@inproceedings{2ee684e4a6984c6abc95f94be1599d8c,

title = "Playing {"}hide-and-seek{"} with numbers: the hidden number problem, lattices and exponential sums",

abstract = "We give a survey of recent results on the hidden number problem introduced by Boneh and Venkatesan in 1996 and its numerous generalizations. Many of the results in this area are based on a rather surprising combination of two celebrated number theoretic techniques: bounds of exponential sums and lattice basis reduction algorithms, which are briefly outlined as well. We also describe several cryptographic applications and outline some possible directions for further research.",

keywords = "PARTIALLY KNOWN NONCES, DIGITAL SIGNATURE ALGORITHM, SPARSE POLYNOMIAL INTERPOLATION, PSEUDORANDOM BINARY SEQUENCES, DIFFIE-HELLMAN BITS, FINITE-FIELDS, QUADRATIC RESIDUES, SECURITY, GENERATORS, COMPLEXITY",

author = "IE Shparlinski",

year = "2005",

language = "English",

isbn = "0821833650",

series = "Proceedings of Symposia in Applied Mathematics",

publisher = "American Mathematical Society",

pages = "153--177",

editor = "P Garret and D Lieman",

booktitle = "Public-key cryptography",

address = "United States",

note = "Joint Annual Meeting of the American-Mathematical-Society/Mathematical-Association-of-America ; Conference date: 17-01-2003",

}