Title :
A Parallel GNFS Algorithm with the Improved Linbox Montgomery Block Lanczos Method for Integer Factorization
Author :
Yang, Laurence Tianruo ; Xu, Li ; Park, Jong Hyuk
Author_Institution :
Dept. of Comput. Sci., St. Francis Xavier Univ., Antigonish, NS
Abstract :
RSA algorithm is a very popular public key cryptosystem which has been widely used in industries. Its security relies on the difficulty of factoring large integers. The general number field sieve (GNFS) is so far the best known algorithm for factoring large integers over 110 digits. The Montgomery´s block Lanczos method from Linbox is for solving large and sparse linear systems over finite fields and it can be integrated into GNFS algorithm. This paper introduces an improved Montgomery block Lanczos method, based on the version developed in Linbox, integrated with our previously developed parallel GNFS algorithm. This method has a better performance comparing with the original one, can find more solutions or dependencies than the original one with less time complexities. Implementation details and experimental results will be provided as well in the paper as well.
Keywords :
parallel algorithms; public key cryptography; Linbox Montgomery block Lanczos method; RSA algorithm; general number field sieve; integer factorization; parallel GNFS algorithm; public key cryptosystem; Computer industry; Computer science; Galois fields; Information security; Internet; Libraries; Linear systems; Public key; Public key cryptography; Sparse matrices; GNFS method; RSA; integer factorization; parallel; public-key crypsystems;
Conference_Titel :
Information Security and Assurance, 2008. ISA 2008. International Conference on
Conference_Location :
Busan
Print_ISBN :
978-0-7695-3126-7
DOI :
10.1109/ISA.2008.113
