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Mathematics of Public Key Cryptography
The Diffie–Hellman problem and cryptographic applications
monograph
Author(s):
Steven D. Galbraith
Publication date
(Online):
2009
Publisher:
Cambridge University Press
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There is no author summary for this book yet. Authors can add summaries to their books on ScienceOpen to make them more accessible to a non-specialist audience.
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Electrospinning for biomedical applications
Author and book information
Book Chapter
Pages
: 405-417
DOI:
10.1017/CBO9781139012843.021
SO-VID:
4f376db9-bf5a-421a-ad98-4d6798cfd660
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Book chapters
pp. xiii
Preface
pp. 1
Introduction
pp. 13
Basic algorithmic number theory
pp. 54
Hash functions and MACs
pp. 61
Preliminary remarks on algebraic groups
pp. 66
Varieties
pp. 86
Tori, LUC and XTR
pp. 101
Curves and divisor class groups
pp. 121
Rational maps on curves and divisors
pp. 138
Elliptic curves
pp. 178
Hyperelliptic curves
pp. 215
Basic algorithms for algebraic groups
pp. 238
Primality testing and integer factorisation using algebraic groups
pp. 246
Basic discrete logarithm algorithms
pp. 262
Factoring and discrete logarithms using pseudorandom walks
pp. 301
Factoring and discrete logarithms in subexponential time
pp. 337
Lattices
pp. 347
Lattice basis reduction
pp. 366
Algorithms for the closest and shortest vector problems
pp. 380
Coppersmith's method and related applications
pp. 405
The Diffie–Hellman problem and cryptographic applications
pp. 418
The Diffie–Hellman problem
pp. 452
Digital signatures based on discrete logarithms
pp. 469
Public key encryption based on discrete logarithms
pp. 485
The RSA and Rabin cryptosystems
pp. 515
Isogenies of elliptic curves
pp. 545
Pairings on elliptic curves
pp. 564
Background mathematics
pp. 579
References
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