Cryptanalysis of the Dickson-scheme
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
LUC public key encryption: a secure alternative to RSA
Dr. Dobb's Journal
A subexponential algorithm for discrete logarithms over all finite fields
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On the security of the Lucas function
Information Processing Letters
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
IFIP/Sec '93 Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
On the importance of securing your bins: the garbage-man-in-the-middle attack
Proceedings of the 4th ACM conference on Computer and communications security
A Time-Bound Cryptographic Key Assignment Scheme for Access Control in a Hierarchy
IEEE Transactions on Knowledge and Data Engineering
Generalised Cycling Attacks on RSA and Strong RSA Primes
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A traceable group signature scheme
Mathematical and Computer Modelling: An International Journal
An efficient probabilistic public-key cryptosystem over quadratic fields quotients
Finite Fields and Their Applications
Polynomial representations of the Lucas logarithm
Finite Fields and Their Applications
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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.