| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * The X448 key-agreement algorithm |
| 4 | * |
| 5 | * (c) 2017 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | #ifndef CATACOMB_X448_H |
| 29 | #define CATACOMB_X448_H |
| 30 | |
| 31 | #ifdef __cplusplus |
| 32 | extern "C" { |
| 33 | #endif |
| 34 | |
| 35 | /*----- Notes on the X448 key-agreement algorithm -------------------------* |
| 36 | * |
| 37 | * This is X448, as described in RFC7748, based on the elliptic curve defined |
| 38 | * in Mike Hamburg, `Ed448-Goldilocks, a new elliptic curve', EUROCRYPT 2016, |
| 39 | * https://eprint.iacr.org/2015/625/. (The curve here is 4-isogenous to |
| 40 | * Hamburg's curve.) |
| 41 | * |
| 42 | * The RFC-specified operation is simpler than the Diffie--Hellman function |
| 43 | * described in Hamburg's paper, since it doesn't involve the `Decaf' |
| 44 | * cofactor elimination procedure. Indeed, it looks very much like X25519 |
| 45 | * with Hamburg's curve slotted in in place of Bernstein's. |
| 46 | * |
| 47 | * The @x448@ function essentially performs incompatible cofactor |
| 48 | * multiplication on the elliptic curve %$E(k)$% containing points %$(x, y)$% |
| 49 | * in %$\proj^2(k)$% satisfying the Montgomery-form equation |
| 50 | * |
| 51 | * %$y^3 = x^3 + 156326 x^2 + x$% , |
| 52 | * |
| 53 | * where $k = \gf{p}$, with $p = \phi^2 - \phi - 1$%, where |
| 54 | * %$\phi = 2^{224}$%. The curve has %$n = (p + 1) + {}$% |
| 55 | * %$28312320572429821613362531907042076847709625476988141958474579766324$% |
| 56 | * points; this is four times a prime %$\ell$%. The points with |
| 57 | * %$x$%-coordinate 5 have order %$\ell$%. |
| 58 | */ |
| 59 | |
| 60 | /*----- Header files ------------------------------------------------------*/ |
| 61 | |
| 62 | #include <mLib/bits.h> |
| 63 | |
| 64 | #ifndef CATACOMB_KEY_H |
| 65 | # include "key.h" |
| 66 | #endif |
| 67 | |
| 68 | /*----- Key fetching ------------------------------------------------------*/ |
| 69 | |
| 70 | typedef struct x448_priv { key_bin priv, pub; } x448_priv; |
| 71 | typedef struct x448_pub { key_bin pub; } x448_pub; |
| 72 | |
| 73 | extern const key_fetchdef x448_pubfetch[], x448_privfetch[]; |
| 74 | #define X448_PUBFETCHSZ 3 |
| 75 | #define X448_PRIVFETCHSZ 6 |
| 76 | |
| 77 | /*----- Important constants -----------------------------------------------*/ |
| 78 | |
| 79 | #define X448_KEYSZ 56 |
| 80 | #define X448_PUBSZ 56 |
| 81 | #define X448_OUTSZ 56 |
| 82 | |
| 83 | extern const octet x448_base[56]; |
| 84 | |
| 85 | /*----- Functions provided ------------------------------------------------*/ |
| 86 | |
| 87 | /* --- @x448@ --- * |
| 88 | * |
| 89 | * Arguments: @octet zz[X448_OUTSZ]@ = where to put the result |
| 90 | * @const octet k[X448_KEYSZ]@ = pointer to private key |
| 91 | * @const octet qx[X448_PUBSZ]@ = pointer to public value |
| 92 | * |
| 93 | * Returns: --- |
| 94 | * |
| 95 | * Use: Calculates X448 of @k@ and @qx@. |
| 96 | */ |
| 97 | |
| 98 | extern void x448(octet /*zz*/[X448_OUTSZ], |
| 99 | const octet /*k*/[X448_KEYSZ], |
| 100 | const octet /*qx*/[X448_PUBSZ]); |
| 101 | |
| 102 | /*----- That's all, folks -------------------------------------------------*/ |
| 103 | |
| 104 | #ifdef __cplusplus |
| 105 | } |
| 106 | #endif |
| 107 | |
| 108 | #endif |