why2 1.5.0

Lightweight, fast, secure, and easy to use encryption system.
Documentation 
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/*
This is part of WHY2
Copyright (C) 2022-2026 Václav Šmejkal

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <https://www.gnu.org/licenses/>.
*/

//! # Maximum Distance Separable (MDS) Matrices
//!
//! This module provides precomputed Cauchy matrices used for the linear diffusion layer
//! in the WHY2 algorithm. These matrices are essential for the `MixColumns` transformation,
//! ensuring optimal diffusion across the cipher's state for various grid sizes.
//!
//! ## The MDS Property
//!
//! A Maximum Distance Separable (MDS) matrix of dimensions $n \times n$ guarantees an optimal
//! branch number of $\mathcal{B} = n + 1$. In cryptographic terms, this means that a change in
//! a single input word will propagate to all $n$ output words. This property provides perfect,
//! rapid avalanche characteristics, effectively thwarting differential and linear cryptanalysis.
//!
//! ## Cauchy Matrix Construction
//!
//! The matrices defined in this module are constructed as Cauchy matrices. A Cauchy matrix is
//! defined by two disjoint sequences $X = (x_1, \dots, x_n)$ and $Y = (y_1, \dots, y_n)$.
//! The individual elements of the matrix $A$ are generated according to the formula:
//!
//! $$ M_{ij} = (x_i \oplus y_j)^{-1} $$
//!
//! An inherent mathematical property of Cauchy matrices is that every square submatrix is
//! strictly invertible (non-singular). When operations are evaluated over the cipher's
//! algebraic structure, this guarantees the strict MDS property without the need for
//! computationally expensive search algorithms to verify maximum distance separability.

/// A 4×4 MDS Cauchy matrix.
///
/// This matrix provides optimal linear diffusion for WHY2 configurations utilizing a
/// 4-column grid state (e.g., $4 \times 4$ configurations). It achieves a branch number of 5.
///
/// This value is cryptographically sensitive and should not be changed casually.
pub const MDS_4: [[u64; 4]; 4] =
[
    [0xC00000000000000B, 0x5555555555555552, 0x7FFFFFFFFFFFFFFB, 0xB6DB6DB6DB6DB6D4],
    [0x5555555555555552, 0xC00000000000000B, 0xB6DB6DB6DB6DB6D4, 0x7FFFFFFFFFFFFFFB],
    [0x7FFFFFFFFFFFFFFB, 0xB6DB6DB6DB6DB6D4, 0xC00000000000000B, 0x5555555555555552],
    [0xB6DB6DB6DB6DB6D4, 0x7FFFFFFFFFFFFFFB, 0x5555555555555552, 0xC00000000000000B],
];

/// An 8×8 MDS Cauchy matrix.
///
/// This matrix provides optimal linear diffusion for the default WHY2 grid configuration
/// (width $W = 8$). It strictly ensures a branch number of 9, maximizing the avalanche
/// effect across standard block sizes.
///
/// This value is cryptographically sensitive and should not be changed casually.
pub const MDS_8: [[u64; 8]; 8] =
[
    [0xE000000000000008, 0x9249249249249245, 0x2AAAAAAAAAAAAAA9, 0xCB972E5CB972E5C0, 0xBFFFFFFFFFFFFFF0, 0xE9D3A74E9D3A74E1, 0x5B6DB6DB6DB6DB6A, 0xCCCCCCCCCCCCCCC7],
    [0x9249249249249245, 0xE000000000000008, 0xCB972E5CB972E5C0, 0x2AAAAAAAAAAAAAA9, 0xE9D3A74E9D3A74E1, 0xBFFFFFFFFFFFFFF0, 0xCCCCCCCCCCCCCCC7, 0x5B6DB6DB6DB6DB6A],
    [0x2AAAAAAAAAAAAAA9, 0xCB972E5CB972E5C0, 0xE000000000000008, 0x9249249249249245, 0x5B6DB6DB6DB6DB6A, 0xCCCCCCCCCCCCCCC7, 0xBFFFFFFFFFFFFFF0, 0xE9D3A74E9D3A74E1],
    [0xCB972E5CB972E5C0, 0x2AAAAAAAAAAAAAA9, 0x9249249249249245, 0xE000000000000008, 0xCCCCCCCCCCCCCCC7, 0x5B6DB6DB6DB6DB6A, 0xE9D3A74E9D3A74E1, 0xBFFFFFFFFFFFFFF0],
    [0xBFFFFFFFFFFFFFF0, 0xE9D3A74E9D3A74E1, 0x5B6DB6DB6DB6DB6A, 0xCCCCCCCCCCCCCCC7, 0xE000000000000008, 0x9249249249249245, 0x2AAAAAAAAAAAAAA9, 0xCB972E5CB972E5C0],
    [0xE9D3A74E9D3A74E1, 0xBFFFFFFFFFFFFFF0, 0xCCCCCCCCCCCCCCC7, 0x5B6DB6DB6DB6DB6A, 0x9249249249249245, 0xE000000000000008, 0xCB972E5CB972E5C0, 0x2AAAAAAAAAAAAAA9],
    [0x5B6DB6DB6DB6DB6A, 0xCCCCCCCCCCCCCCC7, 0xBFFFFFFFFFFFFFF0, 0xE9D3A74E9D3A74E1, 0x2AAAAAAAAAAAAAA9, 0xCB972E5CB972E5C0, 0xE000000000000008, 0x9249249249249245],
    [0xCCCCCCCCCCCCCCC7, 0x5B6DB6DB6DB6DB6A, 0xE9D3A74E9D3A74E1, 0xBFFFFFFFFFFFFFF0, 0xCB972E5CB972E5C0, 0x2AAAAAAAAAAAAAA9, 0x9249249249249245, 0xE000000000000008],
];

/// A 16×16 MDS Cauchy matrix.
///
/// This extended matrix provides linear diffusion for maximum-width WHY2 configurations
/// (width $W = 16$, processing 16384 bits per block). It achieves an exceptional branch
/// number of 17.
///
/// This value is cryptographically sensitive and should not be changed casually.
pub const MDS_16: [[u64; 16]; 16] =
[
    [0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x9555555555555559, 0xE79E79E79E79E796, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xE66666666666666E, 0x94A5294A5294A525],
    [0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x5E26BC4D789AF132, 0xC92492492492492F, 0xE79E79E79E79E796, 0x9555555555555559, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x94A5294A5294A525, 0xE66666666666666E],
    [0xC92492492492492F, 0x5E26BC4D789AF132, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x9555555555555559, 0xE79E79E79E79E796, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xE66666666666666E, 0x94A5294A5294A525, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340],
    [0x5E26BC4D789AF132, 0xC92492492492492F, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xE79E79E79E79E796, 0x9555555555555559, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x94A5294A5294A525, 0xE66666666666666E, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5],
    [0x9555555555555559, 0xE79E79E79E79E796, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xE66666666666666E, 0x94A5294A5294A525, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3],
    [0xE79E79E79E79E796, 0x9555555555555559, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x5E26BC4D789AF132, 0xC92492492492492F, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x94A5294A5294A525, 0xE66666666666666E, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D],
    [0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x9555555555555559, 0xE79E79E79E79E796, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0xE66666666666666E, 0x94A5294A5294A525, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7],
    [0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xE79E79E79E79E796, 0x9555555555555559, 0x5E26BC4D789AF132, 0xC92492492492492F, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x94A5294A5294A525, 0xE66666666666666E, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8],
    [0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xE66666666666666E, 0x94A5294A5294A525, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x9555555555555559, 0xE79E79E79E79E796, 0x65CB972E5CB972E0, 0x58B162C58B162C5F],
    [0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x94A5294A5294A525, 0xE66666666666666E, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x5E26BC4D789AF132, 0xC92492492492492F, 0xE79E79E79E79E796, 0x9555555555555559, 0x58B162C58B162C5F, 0x65CB972E5CB972E0],
    [0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xE66666666666666E, 0x94A5294A5294A525, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x9555555555555559, 0xE79E79E79E79E796],
    [0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x94A5294A5294A525, 0xE66666666666666E, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x5E26BC4D789AF132, 0xC92492492492492F, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xE79E79E79E79E796, 0x9555555555555559],
    [0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xE66666666666666E, 0x94A5294A5294A525, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x9555555555555559, 0xE79E79E79E79E796, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4, 0xC92492492492492F, 0x5E26BC4D789AF132],
    [0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x94A5294A5294A525, 0xE66666666666666E, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0xE79E79E79E79E796, 0x9555555555555559, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004, 0x5E26BC4D789AF132, 0xC92492492492492F],
    [0xE66666666666666E, 0x94A5294A5294A525, 0x2DB6DB6DB6DB6DB5, 0x468D1A3468D1A340, 0xF4E9D3A74E9D3A7D, 0x71C71C71C71C71C3, 0x5FFFFFFFFFFFFFF8, 0xC8F591EB23D647A7, 0x65CB972E5CB972E0, 0x58B162C58B162C5F, 0x9555555555555559, 0xE79E79E79E79E796, 0xC92492492492492F, 0x5E26BC4D789AF132, 0x7000000000000004, 0xBBBBBBBBBBBBBBB4],
    [0x94A5294A5294A525, 0xE66666666666666E, 0x468D1A3468D1A340, 0x2DB6DB6DB6DB6DB5, 0x71C71C71C71C71C3, 0xF4E9D3A74E9D3A7D, 0xC8F591EB23D647A7, 0x5FFFFFFFFFFFFFF8, 0x58B162C58B162C5F, 0x65CB972E5CB972E0, 0xE79E79E79E79E796, 0x9555555555555559, 0x5E26BC4D789AF132, 0xC92492492492492F, 0xBBBBBBBBBBBBBBB4, 0x7000000000000004],
];