9783034897235 - Number Theoretic Methods in Cryptography: Complexity lower bounds: 17 di Shparlinski, Igor (12 risultati)

PF. Condizione: New.

Condizione: New. In.

Condizione: New.

Condizione: New. pp. 198.

Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.

Paperback. Condizione: Like New. Like New. book.

Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - 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. 198 pp. Englisch.

Condizione: New. Print on Demand pp. 198 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.

Condizione: New. PRINT ON DEMAND pp. 198.

Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 equati.

Taschenbuch. Condizione: Neu. 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 Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 198 pp. Englisch.

Taschenbuch. Condizione: Neu. Number Theoretic Methods in Cryptography | Complexity lower bounds | Igor Shparlinski | Taschenbuch | ix | Englisch | 2012 | Birkhäuser | EAN 9783034897235 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.