@inproceedings{efe7f0387ae642679e6a59b22ff16662,

title = "Hard instances of the constrained discrete logarithm problem",

abstract = "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 Erd{\"o}s 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.",

author = "Ilya Mironov and Anton Mityagin and Kobbi Nissim",

year = "2006",

month = jan,

day = "1",

doi = "10.1007/11792086_41",

language = "English",

isbn = "3540360751",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "582--598",

booktitle = "Algorithmic Number Theory - 7th International Symposium, ANTS-VII, Proceedings",

address = "Germany",

note = "7th International Symposium on Algorithmic Number Theory, ANTS-VII ; Conference date: 23-07-2006 Through 28-07-2006",

}