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Number Theoretic Methods in Cryptography : Complexity Lower Bounds by Igor Shparlinski (auth.) is a nonfiction available to read on EtoBox.

What is Number Theoretic Methods in Cryptography : Complexity Lower Bounds about?

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 resu

Who reads Number Theoretic Methods in Cryptography : Complexity Lower Bounds?

Author

Igor Shparlinski (auth.)

Publisher

Birkhäuser Basel

Published

1999

Language

EN

ISBN

9783034897235

Category

nonfiction

Subjects

Science, Computer Science, Mathematics