Summary The problem of designing efficient parallel algorithms to calculate the product of n numbers when the multipliers are large is a fundamental problem in many applications of computer science such as cryptography. In this work, we present a new parallel algorithm on exclusive read shared memory model. The performance of the introduced algorithm is measured based on three factors, namely, (1) the number of cores, (2) the size of the array, and (3) the size of the multiplier. The experimental study on a multi core system reveals that the introduced algorithm is faster than the best‐known optimal parallel algorithm. The improvement of the proposed algorithm in processing time compared to the best known parallel algorithm is 80% when the size of the array was 220 and the sizes of the multiplier were 1024, 2048, and 4096 bits. Moreover, our algorithm is a highly scalable parallel algorithm compared with the best‐known optimal parallel algorithm.

Let (n = pq, e) be an RSA public key with private exponent d = ndelta, where p and q are large primes of the same bit size. Suppose that poges radicn be an approximation of p with |p - po| les 1/8nalpha, alpha les 1/2. Using continued fractions, we show that the system is insecure if delta < 1-alpha/2. Our result is deterministic polynomial time and an extension of Coppersmith's result on a factorization.