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A Public-Key Cryptography Algorithm which uses Prime Factorization as the Trapdoor Function. Define
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Let the message be converted to a number . The sender then makes
and
public and sends
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It is possible to break the cryptosystem by repeated encryption if a unit of
has small
Order (Simmons and Norris 1977, Meijer 1996), where
is the Ring of
Integers between 0 and
under addition and multiplication (mod
). Meijer (1996) shows that
``almost'' every encryption exponent
is safe from breaking using repeated encryption for factors of the form
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(7) |
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(8) |
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(9) |
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(10) |
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(11) |
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Using the RSA system, the identity of the sender can be identified as genuine without revealing his private code.
See also Public-Key Cryptography
References
Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 166-173, 1985.
Meijer, A. R. ``Groups, Factoring, and Cryptography.'' Math. Mag. 69, 103-109, 1996.
Rivest, R. L. ``Remarks on a Proposed Cryptanalytic Attack on the MIT Public-Key Cryptosystem.'' Cryptologia 2, 62-65, 1978.
Rivest, R.; Shamir, A.; and Adleman, L. ``A Method for Obtaining Digital Signatures and Public Key Cryptosystems.''
Comm. ACM 21, 120-126, 1978.
RSA Data Security.
Simmons, G. J. and Norris, M. J. ``Preliminary Comments on the MIT Public-Key Cryptosystem.'' Cryptologia 1, 406-414, 1977.
A Security Dynamics Company. http://www.rsa.com.
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© 1996-9 Eric W. Weisstein