On the implementation of composite-order bilinear groups in cryptographic protocols

Cryptography;Bilinear Pairings;Composite Order Groups

Sisneros, Severiano ; Blahut ; Richard E.

关键词: Cryptography;    Bilinear Pairings;    Composite Order Groups;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/42280/Severiano_Sisneros.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis we present the latest developments in composite-order pairing basedcryptography. We first develop the necessary mathematical background. We describeelliptic curves over finite fields, as well as rational functions and divisors on such curves.Bilinear pairings on elliptic curves are explained. We then introduce bilinear groups ofcomposite order and how they are used to create pairing-based cryptosystems. We presenttwo cryptosystems using composite-order groups. We conclude with a discussion of currentresearch.