Paper 2003/219 Original: eprint.iacr.org/2003/219 ↗

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

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.