Cryptology ePrint Archive: Report 2003/219

Cryptanalysis of the Repaired Public-key Encryption Scheme Based on the Polynomial Reconstruction Problem

Jean-Sebastien Coron

Abstract: At Eurocrypt 2003, Augot and Finiasz proposed a new public-key encryption scheme based on the polynomial reconstruction problem. The scheme was subsequently broken by Coron, who showed that given the public-key and a ciphertext, one could recover the corresponding plaintext in polynomial time. Recently, Augot, Finiasz and Loidreau published on the IACR eprint archive a reparation of the cryptosystem. The reparation is based on the trace operator, and is resistant against the previous attack. However, we describe a new cryptanalysis of the repaired scheme. Given the public-key and a ciphertext, we can still recover the corresponding plaintext in polynomial time. Our technique is a variant of the Berlekamp-Welsh algorithm, and works very well in practice, as for the proposed parameters, we recover the plaintext in less than 8 minutes on a single PC.

Category / Keywords: public-key cryptography / Cryptanalysis, Augot and Finiasz cryptosystem.

Date: received 10 Oct 2003, last revised 13 Oct 2003

Contact author: coron at clipper ens fr

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Version: 20031013:191821 (All versions of this report)

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