Efficient modular exponential algorithms compatible with hardware implementation of public‐key cryptography. Issue 16 (25th July 2016)

• Record Type: Journal Article
• Authors: Vollala, Satyanarayana; Geetha, Krishnan; Ramasubramanian, Natarajan
• Is Part Of: Security and communication networks. Volume 9:Issue 16(2016)
• Page Start: 3105
• Page End: 3115
• Publication Date: 2016-07-25
• Subjects: modular multiplication -- modular exponentation -- public‐key cryptography -- Montgomery multiplication; Computer networks -- Security measures -- Periodicals; Computer security -- Periodicals; Cryptography -- Periodicals; 005.805
• DOI: 10.1002/sec.1511
• Languages: English
• ISSNs: 1939-0114

Abstract

Abstract: It is widely recognized that the public‐key cryptosystem is playing a pivotal role to provide the security services not only in electronic world but also for secured key exchanges in military applications. Modular exponentiation is the crucial, but expensive, operation in several public‐key cryptostyems, which makes use of repeated modular multiplications. So, the performance of public‐key cryptography is highly influenced by the competent implementation of modular exponentiation. In order to speed up the entire process, it is essential to develop the modular exponential algorithms, which reduces the frequency of modular multiplications, and the time required to implement each modular multiplication. In this paper, we present the bit forwarding (BFW) techniques to reduce the count of modular multiplications for hardware implementation of modular exponentiation. Montgomery multiplication method is customized according to the needs of BFW techniques and implemented with radix‐2, named as adaptable Montgomery multiplication, and also implemented with high radix and named as adaptable high‐radix Montgomery multiplication. It has been computed that it is possible to reduce 11.16%, 15.14% and 18.20% of modular multiplications by BFW1, BFW2, and BFW3 algorithms, respectively, for 1024‐bit exponent in comparison with prevailing techniques. This reduction will result in increased throughput and decreased power consumption. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : Bit forwarding techniques have been proposed for hardware implementation of modular exponentiation. They claim reduction in number of modular multiplications that will end up in increased throughput and decreased power consumption. In addition to these algorithms, adaptable Montgomery multiplication and adaptable high‐radix Montgomery multiplication have also been proposed to compute modular exponentiation and also for point arithmetic in other cryptographic techniques such as elliptic curve cryptography. The correctness of all the proposed algorithms has been ratified with relevant mathematical procedures.