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Topics in Computational Number Theory Inspired by Peter L. Montgomery (Hardcover)
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Topics in Computational Number Theory Inspired by Peter L. Montgomery (Hardcover)
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Peter L. Montgomery has made significant contributions to
computational number theory, introducing many basic tools such as
Montgomery multiplication, Montgomery simultaneous inversion,
Montgomery curves, and the Montgomery ladder. This book features
state-of-the-art research in computational number theory related to
Montgomery's work and its impact on computational efficiency and
cryptography. Topics cover a wide range of topics such as
Montgomery multiplication for both hardware and software
implementations; Montgomery curves and twisted Edwards curves as
proposed in the latest standards for elliptic curve cryptography;
and cryptographic pairings. This book provides a comprehensive
overview of integer factorization techniques, including dedicated
chapters on polynomial selection, the block Lanczos method, and the
FFT extension for algebraic-group factorization algorithms.
Graduate students and researchers in applied number theory and
cryptography will benefit from this survey of Montgomery's work.
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