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[crypto] Use Montgomery reduction for modular exponentiation

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Speed up modular exponentiation by using Montgomery reduction rather
than direct modular reduction.

Montgomery reduction in base 2^n requires the modulus to be coprime to
2^n, which would limit us to requiring that the modulus is an odd
number.  Extend the implementation to include support for
exponentiation with even moduli via Garner's algorithm as described in
"Montgomery reduction with even modulus" (Koç, 1994).

Since almost all use cases for modular exponentation require a large
prime (and hence odd) modulus, the support for even moduli could
potentially be removed in future.

Signed-off-by: Michael Brown <mcb30@ipxe.org>
This commit is contained in:
Michael Brown
2024-11-25 15:59:22 +00:00
parent 4f7dd7fbba
commit 83ac98ce22
5 changed files with 164 additions and 29 deletions
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src/crypto/rsa.c
+1 -2
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@@ -109,8 +109,7 @@ static int rsa_alloc ( struct rsa_context *context, size_t modulus_len,
unsigned int size = bigint_required_size ( modulus_len );
unsigned int exponent_size = bigint_required_size ( exponent_len );
bigint_t ( size ) *modulus;
bigint_t ( exponent_size ) *exponent;
size_t tmp_len = bigint_mod_exp_tmp_len ( modulus, exponent );
size_t tmp_len = bigint_mod_exp_tmp_len ( modulus );
struct {
bigint_t ( size ) modulus;
bigint_t ( exponent_size ) exponent;