Method to obtain modular inverse matrices logarithmic-time nlog(n!) + (log(m!))/log(φ)). Developed method to obtain modular inverse matrices sized n x n considering computational-complexity more efficiency and applications in symmetric cryptography.

The proposed Montante-Jacques method to obtain modular inverse matrices with logarithmic complexity.

This is a Node.js module.

Installation is done using the npm install command:

    npm i montante-jacques

This method uses the Bareiss Algorithm to calculate the determinant of the matrix. See:

• https://www.npmjs.com/package/bareiss

    npm i bareiss

Bareiss Algorithm.

// Import the module
const MontanteJacques = require( 'montante-jacques' );

// Let K a (N x N) matrix
let K =
    [ [ 42, 97, 23 ],
    [ 51, 30, 77 ],
    [ 33, 7, 66 ] ];

// Let m a prime number, referred as modulo.
const m = 131;

K = MontanteJacques.inverseModular( K, m );

console.log( K )

    //[ [ 0, 42, 82 ], [ 85, 107, 48 ], [ 120, 53, 75 ] ];

The main function is:

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

• Code:

  • Adolfo Solis-Rosas

• Author of the Gauss-Jacques method:

  • Fausto Abraham Jacques-García