On computing ordN(2) and its application

Authors:
Lihua Liu;Zhengjun Cao
Affiliations:
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China;Inst. of Sys. Sci., Academy of Math. and Sys. Sci., Ch. Acad. of Sci. and Dept. of Math., Shanghai Univ., Shanghai, China and Key Lab of Math. Mech., Acad. of Math. and Sys. Sci., Ch. Acad. of Sci ...
Venue:
Information and Computation
Year:
2006

Citing 2
Cited 0

The quadratic sieve factoring algorithm

Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

SIAM Journal on Computing

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Abstract

Shor proposed a polynomial time algorithm for prime factorization on quantum computers. For a given number N, he gave an algorithm for finding the order r of an element x in the multiplicative group (mod N). The method succeeds because factorization can be reduced to finding the order of an element using randomization. But the algorithm has two shortcomings, the order of the number must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome in a particular case, i.e., N is an RSA modulus. In this paper, we propose a new quantum algorithm for factoring RSA modulus without the two drawbacks. Moreover, we show that the cost of the algorithm mainly depends on the calculation of ordN(2).