Extension of Brickell’s algorithm for breaking high density knapsacks

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Abstract

A knapsack (or subset-sum) problem that is useful for cryptographic purposes, consists of a set of n positive integers a = {a1, a2,.. an}, called the knapsack a, and a sum s. The density d of a knapsack is defined to be n /log2 (ai)max. The knapsack problem then consists of finding the set, if any, of binary numbers x = {x1, x2,.., xn}, such that Σxi·ai = s.

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Jorissen, F., Vandewalle, J., & Govaerts, R. (1988). Extension of Brickell’s algorithm for breaking high density knapsacks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 304 LNCS, pp. 109–115). Springer Verlag. https://doi.org/10.1007/3-540-39118-5_11

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