Merkle-Hellman Revisited: A Cryptanalysis of the Qu-Vanstone Cryptosystem Based on Group Factorizations
نویسندگان
چکیده
Cryptosystems based on the knapsack problem were among the rst public key systems to be invented and for a while were considered quite promising. Basically all knapsack cryptosystems that have been proposed so far have been broken, mainly by means of lattice reduction techniques. However, a few knapsack-like cryptosystems have withstood cryptanalysis, among which the Chor-Rivest scheme 2] even if this is debatable (see 16]), and the Qu-Vanstone scheme proposed at the Dagstuhl'93 workshop 13] and published in 14]. The Qu-Vanstone scheme is a public key scheme based on group factorizations in the additive group of integers modulo n that generalizes Merkle-Hellman cryp-tosystems. In this paper, we present a novel use of lattice reduction, which is of independent interest, exploiting in a systematic manner the notion of an orthogonal lattice. Using the new technique, we successfully attack the Qu-Vanstone cryptosystem. Namely, we show how to recover the private key from the public key. The attack is based on a careful study of the so-called Merkle-Hellman transformation.
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