Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation
Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((213)23) instead of in GF(2299). Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.
Guajardo, Jorge, Efficient Algorithms for Elliptic Curve Cryptosystem, Master’s thesis, Worcester Polytechnic Institute, 1997.
Savas, E. & Koc, C.K., Efficient Methods for Composite Fields Arithmetic, Technical report, Oregon State University, 1999.
Paar, Christof, Efficient VLSI Architectures for Bit-parallel Computation in Galois Fields, PhD thesis, 1994.
Deschamps, Jean-Pierre, Imana, Jose Luis& Sutter, Gustavo D., Hardware Implementation of Finite-Field Arithmetic, The McGraw Hill Companies, Inc., 2009.
Hoffstein, Jeffrey, Pipher, Jill & Silverman, Joseph H., An Introduction to Mathematical Cryptography, Springer Science+Business Media, LLC, 2008.
Edoardo, Mastrovito, VLSI Architecture for Computations in Galois Fields, PhD thesis, Linkoping University, 1991.
Paar, Christof, Fast Arithmetic Architectures for Public-Key Algorithms over Galois Fields GF((2n)m), Number 1233 in Lecture Notes in Computer Science, Springer-Verlag, pp. 363–378, 1997.
Paar, Christof & Fleischmann, Peter, Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents, IEEE Transactions on Computers, 48(10), pp. 1025–1034, October 1999.
Rosner, Martin Christopher, Elliptic Curve Cryptosystems on Reconfigurable Hardware, Master’s thesis, Worcester Polytechnic Institute, May 1998.
- There are currently no refbacks.
ITB Journal Publisher, LPPM – ITB,
Center for Research and Community Services (CRCS) Building Floor 7th,
Jl. Ganesha No. 10 Bandung 40132, Indonesia,