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Lecture Notes in Computer Science

Advances in Cryptology

Proceedings of CRYPTO '84

Editors: Blakely, G.R., Chaum, D. (Eds.)

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About this book

Recently, there has been a lot of interest in provably "good" pseudo-random number generators [lo, 4, 14, 31. These cryptographically secure generators are "good" in the sense that they pass all probabilistic polynomial time statistical tests. However, despite these nice properties, the secure generators known so far suffer from the han- cap of being inefiicient; the most efiicient of these take n2 steps (one modular multip- cation, n being the length of the seed) to generate one bit. Pseudc-random number g- erators that are currently used in practice output n bits per multiplication (n2 steps). An important open problem was to output even two bits on each multiplication in a cryptographically secure way. This problem was stated by Blum, Blum & Shub [3] in the context of their z2 mod N generator. They further ask: how many bits can be o- put per multiplication, maintaining cryptographic security? In this paper we state a simple condition, the XOR-Condition and show that any generator satisfying this condition can output logn bits on each multiplication. We show that the XOR-Condition is satisfied by the lop least significant bits of the z2-mod N generator. The security of the z2 mod N generator was based on Quadratic Residu- ity [3]. This generator is an example of a Trapdoor Generator [13], and its trapdoor properties have been used in protocol design. We strengthen the security of this gene- tor by proving it as hard as factoring.

Table of contents (40 chapters)

  • A Prototype Encryption System Using Public Key

    Serpell, S C (et al.)

    Pages 3-9

  • A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms

    ElGamal, Taher

    Pages 10-18

  • A Public-Key Cryptosystem Based on the Word Problem

    Wagner, Neal R. (et al.)

    Pages 19-36

  • Efficient Signature Schemes Based on Polynomial Equations (preliminary version)

    Ong, H. (et al.)

    Pages 37-46

  • Identity-Based Cryptosystems and Signature Schemes

    Shamir, Adi

    Pages 47-53

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-3-540-39568-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-3-540-15658-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Cryptology
Book Subtitle
Proceedings of CRYPTO '84
Editors
  • G.R. Blakely
  • D. Chaum
Series Title
Lecture Notes in Computer Science
Series Volume
196
Copyright
1985
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-39568-3
DOI
10.1007/3-540-39568-7
Softcover ISBN
978-3-540-15658-1
Series ISSN
0302-9743
Edition Number
1
Number of Pages
XII, 496
Topics