Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p
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| Format: | Artículo científico |
| Sprache: | en |
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Instituto Politécnico Nacional
2009
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| _version_ | 1876423059648282624 |
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| author | Subhamoy Maitra |
| author_facet | Subhamoy Maitra |
| contents | Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p Subhamoy Maitra Y. V. Subba Rao Pantelimon Stanica Sugata Gangopadhyay Computación Prime Numbers Discrete Log Problem Cubic Sieve Congruence In this paper we discuss the problem of finding nontrivial solutions to the Cubic Sieve Congruence problem, that is, solutions of x³ = y²z (mod p), where x,y,z <<img border=0 src="../../../../../img/revistas/cys/v12n3/a2s2.jpg"> 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 motivating by itself from a number theoretic point of view. Though we could not solve the problem completely, we could identify certain sub classes of primes where the problem can be solved in time polynomial in log p. Further we could extend the idea of Reyneri's sieve and identify some cases in it where the problem can even be solved in constant time. Designers of cryptosystems should avoid all primes contained in our detected cases. 2009 artículo científico 1405-5546 https://www.redalyc.org/articulo.oa?id=61513252002 en http://www.redalyc.org/revista.oa?id=615 Computación y Sistemas application/pdf Instituto Politécnico Nacional Computación y Sistemas (México) Num.3 Vol.12 |
| format | Artículo científico |
| id | redalyc_61513252002 |
| institution | Redalyc |
| language | en |
| publishDate | 2009 |
| publisher | Instituto Politécnico Nacional |
| spellingShingle | Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p Subhamoy Maitra Computación Prime Numbers Discrete Log Problem Cubic Sieve Congruence Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p Subhamoy Maitra Y. V. Subba Rao Pantelimon Stanica Sugata Gangopadhyay Computación Prime Numbers Discrete Log Problem Cubic Sieve Congruence In this paper we discuss the problem of finding nontrivial solutions to the Cubic Sieve Congruence problem, that is, solutions of x³ = y²z (mod p), where x,y,z <<img border=0 src="../../../../../img/revistas/cys/v12n3/a2s2.jpg"> 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 motivating by itself from a number theoretic point of view. Though we could not solve the problem completely, we could identify certain sub classes of primes where the problem can be solved in time polynomial in log p. Further we could extend the idea of Reyneri's sieve and identify some cases in it where the problem can even be solved in constant time. Designers of cryptosystems should avoid all primes contained in our detected cases. 2009 artículo científico 1405-5546 https://www.redalyc.org/articulo.oa?id=61513252002 en http://www.redalyc.org/revista.oa?id=615 Computación y Sistemas application/pdf Instituto Politécnico Nacional Computación y Sistemas (México) Num.3 Vol.12 |
| title | Nontrivial Solutions to the Cubic Sieve Congruence Problem: x³ = y²z mod p |
| topic | Computación Prime Numbers Discrete Log Problem Cubic Sieve Congruence |
| url | https://www.redalyc.org/articulo.oa?id=61513252002 |