A Preliminary Report on the Cryptanalysis of Merkle-Hellman Knapsack Cryptosystems

In April, 1982, Adi Shamir caused a furor with the announcement [1] of “A Polynomial Time Algorithm for Breaking Merkle-Hellman Cryptosystems.” Like many others who received his “extended abstract,” members of the mathematics department at the Sandia National Laboratories undertook a careful study of both the algorithm and the underlying mathematical concepts. This paper summarizes some of our findings. In order to meet the deadline for Crypto’82 the style will be deliberately telegraphic -- and informal. A complete paper will be presented this fall at the Twelfth Conference on Numerical Mathematics and Computing at Winnipeg, the proceedings of which will be published in Congressus Numerantium. It should also be remarked that in discussions with Adi at Crypto’82, we learned that some of the results presented here as new were also arrived at independently by him in the period since his original announcement.