Number Theoretic Methods in Cryptography
Language: English
Published by Birkhäuser, Birkhäuser Okt 2012, 2012
- Softcover
- New
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This item is printed on demand - Print on Demand Titel. Neuware -The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields and residue rings. It also contains a number of open problems and proposals for further research. We obtain several lower bounds, exponential in terms of logp, on the de grees and orders of ¿ polynomials; ¿ algebraic functions; ¿ Boolean functions; ¿ linear recurring sequences; coinciding with values of the discrete logarithm modulo a prime p at suf ficiently many points (the number of points can be as small as pI/He). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the right most bit of the discrete logarithm and defines whether the argument is a quadratic residue. We also obtain non-trivial upper bounds on the de gree, sensitivity and Fourier coefficients of Boolean functions on bits of x deciding whether x is a quadratic residue. These results are used to obtain lower bounds on the parallel arithmetic and Boolean complexity of computing the discrete logarithm. For example, we prove that any unbounded fan-in Boolean circuit. of sublogarithmic depth computing the discrete logarithm modulo p must be of superpolynomial size.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 198 pp. Englisch.…
Seller Inventory # 9783034897235
- Title
- Number Theoretic Methods in Cryptography
- Author
- Igor Shparlinski
- Publisher
- Birkhäuser, Birkhäuser Okt 2012
- Publication year
- 2012
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3034897235
- ISBN 13
- 9783034897235
- Item weight
- 309 grams
- Dimensions
- 235x155x11 mm
"Synopsis" may belong to another edition of this title.
Review
"This volume gives a thorough treatment of the complexity of the discrete logarithm problem in a prime field, as well as related problems. The final chapter on further directions gives an interesting selection of problems."
--Zentralblatt Math
"About the title" may belong to another edition of this title.
buchversandmimpf2000
Emtmannsberg, BAYE, Germany
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