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RT Book, Whole SR Electronic DC OPAC T1 Number Theoretic Methods in Cryptography : Complexity lower bounds / by Igor Shparlinski T2 Progress in Computer Science and Applied Logic A1 Shparlinski, Igor A1 SpringerLink (Online service) YR 1999 FD 1999 SP IX, 182 p K1 Mathematics K1 Data structures (Computer science) K1 Data encryption (Computer science) K1 Computers K1 Number theory K1 Mathematics K1 Number Theory K1 Data Encryption K1 Theory of Computation K1 Data Structures, Cryptology and Information Theory PB Birkhäuser Basel : Imprint: Birkhäuser PP Basel SN 9783034886642 LA English (英語) CL DC23:512.7 NO 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 NO 書誌ID=1002995500; LK [E Book]http://dx.doi.org/10.1007/978-3-0348-8664-2 OL 30