Some Remarks on Lucas-Based Cryptosystems
Daniel Bleichenbacher, Wieb Bosma, and Arjen K. Lenstra
Advances in Cryptology — CRYPTO '95, Lecture Notes in Computer Science, Springer-Verlag, vol. 963, pp. 386–396, Aug 1995.
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 proerties their re-inventors were apparently not aware of. In particular, we present a chosen-message forgery for 'LUC', and we show that 'LUCELG' and 'LUCDIF' are vulnerable to subexponential time attacks. This proves that various claims that were made about Lucas-based cryptosystems are incorrect.
BibTeX Citation
@inproceedings{BlBoLe95, author = {Daniel Bleichenbacher and Wieb Bosma and Arjen K. Lenstra}, title = {Some Remarks on {L}ucas-Based Cryptosystems}, editor = {Don Coppersmith}, booktitle = {Advances in Cryptology --- CRYPTO~'95}, pages = {386--396}, series = {Lecture Notes in Computer Science}, volume = {963}, year = {1995}, month = {8}, publisher = {Springer-Verlag}, }