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 (3 chapter)

  • A Knapsack Type Public Key Cryptosystem Based On Arithmetic in Finite Fields (preliminary draft)

    Benny Chor, Ronald L. Rivest

    Pages 54-65

    Buy Chapter $29.95
  • An LSI Digital Encryption Processor (DEP)

    R. C. Fairfield, A. Matusevich, J. Plany

    Pages 115-143

    Buy Chapter $29.95
  • Efficient hardware and software implementations for the DES

    Marc Davio, Yvo Desmedt, Jo Goubert, et al.

    Pages 144-146

    Buy Chapter $29.95
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Buy this book

eBook $49.99 net
( price for USA )
  • ISBN 978-3-540-39568-3
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $69.99 net
( price for USA )
  • 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
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
Topics