EC_POINT_ADD(3)

💅 EC_POINT_ADD — bestie edition ✨

okay so this is a page from the Library Functions Manual, and it's all about libcrypto — the crypto library that lives on your system. It's giving "math class but make it fashion," and honestly? We're obsessed. 🎀

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✨ NAME ✨

EC_POINT_add, EC_POINT_dbl, EC_POINT_invert, EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp, EC_POINT_make_affine, EC_POINT_mul — literally all of them do mathematical operations and tests on EC_POINT objects. That's the whole vibe. 💜

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🦋 SYNOPSIS 🦋

First things first, bestie, you gotta pull in the library and the headers:

library “libcrypto” #include <openssl/ec.h>
#include <openssl/bn.h>

and then the actual functions, in all their glory:

int
EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
    const EC_POINT *b, BN_CTX *ctx);

int
EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
    BN_CTX *ctx);

int
EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);

int
EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);

int
EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
    BN_CTX *ctx);

int
EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a,
    const EC_POINT *b, BN_CTX *ctx);

int
EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point,
    BN_CTX *ctx);

int
EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n,
    const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);

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🌸 DESCRIPTION 🌸

So these functions all operate on EC_POINT objects, which are created by EC_POINT_new(3). No cap, that's where they come from. 💫

• EC_POINT_add() — adds the two points a and b, and drops the result into r. Math but cute. ✨
• EC_POINT_dbl() — doubles the point a and puts the result in r. Same energy, just one point doing overtime. 💪

and yes, for both of those, it's totally valid for r to be one of a or b — the function can write over its own input, it's fine, she's flexible like that. 🫶

• EC_POINT_invert() — calculates the inverse of the supplied point a, and the result gets placed back in a. In place, periodt. 💅
• EC_POINT_is_at_infinity() — tests whether the supplied point is at infinity or not. Is she infinitely far away or nah? That's the question. 🌀
• EC_POINT_is_on_curve() — tests whether the supplied point is on the curve or not. Vibe check for points, basically. ✅
• EC_POINT_cmp() — compares the two supplied points and tests whether or not they're equal. Are they the same girl? 👯
• EC_POINT_mul() — this one's the main character. It calculates:

generator * n + q * m

and stores the result in r. 🔥

okay and here's the tea: the value n may be NULL, in which case the result is just:

q * m.

See EC_GROUP_new_curve_GFp(3) for the info about the generator — that's where she lives, iykyk. 🌈

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👑 RETURN VALUES 👑

The following functions return 1 on success or 0 on error — classic:

• EC_POINT_add()
• EC_POINT_dbl()
• EC_POINT_invert()
• EC_POINT_make_affine()
• EC_POINT_mul()

EC_POINT_is_at_infinity() returns 1 if the point is at infinity, or 0 otherwise. 💫

EC_POINT_is_on_curve() returns 1 if the point is on the curve, 0 if it's not, or -1 on error. Three whole moods. 😭

EC_POINT_cmp() returns 1 if the points are not equal, 0 if they are, or -1 on error. Yes bestie, it's inverted — read it twice, I had to. 🔁

careful with that EC_POINT_cmp() return value, it's giving "yes means no" and that's exactly the kind of thing that'll ruin your whole afternoon if you skim it. 🙈

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🧚 SEE ALSO 🧚

Go read these too, they're all linked and they all slay in their own way:

crypto(3), d2i_ECPKParameters(3), EC_GROUP_check(3), EC_GROUP_get_curve_name(3), EC_GROUP_new_by_curve_name(3), EC_GROUP_new_curve_GFp(3), EC_KEY_METHOD_new(3), EC_KEY_new(3), EC_POINT_get_affine_coordinates(3), EC_POINT_new(3), EC_POINT_point2oct(3)

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⭐ HISTORY ⭐

EC_POINT_add(), EC_POINT_dbl(), EC_POINT_invert(), EC_POINT_is_at_infinity(), EC_POINT_is_on_curve(), EC_POINT_cmp(), EC_POINT_make_affine(), and EC_POINT_mul() first appeared in OpenSSL 0.9.7 and have been available since OpenBSD 3.2. iconic behavior, honestly. 👑

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and that's the whole page, bestie!! 💖 this beauty is from the Debian edition of the manual, dated June 8, 2025, and it's filed under EC_POINT_ADD(3) — go forth and do math responsibly, mwah 🫶✨🎀