BN_MOD_MUL_MONTGOMERY(3ossl)

📦
version 15.1 · 2 versions
, in freebsd 15.1

💖 BN_MOD_MUL_MONTGOMERY(3ossl) 💖

okay so bestie, this is BN_MOD_MUL_MONTGOMERY(3ossl), aka the OpenSSL manual page for Montgomery multiplication. it’s giving big math energy, but honestly it’s lowkey iconic once you see what each function does. let’s get into it 💅✨

🌸 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 🦋

These functions implement Montgomery multiplication. They are used automatically when BN_mod_exp(3) is called with suitable input, but they may be useful when several operations are to be performed using the same modulus. literally the “set it up once and keep the vibe going” situation ✨

  • BN_MONT_CTX_new() — allocates and initializes a BN_MONT_CTX structure. new struct, fresh start, main character energy 👑
  • BN_MONT_CTX_set() — sets up the mont structure from the modulus m by precomputing its inverse and a value R. it’s doing the pre-work so future-you can slay faster 💅
  • BN_MONT_CTX_copy() — copies the BN_MONT_CTX from from to to. no cap, it’s a copy-paste but for Montgomery context 🫶
  • 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. cleanup era, we love to see it 🧚
  • BN_mod_mul_montgomery() — computes Mont(a,b):=a*b*R^-1 and places the result in r. that’s the whole Montgomery mul moment 🔥
  • BN_from_montgomery() — performs the Montgomery reduction r = a*R^-1. bringing it back out of Montgomery-land 💫
  • BN_to_montgomery() — computes Mont(a,R^2), i.e. a*R. Note that a must be nonnegative and smaller than the modulus. very important, bestie, do not skip that note 😭

For all functions, ctx is a previously allocated BN_CTX used for temporary variables. it’s the little scratchpad helper for the math vibes 🎀

🌈 RETURN VALUES 🌈

  • BN_MONT_CTX_new() — returns the newly allocated BN_MONT_CTX, and NULL on error. so if you get NULL, that’s the error signal, periodt 💀
  • BN_MONT_CTX_free() — has no return value. it just frees and dips 👋
  • For the other functions, 1 is returned for success, 0 on error. The error codes can be obtained by ERR_get_error(3). success = 1, error = 0, and ERR_get_error(3) is the receipts 🧾✨

👑 WARNINGS 👑

⚠️ okay bestie, real talk: The inputs must be reduced modulo m, otherwise the result will be outside the expected range. that’s the vibe check. do not skip it, fr fr 😭

🍓 SEE ALSO 🍓

go read those too, iykyk 📚💖

🎀 HISTORY 🎀

BN_MONT_CTX_init() was removed in OpenSSL 1.1.0. not me mourning the old function, but she’s gone, bestie 💔

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>.

this page is from OpenSSL 3.5.6, dated 2026-04-07 — shoutout to the version/date combo, and bye bestie, go do iconic Montgomery math 💖✨🦋

📦 where this page comes from