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Generalized Mersenne Numbers in Pairing-Based Cryptography

01 Jan 2006-

TL;DR: The author’s home country, the United States, and some of the characters from the film adaptation are fictitious.

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter

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Journal ArticleDOI
TL;DR: This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
Abstract: Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper suggests ways to solve these currently open problems. It also discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.

14,068 citations


Book
01 Jan 1996
TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Abstract: From the Publisher: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

13,370 citations



Journal ArticleDOI
Taher Elgamal1
23 Aug 1985
TL;DR: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem that relies on the difficulty of computing discrete logarithms over finite fields.
Abstract: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.

6,871 citations


Book ChapterDOI
19 Aug 2001
TL;DR: This work proposes a fully functional identity-based encryption scheme (IBE) based on the Weil pairing that has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem.
Abstract: We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

6,596 citations