Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method

Koyama, Kenji; Tsuruoka, Yukio

doi:10.1007/3-540-48071-4_25

Cited by 84 publications

(73 citation statements)

References 12 publications

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“…The best known method for general elliptic scalar multiplication is the sliding window algorithm using addition/subtraction chains [12,6,23]. For this, we need to precompute and store odd multiples of P , P i = iP for odd i's less than 2 w , which requires 2 w−1 − 1 elliptic additions and one elliptic doubling.…”

Section: Elliptic Scalar Multiplicationmentioning

confidence: 99%

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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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Section: Elliptic Scalar Multiplicationmentioning

confidence: 99%

“…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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“…-The cost of solving the quadratic equation (3) and determining the right solution is about half of that of a field multiplication (this is true for the finite field implementation given in [6], but no efficient method is known for tower fields [7]). …”

Section: Performance Analysismentioning

confidence: 99%

“…The fastest methods for computing a scalar multiplication [6,3] perform five point doublings for every point-addition, on average. Table 1 compares our formula, in performing a scalar multiplication, for different values of the cost-ratio r of inversion to multiplication.…”

Section: Performance Analysismentioning

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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“…In this paper, we denote affine coordinate as A [6,12], projective coordinate P [9,6], Jacobian coordinate J [3], modified Jacobian coordinate J m [10] and Chudnovsky-Jacobian coordinate J C [3]. Note that we use a different Modified Jacobian coordinate system.…”

Section: Mixed Coordinates Systemmentioning

confidence: 99%

Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor

Chung

Sim

Lee

2000

Cryptographic Hardware and Embedded Systems — CHES 2000

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Abstract. In this paper, we propose fast finite field and elliptic curve (EC) algorithms useful for embedding cryptographic functions on high performance device such that most instructions take just one cycle. In such case, the integer multiplications and additions have the same computational cost so that the computational cost analyses that were previously done in traditional manner may be invalid and in some cases the new algorithms should be introduced for fast computation. In our implementation, column major method for field multiplication and BP inversion algorithm are used for fast field arithmetic, and mixed coordinates method is used for efficient EC exponentiation. We give here analyses on various algorithms that are useful for implementing EC exponentiation on CalmRISC microcontroller with MAC2424 coprocessor, as well as new exact analyses on BP (Bailey-Paar) inversion algorithm and EC exponentiation. Using techniques shown in this paper, we implemented EC exponentiation for various coordinate systems and the best result took 122ms, assuming 50ns clock cycle.

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Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method

Cited by 84 publications

References 12 publications

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

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

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

Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor

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