From 10168903cc4b27e9221a0ce4a015f06a467d61f5 Mon Sep 17 00:00:00 2001 From: makejian Date: Wed, 6 Sep 2023 20:32:53 +0800 Subject: [PATCH] crypto/bn: add method to calculate inv mod and gcd Signed-off-by: makejian --- crypto/bn.c | 194 +++++++++++++++++++++++++++++++++++++++++++- include/crypto/bn.h | 12 +++ 2 files changed, 204 insertions(+), 2 deletions(-) diff --git a/crypto/bn.c b/crypto/bn.c index 8b9db2a40d..235a2f9f17 100644 --- a/crypto/bn.c +++ b/crypto/bn.c @@ -514,7 +514,9 @@ void bignum_div(FAR struct bn *a, FAR struct bn *b, FAR struct bn *c) while (!bignum_is_zero(¤t)) /* while (current != 0) */ { - if (bignum_cmp_abs(&tmp, &denom) != SMALLER) /* if (dividend >= denom) */ + /* if (dividend >= denom) */ + + if (bignum_cmp_abs(&tmp, &denom) != SMALLER) { bignum_sub_abs(&tmp, &denom, &tmp); /* dividend -= denom; */ bignum_or(c, ¤t, c); /* answer |= current; */ @@ -872,7 +874,9 @@ void pow_mod_faster(FAR struct bn *a, FAR struct bn *b, while (1) { - if (tmpb.array[0] & 1) /* if (b % 2) */ + /* if (b % 2) */ + + if (tmpb.array[0] & 1) { bignum_mul(res, &tmpa, &tmp); /* r = r * a % m */ bignum_mod(&tmp, n, res); @@ -890,3 +894,189 @@ void pow_mod_faster(FAR struct bn *a, FAR struct bn *b, bignum_mod(&tmp, n, &tmpa); } } + +int bignum_lsb(FAR struct bn *a) +{ + int i; + int j; + int count; + + require(a, "n is null"); + + for (i = 0, count = 0; i < BN_ARRAY_SIZE; i++) + { + for (j = 0; j < WORD_SIZE * 8; j++, count++) + { + if (((a->array[i] >> j) & 1) != 0) + { + return count; + } + } + } + + return 0; +} + +void bignum_gcd(FAR struct bn *a, FAR struct bn *b, FAR struct bn *g) +{ + size_t lz; + size_t lzt; + struct bn ta; + struct bn tb; + + require(a, "a is null"); + require(b, "b is null"); + require(g, "g is null"); + + bignum_init(&ta); + bignum_init(&tb); + + bignum_assign(&ta, a); + bignum_assign(&tb, b); + + lz = bignum_lsb(&ta); + lzt = bignum_lsb(&tb); + + if (lzt == 0 && (tb.array[0] & 1) == 0) + { + bignum_assign(g, a); + return; + } + + if (lzt < lz) + { + lz = lzt; + } + + ta.s = tb.s = 1; + + while (bignum_is_zero(&ta) != 1) + { + bignum_rshift(&ta, &ta, bignum_lsb(&ta)); + bignum_rshift(&tb, &tb, bignum_lsb(&tb)); + + if (bignum_cmp(&ta, &tb) >= 0) + { + bignum_sub(&ta, &tb, &ta); + bignum_rshift(&ta, &ta, 1); + } + else + { + bignum_sub(&tb, &ta, &tb); + bignum_rshift(&tb, &tb, 1); + } + } + + bignum_lshift(&tb, &tb, lz); + bignum_assign(g, &tb); +} + +int bignum_inv_mod(FAR struct bn *a, FAR struct bn *n, FAR struct bn *c) +{ + struct bn g; + struct bn ta; + struct bn tu; + struct bn u1; + struct bn u2; + struct bn tb; + struct bn tv; + struct bn v1; + struct bn v2; + struct bn num_one; + struct bn num_zero; + + require(a, "a is null"); + require(n, "n is null"); + require(c, "c is null"); + + bignum_init(&g); + bignum_init(&ta); + bignum_init(&tu); + bignum_init(&u1); + bignum_init(&u2); + bignum_init(&tb); + bignum_init(&tv); + bignum_init(&v1); + bignum_init(&v2); + bignum_init(&num_one); + bignum_init(&num_zero); + bignum_from_int(&num_one, 1); + + if (bignum_cmp(n, &num_one) <= 0) + { + return -EINVAL; + } + + bignum_gcd(a, n, &g); + + if (bignum_cmp(&g, &num_one) != 0) + { + return -EFAULT; + } + + bignum_mod(a, n, &ta); + bignum_assign(&tu, &ta); + bignum_assign(&tb, n); + bignum_assign(&tv, n); + bignum_from_int(&u1, 1); + bignum_from_int(&u2, 0); + bignum_from_int(&v1, 0); + bignum_from_int(&v2, 1); + + do + { + while ((tu.array[0] & 1) == 0) + { + bignum_rshift(&tu, &tu, 1); + + if ((u1.array[0] & 1) != 0 || (u2.array[0] & 1) != 0) + { + bignum_add(&u1, &tb, &u1); + bignum_sub(&u2, &ta, &u2); + } + + bignum_rshift(&u1, &u1, 1); + bignum_rshift(&u2, &u2, 1); + } + + while ((tv.array[0] & 1) == 0) + { + bignum_rshift(&tv, &tv, 1); + if ((v1.array[0] & 1) != 0 || (v2.array[0] & 1) != 0) + { + bignum_add(&v1, &tb, &v1); + bignum_sub(&v2, &ta, &v2); + } + + bignum_rshift(&v1, &v1, 1); + bignum_rshift(&v2, &v2, 1); + } + + if (bignum_cmp(&tu, &tv) >= 0) + { + bignum_sub(&tu, &tv, &tu); + bignum_sub(&u1, &v1, &u1); + bignum_sub(&u2, &v2, &u2); + } + else + { + bignum_sub(&tv, &tu, &tv); + bignum_sub(&v1, &u1, &v1); + bignum_sub(&v2, &u2, &v2); + } + } + while (bignum_is_zero(&tu) != 1); + + while (bignum_cmp(&v1, &num_zero) < 0) + { + bignum_add(&v1, n, &v1); + } + + while (bignum_cmp(&v1, n) >= 0) + { + bignum_sub(&v1, n, &v1); + } + + bignum_assign(c, &v1); + return 0; +} diff --git a/include/crypto/bn.h b/include/crypto/bn.h index 91c2b25e78..df39af7119 100644 --- a/include/crypto/bn.h +++ b/include/crypto/bn.h @@ -224,4 +224,16 @@ void bignum_assign(FAR struct bn *dst, FAR struct bn *src); void pow_mod_faster(FAR struct bn *a, FAR struct bn *b, FAR struct bn *n, FAR struct bn *res); +/* Return the number of less significant zero-bits */ + +int bignum_lsb(FAR struct bn *a); + +/* g = gcd(a, b) */ + +void bignum_gcd(FAR struct bn *a, FAR struct bn *b, FAR struct bn *g); + +/* Modular inverse: c = a^-1 mod n */ + +int bignum_inv_mod(FAR struct bn *a, FAR struct bn *n, FAR struct bn *c); + #endif /* __INCLUDE_CRYPTO_BIGNUM_H */