Evolution of Hyperelliptic Curve Cryptosystems

Chatterjee, Kakali; Gupta, Daya

doi:10.1007/978-3-642-11659-9_23

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…The idea to use HEC for cryptographic applications has been further analyzed and implemented in software and hardware oriented platforms by Kuroki et al [26], Sakai and Sakurai [27], Nagao [28], and Smith [29]. We discussed the evolution of Hyperelliptic Curve Cryptosystems in [30].…”

Section: Explicit Formula For Genus 3 Curvesmentioning

confidence: 99%

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Performance Study of genus 3 Hyperelliptic Curve Cryptosystem

Gupta¹,

De²,

Chatterjee³

2012

Journal of Information Processing Systems

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Hyperelliptic Curve Cryptosystem (HECC) is well suited for all kinds of embedded processor architectures, where resources such as storage, time, or power are constrained due to short operand sizes. We can construct genus 3 HECC on 54-bit finite fields in order to achieve the same security level as 160-bit ECC or 1024-bit RSA due to the algebraic structure of Hyperelliptic Curve. This paper explores various possible attacks to the discrete logarithm in the Jacobian of a Hyperelliptic Curve (HEC) and addition and doubling of the divisor using explicit formula to speed up the scalar multiplication. Our aim is to develop a cryptosystem that can sign and authenticate documents and encrypt / decrypt messages efficiently for constrained devices in wireless networks. The performance of our proposed cryptosystem is comparable with that of ECC and the security analysis shows that it can resist the major attacks in wireless networks.

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Section: Explicit Formula For Genus 3 Curvesmentioning

confidence: 99%

“…We have considered the hyperelliptic curve : +1 of genus 3 over the finite field 2 7 . P=( 30 1 (after the first round). The timings have been measured on a PC with an Intel Core 2DUO CPU T6400@ 2.00GHz and windows vista operating system having jdk1.…”

Section: Performance Analysismentioning

confidence: 99%

Performance Study of genus 3 Hyperelliptic Curve Cryptosystem

Gupta¹,

De²,

Chatterjee³

2012

Journal of Information Processing Systems

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“…Pelzl and Wollinger [6], [15], [16] propose a cost effective explicit formula for genus 2 and 3 curves and give first implementation of a HEC cryptosystem on an embedded processor. We have discussed Evolution of Hyperelliptic Curve Cryptosystems in [17].…”

Section: Fig 1: Hierarchy Of Operations Of Curve Based Cryptosystemsmentioning

confidence: 99%

Software Implementation of Curve based Cryptography for Constrained Devices

Chatterjee¹,

De²,

Gupta³

2011

IJCA

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Curve based cryptography are preferred for embedded hardware since they require shorter operand size than RSA to attain the same security level. So ECC and HECC are more suitable in constrained environment such as smart cards if we can select suitable curves and efficient scalar multiplication technique to speed up arithmetic on the curve. With this in view, this paper explores in details the main operations like scalar multiplication, group operations on Jacobian, finite field operations etc which are the prime steps for efficient implementation of ECC / HECC. We also have compared the timings of main operations like scalar multiplication, encryption and decryption of Elliptic and Hyperelliptic curve cryptosystems to study the relative performance of these cryptosystems.

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Evolution of Hyperelliptic Curve Cryptosystems

Cited by 2 publications

References 8 publications

Performance Study of genus 3 Hyperelliptic Curve Cryptosystem

Performance Study of genus 3 Hyperelliptic Curve Cryptosystem

Software Implementation of Curve based Cryptography for Constrained Devices

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