Efficient explicit formulae for genus 3 hyperelliptic curve cryptosystems over binary fields

نویسندگان

  • Xinxin Fan
  • Thomas J. Wollinger
  • Guang Gong
چکیده

The ideal class groups of hyperelliptic curves(HECs) can be used in cryptosystems based on the discrete loga-rithm problem. Recent developments of computational technolo-gies for scalar multiplications of divisor classes have shown thatthe performance of hyperelliptic curve cryptosystems (HECC) iscompatible to that of elliptic curve cryptosystems (ECC). Espe-cially, genus 3 HECC are well suited for all kinds of embeddedprocessor architectures, where resources such as storage, time orpower are constrained, because of their short operand sizes. Inthis paper, we investigate the efficient explicit formulae for genus3 HECs over both prime fields and binary fields, and analyze howmany field operations are needed. First, we improve the explicitformulae for genus 3 HECs over binary fields using the thetadivisors which can save about 20% ∼ 50% multiplications forfour cases, and extend the method to genus 3 HECs over primefields. We then discuss acceleration of the divisor class doublingfor genus 3 HECs over binary fields. By constructing birationaltransformations of variables, we find four types of curves whichcan lead to much faster divisor class doubling and give thecorresponding explicit formulae. Especially, for special genus 3HECs over binary fields with h(X) = 1, we obtain the fastestexplicit doubling formula which only requires 1I + 10M + 11S.Thirdly, we propose the inversion-free explicit formulae for genus3 HEC over both prime fields and binary fields by introducingone more coordinate to collect the common denominator of theusual six coordinates. Finally, comparisons with the known resultsin terms of field operations and an implementation of genus 3HECC over three binary fields on a Pentium-4 processor areprovided.

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عنوان ژورنال:
  • IET Information Security

دوره 1  شماره 

صفحات  -

تاریخ انتشار 2007