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Universal fixed messages and the Rivest-Shamir-Adleman cryptosystem

Published online by Cambridge University Press:  26 February 2010

Donald R. Smith  and
James T. Palmer
Donald R. Smith
Affiliation:
Department of Mathematics, University of California, San Diego, 92093, U.S.A.
James T. Palmer
Affiliation:
Horizons Technology, Inc., 7830 Clairemont Mesa Blvd., San Diego, 92111, U.S.A.
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Extract

In this note we remark on certain “universal fixed messages” for the Rivest-Shamir-Adleman cryptosystem [1], and we describe how in certain cases these universal fixed messages can play a role in an attempt to break the cryptosystem. This use of the universal fixed messages in an attempt to break the RSA cryptosystem† involves a certain prime factorization technique using the fixed messages. We characterize the situation in which such an attempt would be successful in practice, and we show that a user of the RSA cryptosystem can easily arrange to avoid this situation. Hence the use of the present technique does not pose a threat to the security of the RSA cryptosystem.

Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 44 - 52
Copyright
Copyright © University College London 1979

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References

1.Rivest, R. L., Shamir, A., and Adleman, L.. “A method for obtaining digital signatures and public-key cryptosystem”, M.I.T. Laboratory for Computer Science Technical Memo, 82, April 1977, Commun. ACM, 21 (1978), 120–126.Google Scholar
2.Gioia, A. A.. The theory of numbers (Markham Publishing Company, Chicago, 1970).Google Scholar