Fast Key Exchange with Elliptic Curve Systems

Schroeppel, Richard; Orman, Hilarie; O’Malley, Sean; Spatscheck, Oliver

doi:10.1007/3-540-44750-4_4

Cited by 151 publications

(109 citation statements)

References 25 publications

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“…Schroeppel [6] improved the doubling point formula saving the multiplication by the constant b. His improved doubling point formula is :…”

Section: Elliptic Curves Over Gf (N )mentioning

confidence: 99%

“…-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%

“…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%

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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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“…Schroeppel [6] improved the doubling point formula saving the multiplication by the constant b. His improved doubling point formula is :…”

Section: Elliptic Curves Over Gf (N )mentioning

confidence: 99%

Section: Performance Analysismentioning

confidence: 99%

Section: Performance Analysismentioning

confidence: 99%

Section: Complexity Comparisonmentioning

confidence: 99%

See 2 more Smart Citations

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

López

Dahab

1999

Lecture Notes in Computer Science

148

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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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An effective ECC‐based user access control scheme with attribute‐based encryption for wireless sensor networks

Chatterjee

Das

2014

Security Comm Networks

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For critical applications, real-time data access is essential from the nodes inside a wireless sensor network (WSN). Only the authorized users with unique access privilege should access the specific, but not all, sensing information gathered by the cluster heads in a hierarchical WSNs. Access rights for the correct information and resources for different services from the cluster heads to the genuine users can be provided with the help of efficient user access control mechanisms. In this paper, we propose a new user access control scheme with attribute-based encryption using elliptic curve cryptography in hierarchical WSNs. In attribute-based encryption, the ciphertexts are labeled with sets of attributes and secret keys of the users that are associated with their own access structures. The authorized users with the relevant set of attributes can able to decrypt the encrypted message coming from the cluster heads. Our scheme provides high security. Moreover, our scheme is efficient as compared with those for other existing user access control schemes. Through both the formal and informal security analysis, we show that our scheme has the ability to tolerate different known attacks required for a user access control designed for WSNs. Furthermore, we simulate our scheme for the formal security verification using the widelyaccepted automated validation of Internet security protocols and applications tool. The simulation results demonstrate that our scheme is secure. Figure 2. A user access structure, where the user is able to decrypt the sensor node data.Security Comm. Networks (2014)

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Fast Key Exchange with Elliptic Curve Systems

Cited by 151 publications

References 25 publications

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

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

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

An effective ECC‐based user access control scheme with attribute‐based encryption for wireless sensor networks

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