Abstract
This paper presents an efficient algorithm of factoring of integers N=p^r×q for large r. By using the Jacobi signature, our algorithm can be estimated to be much faster than Chida et al.'s algorithm which can factor integers N=p^r×q efficiently if r is large and its factors are small. Chida et al. showed that their algorithm was faster than the elliptic curve method under some conditions. Therefore, this paper insists that the parameter r has to be chosen carefully when we use the encryption or signature scheme based on the hardness of factoring of integers N=p^r×q.
