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Some remarks on Lucas-Based cryptosystems

Bleichenbacher, D.
•
Bosma, W.
•
Lenstra, Arjen K.  
1995
Advances in Cryptology - CRYPTO '95. 15th Annual International Cryptology Conference. Proceedings
Advances in Cryptology - CRYPTO '95. 15th Annual International Cryptology Conference. Proceedings

We review the well-known relation between Lucas sequences and exponentiation. This leads to the observation that certain public-key cryptosystems that are based on the use of Lucas sequences have some elementary properties their re-inventors were apparently not aware of. In particular, we present a chosen-message forgery for LUC' [Smith, 1993] and [Smith and Lennon, 1993], and we show that LUCELG' and `LUCDIF' [Smith, 1994] and [Smith and Skinner, 1994] are vulnerable to subexponential time attacks. This proves that various claims that were made about Lucas-based cryptosystems are incorrect

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EPFL-CONF-149464.pdf

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