Nontrivial solutions to the cubic sieve congruence problem x^3=y^2 z (mod p)
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Authors
Maitra, Submahoy
Rao, Subba, Y. V.
Stănică, Pantelimon
Gangopadhyay, Sugata
Subjects
Cubic Sieve congruence
Discrete Log problem
prime numbers
Discrete Log problem
prime numbers
Advisors
Date of Issue
2009
Date
Publisher
Language
Abstract
In this paper we discuss the problem of finding nontrivial solutions to the Cubic Sieve Congruence probem, that is, solutions of x2 = y2z (mod p), where x,y,z < p1/2 and x3 = y2z. The solutions to this problem are useful in solving the Discrete Log Problem or factorization by index calculus method.. Apart from the cryptographic interest, this problem is motivatin by itself from a number theoretic point of view. Though we could not solve the problem completely, we could identify certain subclasses of primes where the problem can be solved in time polynomial in log p. Further we could extend the idea of Reynert's sieve and identify some cases where the problem can even be solved in constant tiem. Designers of ctyptosystems should avoid all primes contained in our detected cases.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
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Citation
Special Issue on Applied Cryptography & Data Security in Journal of “Computacion y Sistemas” 12:3 (2009) (eds. F. Rodrıguez-Henrıquez, D. Chakraborty), 253-266.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.