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rsa: clarify CRT computation

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Signed-off-by: Manuel Pégourié-Gonnard <manuel.pegourie-gonnard@arm.com>
This commit is contained in:
Manuel Pégourié-Gonnard
2025-12-09 09:26:20 +01:00
parent ec5bc19996
commit d251d73d06
1 changed files with 11 additions and 13 deletions
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24
library/rsa.c
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@@ -1271,28 +1271,26 @@ cleanup:
/*
* Compute T such that T = TP mod P and T = TQ mod Q.
* (This is the Chinese Remainder Theorem - CRT.)
*
* WARNING: uses TP as a temporary, so its value is lost!
*/
static int rsa_apply_crt(mbedtls_mpi *T,
mbedtls_mpi *TP,
const mbedtls_mpi *TP,
const mbedtls_mpi *TQ,
const mbedtls_rsa_context *ctx)
{
int ret;
/*
* T = (TP - TQ) * (Q^-1 mod P) mod P
* Set T = ((TP - TQ) * (Q^-1 mod P) mod P) * Q + TQ
*
* That way we have both:
* mod P: T = (TP - TQ) * (Q^-1 * Q) + TQ = (TP - TQ) * 1 + TQ = TP
* mod Q: T = (...) * Q + TQ = TQ
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(T, TP, TQ));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(TP, T, &ctx->QP));
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(T, TP, &ctx->P));
/*
* T = TQ + T * Q
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(TP, T, &ctx->Q));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(T, TQ, TP));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(T, TP, TQ)); // T = TP - TQ
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(T, T, &ctx->QP)); // T *= Q^-1 mod P
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(T, T, &ctx->P)); // T %= P
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(T, T, &ctx->Q)); // T *= Q
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(T, T, TQ)); // T += TQ
cleanup:
return ret;