BN_MOD_MUL_MONTGOMERY(3ossl)

📦 version 3.5.0, in opensuse-leap 16.0

okay so welcome to the BN_MOD_MUL_MONTGOMERY(3ossl) page, bestie 💖 this is the Montgomery multiplication manual, and we're gonna make it make sense.

✨ NAME ✨

BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery — Montgomery multiplication 🎀

🌸 SYNOPSIS 🌸

#include <openssl/bn.h>

BN_MONT_CTX *BN_MONT_CTX_new(void);
void BN_MONT_CTX_free(BN_MONT_CTX *mont);

int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);

int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
                          BN_MONT_CTX *mont, BN_CTX *ctx);

int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
                       BN_CTX *ctx);

int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
                     BN_CTX *ctx);

💅 DESCRIPTION 💅

okay so these functions are the Montgomery multiplication girlies ✨ They get called automatically under the hood when BN_mod_exp(3) is called with suitable input, but they're also useful when you're doing several operations with the same modulus. lowkey iconic.

  • BN_MONT_CTX_new() — allocates and initializes a BN_MONT_CTX structure 🫶
  • BN_MONT_CTX_set() — sets up the mont structure from the modulus m by precomputing its inverse and a value R ✨
  • BN_MONT_CTX_copy() — copies the BN_MONT_CTX from from to to 💖
  • BN_MONT_CTX_free() — frees the components of the BN_MONT_CTX, and, if it was created by BN_MONT_CTX_new(), also the structure itself. If mont is NULL, nothing is done 🎀
  • BN_mod_mul_montgomery() — computes Mont(a,b):=a*b*R^-1 and places the result in r 💅
  • BN_from_montgomery() — performs the Montgomery reduction r = a*R^-1 🌈
  • BN_to_montgomery() — computes Mont(a,R^2), i.e. a*R. Note that a must be nonnegative and smaller than the modulus ⭐

For all functions, ctx is a previously allocated BN_CTX used for temporary variables 🦋

🦋 RETURN VALUES 🦋

  • BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX, and NULL on error 😭
  • BN_MONT_CTX_free() has no return value 💀
  • For the other functions, 1 is returned for success, 0 on error. The error codes can be obtained by ERR_get_error(3) 👑

💀 WARNINGS 💀

bestie please hear me: the inputs must be reduced modulo m, otherwise the result will be outside the expected range 😭 no cap, don't skip this.

🎀 SEE ALSO 🎀

🌈 HISTORY 🌈

BN_MONT_CTX_init() was removed in OpenSSL 1.1.0 🫶

Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (the "License"). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at <https://www.openssl.org/source/license.html>.

mwah 💋 this page is from OpenSSL 3.5.0, dated 2026-09-25, and yes bestie it's BN_MOD_MUL_MONTGOMERY(3ossl) signing off 💅✨

📦 where this page comes from