Abstract
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’ (cf. [21; 25]), and we show that ‘LUCELG’ and ‘LUCDIF’ (cf. [22, 26]) are vulnerable to subexponential time attacks. This proves that various claims that were made about Lucas-based cryptosystems are incorrect.
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Bleichenbacher, D., Bosma, W., Lenstra, A.K. (1995). Some Remarks on Lucas-Based Cryptosystems. In: Coppersmith, D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44750-4_31
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DOI: https://doi.org/10.1007/3-540-44750-4_31
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