TY - GEN
T1 - Isogenies and the discrete logarithm problem in jacobians of genus 3 hyperelliptic curves
AU - Smith, Benjamin
PY - 2008/6/5
Y1 - 2008/6/5
N2 - We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (ℤ/2ℤ)3 (over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic p∈>∈3. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field.
AB - We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (ℤ/2ℤ)3 (over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic p∈>∈3. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field.
U2 - 10.1007/978-3-540-78967-3_10
DO - 10.1007/978-3-540-78967-3_10
M3 - Conference contribution
AN - SCOPUS:44449086875
SN - 3540789669
SN - 9783540789666
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 163
EP - 180
BT - Advances in Cryptology - EUROCRYPT 2008 - 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
T2 - 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2008
Y2 - 13 April 2008 through 17 April 2008
ER -