BN_MOD_EXP_MONT(3SSL)

📦
version 4.0.3 · 13 versions
, in ubuntu stonking

💖 BN_MOD_EXP_MONT 💖

okay bestie, so this is a page from the OpenSSL manual set (that's the 3SSL collection, iykyk) and it's all about Montgomery exponentiation ✨ like, the math girlies know.

✨ NAME ✨

BN_mod_exp_mont, BN_mod_exp_mont_consttime, BN_mod_exp_mont_consttime_x2 — Montgomery exponentiation 🎀

🌸 SYNOPSIS 🌸

#include <openssl/bn.h>

int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);

int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                              const BIGNUM *m, BN_CTX *ctx,
                              BN_MONT_CTX *in_mont);

int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1,
                                 const BIGNUM *p1, const BIGNUM *m1,
                                 BN_MONT_CTX *in_mont1, BIGNUM *rr2,
                                 const BIGNUM *a2, const BIGNUM *p2,
                                 const BIGNUM *m2, BN_MONT_CTX *in_mont2,
                                 BN_CTX *ctx);

🦋 DESCRIPTION 🦋

<pink>BN_mod_exp_mont()</pink> — the classic 💅

so this one computes a to the p-th power, modulo m — literally "rr=a^p % m" — using Montgomery multiplication. ✨

in_mont is a Montgomery context and it can be NULL. if in_mont is NULL, it gets initialized right there inside the function — so if you already have one ready to go, hand it over and you get to save time on initialization. queen behavior, honestly. 👑

<pink>BN_mod_exp_mont_consttime()</pink> — the secret-keeper 🕵️♀️

this one also computes a to the p-th power modulo m — "rr=a^p % m" — using Montgomery multiplication too. it's a variant of BN_mod_exp_mont(3) that uses fixed windows plus a special precomputation memory layout to limit data-dependency to a minimum, and the whole point of that is to protect secret exponents. 🔐

and here's the iconic part: it gets called automatically when BN_mod_exp_mont(3) is called with parameters a, p, m where any of them has the BN_FLG_CONSTTIME flag. it just shows up. no invitation needed. main character energy fr fr. 💅

<pink>BN_mod_exp_mont_consttime_x2()</pink> — the double feature 👯♀️

this one does two independent exponentiations at once:

  • a1 to the p1-th power modulo m1 ("rr1=a1^p1 % m1") 🍓
  • a2 to the p2-th power modulo m2 ("rr2=a2^p2 % m2") 🍓

both via Montgomery multiplication. for some fixed and equal modulus sizes m1 and m2, it uses optimizations that let it speed up two exponentiations. 🌈

but bestie, in all other cases, this function just reduces to two calls of BN_mod_exp_mont_consttime(3). so it's either the fancy optimized route or the "we move" route. no in-between. 😌

👑 RETURN VALUES 👑

for all of these functions: 1 means success, 0 means error. and the error codes? get them with ERR_get_error(3). periodt. ✨

🌟 SEE ALSO 🌟

Copyright 2000-2021 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>.

and that's the whole page, bestie — no cap, you now know Montgomery exponentiation better than half the internet. 🫶

💌 this has been version 4.0.3, dated 2026-09-29, from the BN_MOD_EXP_MONT(3SSL) page. go slay some modular arithmetic. 🎀💖✨
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