BN_MOD_MUL_MONTGOMERY(3)

📦 version 4.4.0, in alpine 3.24, arch rolling

💅 BN_MOD_MUL_MONTGOMERY(3) 💅

okay so bestie, this is the libcrypto manual page for BN_MOD_MUL_MONTGOMERY(3) — it's literally giving Montgomery multiplication and it's kind of iconic. Let's go ✨

🌸 NAME 🌸

BN_MONT_CTX_new, BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_set_locked, BN_MONT_CTX_copy, BN_mod_mul_montgomery, BN_from_montgomery, BN_to_montgomery — Montgomery multiplication 💖

✨ SYNOPSIS ✨

library “libcrypto” #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_set_locked(BN_MONT_CTX **pmont, int lock, const BIGNUM *m,
    BN_CTX *ctx);

BN_MONT_CTX *
BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from);

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

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

int
BN_to_montgomery(BIGNUM *r, const 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. Slay, reusable setup 💅

BN_MONT_CTX_new() allocates and initializes a BN_MONT_CTX structure. Fresh context, who dis ✨

BN_MONT_CTX_set() sets up the mont structure from the modulus m by precomputing its inverse and a value R. Lowkey doing the prep work so future math can eat 🍓

BN_MONT_CTX_set_locked() is a wrapper around BN_MONT_CTX_new() and BN_MONT_CTX_set() that is useful if more than one thread intends to use the same BN_MONT_CTX and none of these threads is exclusively responsible for creating and initializing the context. BN_MONT_CTX_set_locked() first acquires the specified lock using CRYPTO_lock(3). If *pmont already differs from NULL, no action occurs. Otherwise, a new BN_MONT_CTX is allocated with BN_MONT_CTX_new(), set up with BN_MONT_CTX_set(), and a pointer to it is stored in *pmont. Finally, the lock is released. Thread-safe bestie behavior, fr fr 🫶

BN_MONT_CTX_copy() copies the BN_MONT_CTX from from to to. Dupe it, but make it cute 🎀

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 a NULL pointer, no action occurs. Clean up after yourself, icon behavior 🧚

BN_mod_mul_montgomery() computes

Mont(a, b) := a * b * R^-1

and places the result in r. Math but make it Montgomery 💜

BN_from_montgomery() performs the Montgomery reduction

r = a * R^-1

BN_to_montgomery() computes

Mont(a, R^2) = a * R

Note that a must be non-negative and smaller than the modulus. Important vibe check, no cap 👑

For all functions, ctx is a previously allocated BN_CTX used for temporary variables. It's the little scratchpad bestie 🦋

⚠️ Warning: The inputs must be reduced modulo m, otherwise the result will be outside the expected range. Do not skip the reduction, babe — it's giving chaos otherwise 😭

🫶 RETURN VALUES 🫶

BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX or NULL on error. New context or nope, that's the energy 💫

BN_MONT_CTX_set_locked() returns a pointer to the existing or newly created context or NULL on error. Either way, it's handing you a pointer, periodt 💅

For the other functions, 1 is returned for success or 0 on error. The error codes can be obtained by ERR_get_error(3). Success is 1, error is 0, and the receipts live in ERR_get_error(3) 🔥

👀 SEE ALSO 👀

🕰️ HISTORY 🕰️

BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(), BN_mod_mul_montgomery(), BN_from_montgomery(), and BN_to_montgomery() first appeared in SSLeay 0.6.1 and have been available since OpenBSD 2.4. Vintage but still serving 👑

BN_MONT_CTX_copy() first appeared in SSLeay 0.9.1 and has been available since OpenBSD 2.6. Copy era began, and honestly? Iconic 🌈

BN_MONT_CTX_set_locked() first appeared in OpenSSL 0.9.8 and has been available since OpenBSD 4.0. Locked and loaded, literally ⭐

This page is from Debian, dated June 8, 2025, and it's the BN_MOD_MUL_MONTGOMERY(3) manual page. Byeee bestie, go do safe Montgomery math 💋✨

📦 where this page comes from