On the Cryptocomplexity of Knapsack Systems
Name
MIT-LCS-TM-129.pdf
Size
5.01 MB
Format
Adobe PDF
Checksum (MD5)
1af9d2b00eeaa4f86915eac4e9a59668
Author(s)
Shamir, Adi
Date Issued
April 1979
Series/Report no.
MIT-LCS-TM-129
Abstract
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.
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