Commit e75c7c45 authored by Niels Möller's avatar Niels Möller

Let "affine" points for curve25519 be Edwards coordinates rather than Montgomery coordinates.

parent 74dea233
2014-09-17 Niels Möller <nisse@lysator.liu.se>
* testsuite/ecdh-test.c (test_main): Update curve25519 test to use
Edwards coordinates.
* testsuite/ecdsa-sign-test.c (test_main): Likewise.
* testsuite/ecdsa-verify-test.c (test_main): Likewise.
* ecc-point.c (ecc_point_set): Use Edwards rather than Montgomery
curve.
* ecc-mul-a-eh.c (ecc_mul_a_eh, table_init): Take an Edwards point
as input, not a Montgomery point. Hence, use ecc_a_to_j, not
ecc_a_to_eh.
* ecc-eh-to-a.c (ecc_eh_to_a): Just convert to affine coordinates,
don't transform from Edwards to Montgomery form. Also reduces
scratch need slightly.
* ecc-internal.h (ECC_EH_TO_A_ITCH): Reduced.
* ecdsa-keygen.c (ecdsa_generate_keypair): Use struct ecc_curve
function pointers.
......
......@@ -41,12 +41,12 @@
mp_size_t
ecc_eh_to_a_itch (const struct ecc_curve *ecc)
{
/* Needs 2*ecc->size + scratch for ecc_modq_inv */
/* Needs ecc->size + scratch for ecc_modq_inv */
return ECC_EH_TO_A_ITCH (ecc->size);
}
/* Convert from homogeneous coordinates on the Edwards curve to affine
coordinates on the corresponding Montgomery curve. */
coordinates. */
void
ecc_eh_to_a (const struct ecc_curve *ecc,
int op,
......@@ -54,41 +54,22 @@ ecc_eh_to_a (const struct ecc_curve *ecc,
mp_limb_t *scratch)
{
#define izp scratch
#define sp (scratch + ecc->size)
#define tp (scratch + 2*ecc->size)
#define tp (scratch + ecc->size)
#define xp r
#define yp (r + ecc->size)
#define up p
#define vp (p + ecc->size)
#define wp (p + 2*ecc->size)
/* x = (1+v)/(1-v), y = t x / u (with t = sqrt(b+2))
In homogeneous coordinates,
X = (W + V) U
Y = t (W + V) W
Z = (W - V) U
*/
/* FIXME: Simplify for common case that only x-coordinate is wanted. */
#define xp p
#define yp (p + ecc->size)
#define zp (p + 2*ecc->size)
mp_limb_t cy;
/* NOTE: For the infinity point, this subtraction gives zero (mod
p), which isn't invertible. For curve25519, the desired output is
x = 0, and we should be fine, since ecc_modp_inv returns 0
in this case. */
ecc_modp_sub (ecc, izp, wp, vp);
ecc_modp_mul (ecc, izp + ecc->size, izp, up);
mpn_copyi (tp, zp, ecc->size);
/* Needs 3*size scratch */
ecc_modp_inv (ecc, izp, izp + ecc->size, izp + 2*ecc->size);
ecc_modp_inv (ecc, izp, tp, tp + ecc->size);
ecc_modp_add (ecc, sp, wp, vp);
ecc_modp_mul (ecc, tp, sp, up);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (xp, tp, ecc->p, ecc->size);
cnd_copy (cy, xp, tp, ecc->size);
ecc_modp_mul (ecc, tp, xp, izp);
cy = mpn_sub_n (r, tp, ecc->p, ecc->size);
cnd_copy (cy, r, tp, ecc->size);
if (op)
{
......@@ -96,26 +77,20 @@ ecc_eh_to_a (const struct ecc_curve *ecc,
if (op > 1)
{
/* Reduce modulo q. FIXME: Hardcoded for curve25519,
duplicates end of ecc_25519_modq. */
duplicates end of ecc_25519_modq. FIXME: Is this needed
at all? Full reduction mod p is maybe sufficient. */
mp_limb_t cy;
unsigned shift;
assert (ecc->bit_size == 255);
shift = 252 - GMP_NUMB_BITS * (ecc->size - 1);
cy = mpn_submul_1 (xp, ecc->q, ecc->size,
xp[ecc->size-1] >> shift);
cy = mpn_submul_1 (r, ecc->q, ecc->size,
r[ecc->size-1] >> shift);
assert (cy < 2);
cnd_add_n (cy, xp, ecc->q, ecc->size);
cnd_add_n (cy, r, ecc->q, ecc->size);
}
return;
}
ecc_modp_add (ecc, sp, wp, vp); /* FIXME: Redundant. Also the (W +
V) Z^-1 multiplication is
redundant. */
ecc_modp_mul (ecc, tp, sp, wp);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, ecc->edwards_root);
mpn_copyi (sp, tp, ecc->size); /* FIXME: Eliminate copy */
ecc_modp_mul (ecc, tp, sp, izp);
cy = mpn_sub_n (yp, tp, ecc->p, ecc->size);
cnd_copy (cy, yp, tp, ecc->size);
ecc_modp_mul (ecc, tp, yp, izp);
cy = mpn_sub_n (r + ecc->size, tp, ecc->p, ecc->size);
cnd_copy (cy, r + ecc->size, tp, ecc->size);
}
......@@ -274,7 +274,7 @@ curve25519_eh_to_x (mp_limb_t *xp, const mp_limb_t *p,
/* Current scratch needs: */
#define ECC_MODINV_ITCH(size) (3*(size))
#define ECC_J_TO_A_ITCH(size) (5*(size))
#define ECC_EH_TO_A_ITCH(size) (5*(size))
#define ECC_EH_TO_A_ITCH(size) (4*(size))
#define ECC_A_TO_EH_ITCH(size) (2*(size))
#define ECC_DUP_JJ_ITCH(size) (5*(size))
#define ECC_DUP_EH_ITCH(size) (5*(size))
......
......@@ -63,7 +63,7 @@ ecc_mul_a_eh (const struct ecc_curve *ecc,
unsigned i;
ecc_a_to_eh (ecc, pe, p, pe + 3*ecc->size);
ecc_a_to_j (ecc, pe, p);
/* x = 0, y = 1, z = 1 */
mpn_zero (r, 3*ecc->size);
......@@ -108,7 +108,7 @@ table_init (const struct ecc_curve *ecc,
mpn_zero (TABLE(0), 3*ecc->size);
TABLE(0)[ecc->size] = TABLE(0)[2*ecc->size] = 1;
ecc_a_to_eh (ecc, TABLE(1), p, scratch);
ecc_a_to_j (ecc, TABLE(1), p);
for (j = 2; j < size; j += 2)
{
......
/* ecc-point.c
Copyright (C) 2013 Niels Möller
Copyright (C) 2013, 2014 Niels Möller
This file is part of GNU Nettle.
......@@ -68,15 +68,22 @@ ecc_point_set (struct ecc_point *p, const mpz_t x, const mpz_t y)
mpz_init (lhs);
mpz_init (rhs);
mpz_mul (lhs, y, y);
if (p->ecc->bit_size == 255)
{
/* curve25519 special case. FIXME: Do in some cleaner way? */
/* Check that y^2 = x^3 + 486662 x^2 + x (mod p)*/
mpz_mul (lhs, x, x); /* Reuse lhs as a temporary */
mpz_add_ui (rhs, x, 486662);
mpz_mul (rhs, rhs, lhs);
mpz_add (rhs, rhs, x);
/* ed25519 special case. FIXME: Do in some cleaner way? */
mpz_t x2;
mpz_init (x2);
mpz_mul (x2, x, x);
mpz_mul (rhs, x2, lhs);
/* Check that -x^2 + y^2 = 1 - (121665/121666) x^2 y^2
or 121666 (1 + x^2 - y^2) = 121665 x^2 y^2 */
mpz_sub (lhs, x2, lhs);
mpz_add_ui (lhs, lhs, 1);
mpz_mul_ui (lhs, lhs, 121666);
mpz_mul_ui (rhs, rhs, 121665);
mpz_clear (x2);
}
else
{
......@@ -87,8 +94,6 @@ ecc_point_set (struct ecc_point *p, const mpz_t x, const mpz_t y)
mpz_add (rhs, rhs, mpz_roinit_n (t, p->ecc->b, size));
}
mpz_mul (lhs, y, y);
res = mpz_congruent_p (lhs, rhs, mpz_roinit_n (t, p->ecc->p, size));
mpz_clear (lhs);
......
......@@ -193,11 +193,11 @@ test_main(void)
also with curve25519. */
test_dh ("curve25519", &nettle_curve25519,
"238301186166219052901200372289459967515481170332211409964804596991365959539",
"16689431791973914300519294566135927090340942991104989847654071982531922134636",
"20308418066388251043787233144732111482161260158474210903552303016733832642783",
"14283836751943535877833976277675258994717521964638468784408792140505262281235",
"43912344711849354965202408139054167824861850336739416536288592824181793690574",
"3795950278952272509684177709511717492358770264218705926196469999516028451559",
"33748673775975978547568270043630771161978032265709185964960751948965332685487",
"45040108202870901856797106334440548809561721639881101469282515918034252408802",
"12684624775789228333626692483521764247362476074160626230698999100180553618972",
"22635121008463339848034566659860493350277619617839914078958064757823336329514");
"9468726108732441384988851273894214794301501512287024874346147472389705411936",
"38072138078045635808869930165213470653418146012939584392304609812494425185763",
"10481077163111981870382976851703705086808805457403127024129174358161599078055",
"29260211489972704256554624312266763530759418996739976957020673870747051409679");
}
......@@ -166,8 +166,8 @@ test_main (void)
"e62e1706f54037ff 8486e26153b0fa79", /* k */
SHEX("e99df2a098c3c590 ea1e1db6d9547339"
"ae760d5331496119 5d967fd881e3b0f5"), /* h */
" 62cbc248a549765 3641d1cbedda2733"
"a7357821dca43727 d8081448d608030d", /* r */
" 14726f472f44f84 63fe82c2712231cd"
"937f2aecdcfe9c39 e2ab0d68c390ccf4"); /* s */
" 515c3a485f57432 0daf3353a0d08110"
"64157c556296de09 4132f74865961b37", /* r */
" 9ddd3e2fa87328c 372e28ac7a1c0c65"
"697196d643238fd0 c4caa4d1d88a62fe"); /* s */
}
......@@ -148,14 +148,14 @@ test_main (void)
test_ecdsa (&nettle_curve25519,
/* Public key corresponding to the key in ecdsa-sign-test */
" eb07d9c7931d614 2669124e12273e1f"
"b9f9555f52bed369 a71cdac173da0ceb", /* x */
"2e726b0b1ff3abc4 d50798ebc246399e"
"365777c0900a0d5b 425f819278d4281d", /* y */
"59f8f317fd5f4e82 c02f8d4dec665fe1"
"230f83b8572638e1 b2ac34a30028e24d", /* x */
"1902a72dc1a6525a 811b9c1845978d56"
"fd97dce5e278ebdd ec695349d7e41498", /* y */
SHEX("e99df2a098c3c590 ea1e1db6d9547339"
"ae760d5331496119 5d967fd881e3b0f5"), /* h */
" 62cbc248a549765 3641d1cbedda2733"
"a7357821dca43727 d8081448d608030d", /* r */
" 14726f472f44f84 63fe82c2712231cd"
"937f2aecdcfe9c39 e2ab0d68c390ccf4"); /* s */
" 515c3a485f57432 0daf3353a0d08110"
"64157c556296de09 4132f74865961b37", /* r */
" 9ddd3e2fa87328c 372e28ac7a1c0c65"
"697196d643238fd0 c4caa4d1d88a62fe"); /* s */
}
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