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research-article

Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's fast signature scheme

Published: 01 September 2006 Publication History

Abstract

The basic Merkle-Hellman additive trapdoor knapsack public-key cryptosystem was recently shown to be insecure, and attacks have also been developed on stronger variants of it, such as the Graham-Shamir system and the iterated knapsack cryptosystem. It is shown that some simple variants of another Merkle-Hellman system, the multiplicative knapsack cryptosystem, are insecure. It is also shown that the Shamir fast signature scheme can be broken quickly. Similar attacks can also be used to break the Schöbi-Massey authentication scheme. These attacks have not been rigorously proved to succeed, but heuristic arguments and empirical evidence indicate that they work on systems of practical size.

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  • (2015)Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition methodProceedings of the 8th International Conference on Security of Information and Networks10.1145/2799979.2800026(338-341)Online publication date: 8-Sep-2015
  • (2014)Mathematical model of the polyalphabetic information security system based on the normal generalized knapsackProceedings of the 7th International Conference on Security of Information and Networks10.1145/2659651.2659658(180-185)Online publication date: 9-Sep-2014
  • (2008)Disappearing CryptographyundefinedOnline publication date: 3-Dec-2008
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  1. Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's fast signature scheme

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    cover image IEEE Transactions on Information Theory
    IEEE Transactions on Information Theory  Volume 30, Issue 4
    July 1984
    129 pages

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    IEEE Press

    Publication History

    Published: 01 September 2006

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    View all
    • (2015)Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition methodProceedings of the 8th International Conference on Security of Information and Networks10.1145/2799979.2800026(338-341)Online publication date: 8-Sep-2015
    • (2014)Mathematical model of the polyalphabetic information security system based on the normal generalized knapsackProceedings of the 7th International Conference on Security of Information and Networks10.1145/2659651.2659658(180-185)Online publication date: 9-Sep-2014
    • (2008)Disappearing CryptographyundefinedOnline publication date: 3-Dec-2008
    • (2005)Security analysis and improvement of a double-trapdoor encryption schemeApplied Mathematics and Computation10.1016/j.amc.2004.10.026169:1(41-50)Online publication date: 1-Oct-2005
    • (2004)Travelling salesman cryptosystemFocus on computational neurobiology10.5555/1022385.1022392(65-70)Online publication date: 1-Jan-2004
    • (2002)A Linear Algebraic Attack on the AAFG1 Braid Group CryptosystemProceedings of the 7th Australian Conference on Information Security and Privacy10.5555/646039.678456(176-189)Online publication date: 3-Jul-2002

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