BN_MOD_MUL_MONTGOMERY(3)

BN_MOD_MUL_MONTGOMERY(3) — Montgomery multiplication 💅✨

okay so bestie, this is the Library Functions Manual page for BN_MOD_MUL_MONTGOMERY(3), and it's literally all about Montgomery multiplication. Buckle up, it's giving math but make it cute 🎀

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 🦋

#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. iconic behavior, honestly 💅

• BN_MONT_CTX_new() — allocates and initializes a BN_MONT_CTX structure. fresh context, no cap ✨
• BN_MONT_CTX_set() — sets up the mont structure from the modulus m by precomputing its inverse and a value R. precompute era 🧚
• BN_MONT_CTX_set_locked() — 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. It 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. lock girlie behavior 🔐
• BN_MONT_CTX_copy() — copies the BN_MONT_CTX from to to. yes, that's exactly what it says, bestie 🫶
• 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, clean up 🧹
• BN_mod_mul_montgomery() — computes

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

and places the result in r. math slay 🔥

• 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 lil rule, don't skip it 👑

For all functions, ctx is a previously allocated BN_CTX used for temporary variables. temp storage bestie 🍓

⚠️ Warning: The inputs must be reduced modulo m, otherwise the result will be outside the expected range. no cap, do the reduction first 😭

RETURN VALUES 💙

• BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX or NULL on error.
• BN_MONT_CTX_set_locked() returns a pointer to the existing or newly created context or NULL on error.
• For the other functions, 1 is returned for success or 0 on error. The error codes can be obtained by ERR_get_error(3).

SEE ALSO 👀

• BN_add(3)
• BN_CTX_new(3)
• BN_new(3)
• CRYPTO_lock(3)

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.
• BN_MONT_CTX_copy() first appeared in SSLeay 0.9.1 and has been available since OpenBSD 2.6.
• BN_MONT_CTX_set_locked() first appeared in OpenSSL 0.9.8 and has been available since OpenBSD 4.0.

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That's the whole BN_MOD_MUL_MONTGOMERY(3) tea ☕ — source/version: Debian; date: March 9, 2025. mwah 💋✨