Categories of Pairings

Selection of Pairings Reaching

Hyperelliptic Pairings

We survey recent research on pairings on hyperelliptic curves and present a comparison of the performance characteristics of pairings on elliptic curves and hyperelliptic curves. Our analysis indicates that hyperelliptic curves are not more efficient than elliptic curves for general pairing applications.

Height Pairings

generalizing the Neron-Tate pairing on abelian varieties. Note that our cycles are of a dimension where their expected intersection has dimension −1. Example 1.1 ([9], [3]) Let C/K be a smooth projective curve, with ∞ ∈ C(K) giving i : C ↪→ Pic(C). Let 〈·, ·〉NT : Pic(C)(K)×Pic(C)(K)→ R be the Neron-Tate height pairing, identifying P̂ic(A) ∼= Pic(A) via the theta divisor. Then, once we have defin...

Compressed Pairings

Pairing-based cryptosystems rely on bilinear non-degenerate maps called pairings, such as the Tate and Weil pairings defined over certain elliptic curve groups. In this paper we show how to compress pairing values, how to couple this technique with that of point compression, and how to benefit from the compressed representation to speed up exponentiations involving pairing values, as required i...

Cryptographic Pairings

This article appeared as Chapter 9 of the book Topics in Computational Number Theory inspired by Peter L. Montgomery, edited by Joppe W. Bos and Arjen K. Lenstra and published by Cambridge University Press. See www. cambridge.org/9781107109353. There are cross-references to four chapters of the same book: Chapter