2014/12/18 by Nicholas Coxon, Coxon, Nicholas
Computer Science · Mathematics · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #cs.CR #math.NT
paper · pdf · doi:10.48550/arxiv.1412.6011
arxiv created 2014/12/18 · arxiv updated 2014/12/19
The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on the construction of small modular geometric progressions. Montgomery's method is analysed in this paper and the existence of suitable geometric progressions is considered.