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Books > Computing & IT > Applications of computing > Databases > Data security & data encryption
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Cryptographic Applications of Analytic Number Theory - Complexity Lower Bounds and Pseudorandomness (Hardcover, 2003 ed.)
Loot Price: R2,675
Discovery Miles 26 750
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Cryptographic Applications of Analytic Number Theory - Complexity Lower Bounds and Pseudorandomness (Hardcover, 2003 ed.)
Series: Progress in Computer Science and Applied Logic, 22
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The book introduces new techniques that imply rigorous lower bounds
on the com plexity of some number-theoretic and cryptographic
problems. It also establishes certain attractive pseudorandom
properties of various cryptographic primitives. These methods and
techniques are based on bounds of character sums and num bers of
solutions of some polynomial equations over finite fields and
residue rings. Other number theoretic techniques such as sieve
methods and lattice reduction algorithms are used as well. The book
also contains a number of open problems and proposals for further
research. The emphasis is on obtaining unconditional rigorously
proved statements. The bright side of this approach is that the
results do not depend on any assumptions or conjectures. On the
downside, the results are much weaker than those which are widely
believed to be true. We obtain several lower bounds, exponential in
terms of logp, on the degrees and orders of o polynomials; o
algebraic functions; o Boolean functions; o linear recurrence
sequences; coinciding with values of the discrete logarithm modulo
a prime p at sufficiently many points (the number of points can be
as small as pI/2+O: ). 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 rightmost bit of the
discrete logarithm and defines whether the argument is a quadratic
residue."
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