Abstract
The problem of finite field basis conversion is to convert from the representation of a field element in one basis to the representation of the element in another basis. This paper presents new algorithms for the problem that require much less storage than previous solutions. For the finite field GF(2m), for example, the storage requirement of the new algorithms is only O(m) bits, compared to O(m 2) for previous solutions. With the new algorithms, it is possible to extend an implementation in one basis to support other bases with little additional cost, thereby providing the desired interoperability in many cryptographic applications.
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References
ANSI X9.62: The Elliptic Curve Digital Signature Algorithm (ECDSA), draft, November 1997.
T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. The MIT Press, 1990.
IEEE P1363: Standard Specifications for Public-Key Cryptography, Draft version 3, May 1998. http://stdsbbs.ieee.org/groups/1363/draft.html.
A. Menezes, I. Blake, X. Gao, R. Mullin, S. Vanstone, and T. Yaghoobian. Applications of Finite Fields. Kluwer Academic Publishers, 1993.
A. Menezes. Elliptic Curve Public Key Crypto systems. Kluwer Academic Publishers, 1993.
R. Lidl and H. Niederreiter. Finite Fields, volume 20 of Encyclopedia of Mathematics and Its Applications. Addison-Wesley, 1983.
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© 1999 Springer-Verlag Berlin Heidelberg
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Kaliski, B.S., Yin, Y.L. (1999). Storage-Efficient Finite Field Basis Conversion. In: Tavares, S., Meijer, H. (eds) Selected Areas in Cryptography. SAC 1998. Lecture Notes in Computer Science, vol 1556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48892-8_7
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DOI: https://doi.org/10.1007/3-540-48892-8_7
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