407 u1 = S.retr (e * si) 1408 u2 = S.retr (r * si) 1409 pt0 <- _mul u1 1410 pt1 <- mul_vartime p u2 1411 let capR = add pt0 pt1 1412 guard (capR /= _CURVE_ZERO) 1413 let Affine (S.to . C.retr -> v) _ = affine capR 1414 guard (S.eq_vartime v r) 1415 {-# INLINE _verify_ecdsa_unrestricted #-} 1416