Pub. Date:
Springer US
Recent Advances in RSA Cryptography / Edition 1

Recent Advances in RSA Cryptography / Edition 1

by Stefan Katzenbeisser


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Product Details

ISBN-13: 9780792374381
Publisher: Springer US
Publication date: 09/30/2001
Series: Advances in Information Security , #3
Edition description: 2001
Pages: 140
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

1.Mathematical Background1
1.1Divisibility and the residue class ring Z[subscript n]1
1.3Euler's totient function and Z*[subscript n]6
1.4Polynomial congruences and systems of linear congruences9
1.5Quadratic residues10
2.Computational Complexity13
2.1Turing machines13
2.2Deterministic and nondeterministic machines14
2.3Decision problems and complexity classes16
2.4Reductions, completeness and oracle computations19
2.6Efficient computation and randomized complexity classes22
3.Public Key Cryptography25
3.1Public key cryptography25
3.2Permutation polynomials and RSA-type cryptosystems28
3.3Efficient implementation of RSA30
3.4One-way functions33
3.5On the complexity of an attack against RSA41
4.Factorization Methods49
4.1Trial division and Fermat factorization49
4.2Monte-carlo factorization50
4.3Factor base methods52
4.4The continued fraction method54
4.5Quadratic sieve57
4.6Other Factorization Methods59
5.Properties of the RSA Cryptosystem63
5.1Computing the decryption exponent63
5.2Partial decryption67
5.3Cycling attacks and superencryption68
5.4Incorrect keys71
5.5Partial information on RSA and hard-core predicates73
6.Low-Exponent RSA81
6.1Wiener's attack81
6.2Lattice basis reduction82
6.3The attack of Boneh and Durfee86
6.4Low public exponents91
6.5Polynomially related messages93
6.6Partial key exposure96
7.Protocol and Implementation Attacks99
7.1Simple protocol attacks against RSA99
7.2Hastad's broadcast attack102
7.3Effective security of small RSA messages103
7.4Optimal Asymmetric Encryption104
7.5Faulty encryption106
7.6Timing attacks108
8.RSA Signatures111
8.1Attacks on RSA signatures with redundancy111
8.2Security of hash-and-sign signatures115
8.3Provably secure RSA signatures118
8.4Undeniable signatures122
8.5Threshold signatures125

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