Paper 2021/721

Index Calculus Attacks on Hyperelliptic Jacobians with Effective Endomorphisms

Sulamithe Tsakou and Sorina Ionica


For a hyperelliptic curve defined over a finite field $\bbbf_{q^n}$ with $n>1$, the discrete logarithm problem is subject to index calculus attacks. We exploit the endomorphism of the curve to reduce the size of the factorization basis and hence improve the complexity of the index calculus attack for certain families of ordinary elliptic curves and genus 2 hyperelliptic Jacobians defined over finite fields. This approach adds an extra cost when performing operation on the factor basis, but the experiences show that reducing the size of the factor basis allows to have a gain on the total complexity of index calculus algorithm with respect to the generic attacks.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
elliptic curvesindex calculusattack
Contact author(s)
sorina ionica @ u-picardie fr
sulamithe tsakou @ u-picardie fr
2021-05-31: received
Short URL
Creative Commons Attribution


      author = {Sulamithe Tsakou and Sorina Ionica},
      title = {Index Calculus Attacks on Hyperelliptic Jacobians with Effective Endomorphisms},
      howpublished = {Cryptology ePrint Archive, Paper 2021/721},
      year = {2021},
      note = {\url{}},
      url = {}
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