TAILIEUCHUNG - A Hardware implementation of Winograd Fourier Transform algorithm for Cryptography

This paper presents a hardware implementation of efficient algorithms that uses the mathematical framework. The framework based on the Winograd’s Fourier Transform Algorithm, obtaining a set of formulations that simplify cyclic convolution (CC) computations and CRT. | A Hardware implementation of Winograd Fourier Transform algorithm for Cryptography and bagan 1 Assistant Professor Department of Electronics and Communication Engineering Sri Venkateswara College of Engineering Sriperumbudur -602108. 2Professor Department of Electronics Madras Institute of Technology Anna University Chrompet Campus Chennai-600044 Tamil Nadu. INDIA sathish@ kbb@ ABSTRACT This paper presents a hardware implementation of efficient algorithms that uses the mathematical framework. The framework based on the Winograd s Fourier Transform Algorithm obtaining a set of formulations that simplify cyclic convolution CC computations and CRT. In particularly this work focuses on the arithmetic complexity of a multiplication and when there is multiplication then the product represents a CC computational operation The proposed algorithms is compared against existing algorithms developed making use of the FFT and it is shown that the proposed algorithms exhibit an advantage in computational efficiency .This design is most useful when dealing with large integers and is required by many modern cryptographic systems. The Winograd Fourier Transform Algorithm WFTA is a technique that combines the Rader s index mapping and Winograd s short convolution modules for prime-factors into a composite-N Fourier Transform structure with fewer multipliers O N . While theoretically interesting WFTA s are very complicated and different for every length. It can be implemented on modern processors with few hardware multipliers and hence is very useful in practice today. Keywords Discrete Fourier Transform Chinese Remainder Theorem. INTRODUCTION Many popular crypto-systems like the RSA encryption scheme 12 the Diffie-Hellman DH key agreement scheme 13 or the Digital Signature Algorithm DSA 14 are based on long integer modular exponentiation A major difference between the RSA scheme and cryptosystems based on the discrete logarithm

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• A Hardware implementation
• Winograd Fourier Transform
• Discrete fourier transform
• Winograd fourier transform algorithm
• Winograd’s small convolution algorithm
• Transform algorithm for Cryptography
• Cryptographic Hardware and Embedded Systems
• The Embedded Systems
• The Cryptographic Hardware
• Modular multiplication in hardware
• XTR Implementation on Reconfigurable Hardware
• Secure the computer
• The Modular Multiplication
• The Software Implementation
• The Hardware Implementation
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• Analysis of the Architectures
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• Hardware implementation
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• Power saving
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• CUDA Enabled Graphics Hardware
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• Previous Work of Sequence Alignment CUDA
• Profiling of MAFFT
• A HARDWARE ALGORITHM
• HIGH SPEED MORPHEME EXTRACTION
• ITS IMPLEMENTATION
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