Must_print_DMR_AMM.573.209.pdf - FAULT TOLERANT TECHNIQUES...

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FAULT TOLERANT TECHNIQUES FOR FINITE FIELD MULTIPLIERS B.Sargunam 1,a* and Dr.R.Dhanasekaran 2,b 1 Assistant Professor, Department of Electronics and Communication Engineering, Avinashilingam University for Women, Coimbatore, India. 2 Professor & Director-Research, Department of Electrical and Electronics Engineering, Syed Ammal Engineering College, Ramanathapuram, India. a* [email protected], b [email protected] Keywords: Finite Field, Concurrent Error Detection, Triple Modular Redundancy, Double Modular Redundancy Abstract . The use of finite field multipliers in the critical applications like elliptic curve cryptography needs Concurrent Error Detection (CED) and correction at architectural level to provide high reliability. This paper discusses fault tolerant technique for polynomial representation based finite field multipliers. The detection and correction are done on-line. We use a combination of Double Modular Redundancy (DMR) and Concurrent Error Detection (CED) techniques. The fault tolerant finite field multiplier is coded in VHDL and simulated using Modelsim. Further, the proposed multiplier with fault tolerant capability is synthesized and results are analyzed with respect to area occupied, input and output pin counts and delay. Our technique, when compared with existing techniques, gives better performance. We show that our concurrent error detecting multiplier over GF(2 m ) requires less than 200% extra hardware, whereas with the traditional fault tolerant techniques, such as Triple Modular Redundancy (TMR), overhead is more than 200%. Introduction In recent years, finite fields have received a lot of attention because of their application in error-control coding, cryptography and pseudorandom number generation. They have also been used in digital signal processing to compute convolutions. Finite field GF(2 m ) is defined by an irreducible polynomial of degree m and contains 2 m elements. The elements of GF(2 m ) can be represented in three different bases. These are canonical (or standard or polynomial) basis, normal basis and dual basis. Among the finite field arithmetic operations multiplication is the most important, complex and time consuming[1]. The dual basis multiplier occupies the smallest area if the basis conversion is not included. The normal basis multiplier is more effective in finding inverse or squaring or exponentiation of the finite field element. However, the order of the field goes up, the area of normal basis multiplier increases dramatically. Multiplication in polynomial basis is very simple and need not require any basis conversion. The design and expansion to higher order polynomial basis multipliers are easier due to their regular structure. The polynomial basis multipliers are, therefore, more widely used compared with dual basis multipliers and normal basis multipliers.
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