Download Advances in Cryptology — CRYPTO '97: 17th Annual by Mikael Goldmann, Mats NÄslund (auth.), Burton S. Kaliski Jr. PDF

By Mikael Goldmann, Mats NÄslund (auth.), Burton S. Kaliski Jr. (eds.)

This ebook constitutes the refereed court cases of the seventeenth Annual overseas Cryptology convention, CRYPTO'97, held in Santa Barbara, California, united states, in August 1997 below the sponsorship of the overseas organization for Cryptologic study (IACR).
The quantity provides 35 revised complete papers chosen from a hundred and sixty submissions bought. additionally integrated are invited displays. The papers are geared up in sections on complexity concept, cryptographic primitives, lattice-based cryptography, electronic signatures, cryptanalysis of public-key cryptosystems, info conception, elliptic curve implementation, number-theoretic platforms, disbursed cryptography, hash capabilities, cryptanalysis of secret-key cryptosystems.

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Advances in Cryptology — CRYPTO '97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings

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Additional resources for Advances in Cryptology — CRYPTO '97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings

Example text

To answer this question we have to think about how adding and multi­ plying affect the length of numbers. It is easy to see that the sum of two numbers has length either equal to the length of the larger number or else equal to 1 plus the length of the larger number. If we add n numbers each of length at most k - that is, each less than 2k then the sum will be less than n2k. Hence, the length of the sum will be at most k + length(n). To deal with multiplication, we use the fact that a number m of length k satisfies: 2k-I ::; m < 2k.

There is no known algorithm that can determine primality of the m-th Fermat number in time that is bounded by a fixed power of log2 m. §3. Time Estimates 31 One class o f algorithms that are very far from polynomial time i s the class of exponential time algorithms. These have a time estimate of the form O ( eck) , where c is a constant. Here k is the total binary length of the integers to which the algorithm is being applied. For example, the "trial division" algorithm for factoring an integer n can easily be shown to take time O(n l /Z+< ) (where E: > 0 can be arbitrarily small).

It is almost certain that NP is a much bigger class of problems than P, but this has not been proved. The claim that P#NP is the most famous conjecture in computer science. 3. Let P 1 and P2 be two decision problems. We say that P 1 reduces to P2 (more precisely, reduces to P2 in polynomial time) if there exists an algorithm that is polynomial time as a function of the input length of P 1 and that, given any instance P1 of P1 , constructs an instance P2 of P2 such that the answer for P1 is the same as the answer for P2 .

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