Applications of Bilinear Maps in Cryptography

Mathematics;cryptography;bilinear map;elliptic curve;pairing;identity-based

Gagne, Martin

University of Waterloo

关键词: Mathematics;    cryptography;    bilinear map;    elliptic curve;    pairing;    identity-based;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1134/1/m2gagne2002.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as identity-based encryption, short signatures and one-round tripartite key agreement. This thesis explains the notion of bilinear maps and surveys the applications of bilinear maps in the three main fields of cryptography: encryption, signature and key agreement. We also show how these maps can be constructed using the Weil and Tate pairings in elliptic curves.