We present a novel idea to compute square roots over some families of finite fields. Our algorithms are deterministic polynomial time and can be proved by elementary means (without assuming anyâ€¦ (More)

We present a unconditional deterministic primality proving algorithm for Cullen numbers. The expected running time and the worst case running time of the algorithm are Ã•(logN) bit operations andâ€¦ (More)

We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and theâ€¦ (More)

We first show a deterministic algorithm for taking $r$-th roots over $\F_q$ without being given any $r$-th nonresidue, where $\F_q$ is a finite field with $q$ elements and $r$ is a small prime suchâ€¦ (More)

We present a new record on computing specific bits of Pi, the mathematical constant, and discuss performing such computations on Apache Hadoop clusters. The specific bits represented in hexadecimalâ€¦ (More)

The running time is O(r log n). It can be shown by elementary means that the required r exists in O(log n). So the running time is O(log n). Moreover, by Fouvryâ€™s Theorem [8], such r exists in O(logâ€¦ (More)

We present an algorithm to decide the primality of Proth numbers, N=2^e t+1, without assuming any unproven hypothesis. The expected running time and the worst case running time of the algorithm are Oâ€¦ (More)

We present MapReduce-SSA, an integer multiplication algorithm using the ideas from SchÃ¶nhage-Strassen algorithm (SSA) on MapReduce. SSA is one of the most commonly used large integer multiplicationâ€¦ (More)