Fast Exponentiation Using Data Compression
SIAM Journal on Computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Small generic hardcore subsets for the discrete logarithm: short secret DL-keys
Information Processing Letters
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
Mathematics of Computation
Universal classes of hash functions (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Random small hamming weight products with applications to cryptography
Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
A Note on Bipartite Graphs Without 2k-Cycles
Combinatorics, Probability and Computing
Sets in Zn with distinct sums of pairs
Discrete Applied Mathematics
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
A note on discrete logarithms with special structure
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
A new baby-step giant-step algorithm and some applications to cryptanalysis
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Analysis of Low Hamming Weight Products
Discrete Applied Mathematics
Parameterized splitting systems for the discrete logarithm
IEEE Transactions on Information Theory
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The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent x belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study explicit construction of sets for which the constrained DLP is hard. We draw on earlier results due to Erdös et al. and Schnorr, develop geometric tools such as generalized Menelaus’ theorem for proving lower bounds on the complexity of the constrained DLP, and construct explicit sets with provable non-trivial lower bounds.