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IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 17 - Volume 18
An improvement of key generation algorithm for Gentry's homomorphic encryption scheme
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Exact computation of polynomial zeros expressible by square roots
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Secure accumulators from euclidean rings without trusted setup
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
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a-tint: A polymake extension for algorithmic tropical intersection theory
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A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.