Efficient Root Finding of Polynomials over Fields of Characteristic 2.

Bhaskar Biswas (1) , Vincent Herbert (1)

1 SECRET - Security, Cryptology and Transmissions

Root finding is the most time-consuming stage of McEliece cryptosystem decryption. The best method to find the zeroes of a polynomial for cryptographic parameters is the Berlekamp Trace Algorithm (BTA). Our idea is to mix BTA with ad-hoc methods proposed by Zinoviev. We obtain a significant gain in terms of time complexity for finding roots and so we decrease McEliece decryption time. This paper contains both theoretical and experimental study of this technique.

Mots clés: Binary Goppa codes; Worst-case complexity; Code-based public-key cryptography; Linearized polynomial; Berlekamp Trace Algorithm; Error locator polynomial; Algebraic decoding algorithm; Binary Goppa codes.

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Bhaskar Biswas, Vincent Herbert. Efficient Root Finding of Polynomials over Fields of Characteristic 2.. 2009. ⟨hal-00626997⟩