Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
A model to order the encryption algorithms according to their quality
ACM SIGCOMM Computer Communication Review
Foundations and Trends® in Theoretical Computer Science
New NP-Complete Problems Associated with Lattices
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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A recent trend in cryptographic systems is to base their encryption/decryption functions on NP-complete problems, and in particular on the knapsack problem. To analyze the security of these systems, we need a complexity theory which is less worst-case oriented and which takes into account the extra conditions imposed on the problems to make them cryptographically useful. In this paper we consider the two classes of one-to-one and onto knapsack systems, analyze the complexity of recognizing them and of solving their instances, introduce a new complexity measure (median complexity), and show that this complexity is inversely proportional to the density of the knapsack system. The tradeoff result is based on a fast probabilistic knapsack solving algorithm which is applicable only to one-to-one systems, and it indicates that knapsack-based cryptographic systems in which one can both encrypt and sign messages are relatively insecure. We end the paper with new results about the security of some specific knapsack systems.