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clean up in-comment Sage code (refer to secp256k1_params.sage, update to Python3) #1340

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Jul 10, 2023
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clean up in-comment Sage code (refer to secp256k1_params.sage, update to Python3) #1340

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21 changes: 4 additions & 17 deletions src/ecdsa_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -16,17 +16,8 @@
#include "ecdsa.h"

/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
* sage: for t in xrange(1023, -1, -1):
* .. p = 2**256 - 2**32 - t
* .. if p.is_prime():
* .. print '%x'%p
* .. break
* 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
* 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
* $ sage -c 'load("secp256k1_params.sage"); print(hex(N))'
* 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
*/
static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
Expand All @@ -35,12 +26,8 @@ static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST

/** Difference between field and order, values 'p' and 'n' values defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
* sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
* '14551231950b75fc4402da1722fc9baee'
* $ sage -c 'load("secp256k1_params.sage"); print(hex(P-N))'
* 0x14551231950b75fc4402da1722fc9baee
*/
static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
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17 changes: 5 additions & 12 deletions src/tests.c
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Expand Up @@ -4009,22 +4009,15 @@ static void test_add_neg_y_diff_x(void) {
* which this test is a regression test for.
*
* These points were generated in sage as
* # secp256k1 params
* F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
* C = EllipticCurve ([F (0), F (7)])
* G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
* N = FiniteField(G.order())
*
* # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
* x = polygen(N)
* lam = (1 - x^3).roots()[1][0]
* load("secp256k1_params.sage")
*
* # random "bad pair"
* P = C.random_element()
* Q = -int(lam) * P
* print " P: %x %x" % P.xy()
* print " Q: %x %x" % Q.xy()
* print "P + Q: %x %x" % (P + Q).xy()
* Q = -int(LAMBDA) * P
* print(" P: %x %x" % P.xy())
* print(" Q: %x %x" % Q.xy())
* print("P + Q: %x %x" % (P + Q).xy())
*/
secp256k1_gej aj = SECP256K1_GEJ_CONST(
0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
Expand Down