Paper 2014/385

Jacobian Coordinates on Genus 2 Curves

Huseyin Hisil and Craig Costello


This paper presents a new projective coordinate system and new explicit algorithms which together boost the speed of arithmetic in the divisor class group of genus 2 curves. The proposed formulas generalise the use of Jacobian coordinates on elliptic curves, and their application improves the speed of performing cryptographic scalar multiplications in Jacobians of genus 2 curves over prime fields by an approximate factor of 1.25x. For example, on a single core of an Intel Core i7-3770M (Ivy Bridge), we show that replacing the previous best formulas with our new set improves the cost of generic scalar multiplications from 243,000 to 195,000 cycles, and drops the cost of specialised GLV-style scalar multiplications from 166,000 to 129,000 cycles.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Genus 2hyperelliptic curvesexplicit formulasJacobian coordinatesscalar multiplication.
Contact author(s)
huseyin hisil @ yasar edu tr
2014-05-31: revised
2014-05-30: received
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Short URL
Creative Commons Attribution


      author = {Huseyin Hisil and Craig Costello},
      title = {Jacobian Coordinates on Genus 2 Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2014/385},
      year = {2014},
      note = {\url{}},
      url = {}
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