A method for obtaining digital signatures and public-key cryptosystems
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In this paper new methods, generalizing those of Shamir, are presented for attacking generalizations of the basic system. It is shown how these methods may be applied to the Graham-Shamir public-key crypto-system [2], and the iterated Merkle-Hellman public-key cryptosystem. We are unable to present a rigorous proof that the attacks presented here are effective. However, in the case of the Graham-Shamir system, the methods have been implemented and have performed well in tests. The method of attack uses recent results of Lenstra, Lenstra, and Lovasz [5]. The cryptanalytic problem is treated as a lattice problem rather than a linear programming one as in Shamir's result.