Field extensions and index calculus on algebraic curves

Discrete logarithm index calculus algorithms are usually more efficient for non-hyperelliptic curves (Diem’s method) than for hyperelliptic curves (Gaudry’s method). However when the field of definition is not prime, Nagao’s algorithm is even faster asymptotically, but is more efficient for hyperell...

Full description

Saved in:
Bibliographic Details
Published inArithmetic, Geometry, Cryptography and Coding Theory Vol. 686; pp. 187 - 199
Main Author Vitse, Vanessa
Format Book Chapter
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society
SeriesContemporary Mathematics
Subjects
Jacobian variety
divisor class group
Discrete logarithm problem
index calculus
hyperelliptic curve cryptography
Online AccessGet full text
ISBN9781470428105
1470428105
ISSN0271-4132
1098-3627
DOI10.1090/conm/686/13784

Cover

More Information
Summary:Discrete logarithm index calculus algorithms are usually more efficient for non-hyperelliptic curves (Diem’s method) than for hyperelliptic curves (Gaudry’s method). However when the field of definition is not prime, Nagao’s algorithm is even faster asymptotically, but is more efficient for hyperelliptic curves than for non-hyperelliptic ones. A natural question is then whether it is possible to adapt Nagao’s method and design an index calculus that takes advantage of both the field extension and the non-hyperellipticity. In this work we explain why this is not possible, and why the asymptotic complexity of Nagao’s algorithm is optimal using the known decomposition techniques.
ISBN:9781470428105
1470428105
ISSN:0271-4132
1098-3627
DOI:10.1090/conm/686/13784