Fast Parallel Exponentiation Algorithm for RSA Public-Key Cryptosystem

Abstract

We know the necessity for information security becomes more widespread in these days, especially for hardware-based implementations such as smart cards chips for wireless applications and cryptographic accelerators. Fast modular exponentiation algorithms are often considered of practical significance in public-key cryptosystems. The RSA cryptosystem is one of the most widely used technologies for achieving information security. The main task of the encryption and decryption engine of RSA cryptosystem is to compute M E mod N . Because the bit-length of the numbers M , E, and N would be about 512 to 1024 bits now, the computations for RSA cryptosystem are time-consuming. In this paper, an efficient technique for parallel computation of the modular exponentiation is proposed and our algorithm can reduce time complexity. We can have the speedup ratio as 1.06 or even 2.75 if the proposed technique is used. In Savas-Tenca-Koc algorithm, they design a multiplier with an insignificant increase in chip area (about 2.8%) and no increase in time delay. Our proposed technique is faster than Savas-Tenca-Koc algorithm in time complexity and improves efficiency for RSA cryptosystem.

Note on Optimal Trees for Parallel Hash Functions

“…The present work is in line with what has been done for parallel exponentiation [4,5,1,3,6]. We consider hash tree modes using a rate-1 hash (or compression) function, i.e.…”

State of the Art Parallel Approaches For Rsa Public Key Based Cryptosystem

“…Thereafter in 2004, Chia-Long Wu et al presented "Fast Parallel Exponentiation Algorithm for RSA Public-Key Cryptosystem" [8]. In this paper they proposed an efficient technique for parallel computation of modular exponentiation where they get the speedup of 1.06 to 2.75.…”

Optimization of Tree Modes for Parallel Hash Functions: A Case Study

“…While we focus on the case of trees having all their leaves at the same depth, we are interested in minimizing the depth (parallel time) of the circuit and the width (number of processors involved). This kind of work has been done for parallel exponentiation in finite fields [32,34,1,22,36] where the multiplication operator is both associative and commutative. In the case of parallel hashing, the considered operator can be a FIL (Fixed-Input Length) compression function.…”