A fast software implementation for arithmetic operations in GF(2n)

Win, Erik De; Bosselaers, Antoon; Vandenberghe, Servaas; Gersem, Peter De; Vandewalle, Joos

doi:10.1007/bfb0034836

Cited by 82 publications

(54 citation statements)

References 10 publications

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“…If the elliptic curve is selected at random, then we expect Algorithm 1 to be up to 22% faster than the standard algorithm. For field implementations where r < 3, (for example [6,9]), Schroeppel's method [7] outperforms Algorithm 1.…”

Section: Complexity Comparisonmentioning

confidence: 99%

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

López

Dahab

1999

Lecture Notes in Computer Science

148

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Abstract. This paper describes three contributions for efficient implementation of elliptic curve cryptosystems in GF (2 n ). The first is a new method for doubling an elliptic curve point, which is simpler to implement than the fastest known method, due to Schroeppel, and which favors sparse elliptic curve coefficients. The second is a generalized and improved version of the Guajardo and Paar's formulas for computing repeated doubling points. The third contribution consists of a new kind of projective coordinates that provides the fastest known arithmetic on elliptic curves. The algorithms resulting from this new formulation lead to a running time improvement for computing a scalar multiplication of about 17% over previous projective coordinate methods.

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Section: Complexity Comparisonmentioning

confidence: 99%

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

López

Dahab

1999

Lecture Notes in Computer Science

148

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“…The algorithm reduces inversion in the composite field to inversion in the subfield GF(2~). Unlike the inversion algorithms in [21,22], the inversion algorithm is not based on Euclid's algorithm.…”

Section: M) ~-Gf(2k)mentioning

confidence: 99%

“…More recently, EC systems for the field GF((216) 11) were described independently in [22] and [1]. In all cases, field multiplication is accomplished through table look-up in the subfield GF(2n).…”

Section: Previous Workmentioning

confidence: 99%

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Efficient algorithms for elliptic curve cryptosystems

Guajardo

Paar

1997

Advances in Cryptology — CRYPTO '97

100

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Abstract. This contribution describes three algorithms for efficient implementations of elliptic curve cryptosystems. The first algorithm is an entirely new approach which accelerates the multiplications of points which is the core operation in elliptic curve public-key systems. The algorithm works in conjunction with the k-ary or sliding window method. The algorithm explores computational advantages by computing repeated point doublings directly through closed formulae rather than from individual point doublings. This approach reduces the number of inversions in the underlying finite field at the cost of extra multiplications. For many practical implementations, where field inversion is at least four times as costly as field multiplication, the new approach proofs to be faster than traditional point multiplication methods. The second algorithm deals with efficient inversion in composite Galois fields of the form GF((2'~)'~). Based on an idea of Itoh and Tsujii, we optimize the algorithm for software implementation of elliptic curves. The algorithm reduced inversion in the composite field to inversion in the subfield GF(2~). The third algorithm describes the application of the Karatsuba-Ofman Algorithm to multiplication in GF((2n)'~). We provide a detailed complexity analysis of the algorithm for the case that subfield arithmetic is performed through table look-up. We apply all three algorithms to an implementation of an elliptic curve system over GF ( ( 218) 11 ). We provide absolute performance measures for the field operations and for an entire point multiplication.

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“…In particular, much research has been conducted on fast algorithms and implementation techniques of elliptic curve arithmetic over various finite fields [12,22,24,23,8,7,2,9].…”

Section: Introductionmentioning

confidence: 99%

Fast Implementation of Elliptic Curve Arithmetic in GF(p n )

Lim

Hwang

2000

Public Key Cryptography

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Abstract. Elliptic curve cryptosystems have attracted much attention in recent years and one of major interests in ECC is to develop fast algorithms for field/elliptic curve arithmetic. In this paper we present various improvement techniques for field arithmetic in GF(p n )(p a prime), in particular, fast field multiplication and inversion algorithms, and provide our implementation results on Pentium II and Alpha 21164 microprocessors.

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A fast software implementation for arithmetic operations in GF(2n)

Cited by 82 publications

References 10 publications

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

Efficient algorithms for elliptic curve cryptosystems

Fast Implementation of Elliptic Curve Arithmetic in GF(p n )

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