Advances in Elliptic Curve Cryptography
Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.
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addition algorithm analysis apply assume attacker bits Boneh break called challenge Chapter characteristic choose chosen ciphertext complexity compute consider construction cryptographic decryption defined definition denote derivation divides divisor ECDSA ECIES efficient element elliptic curve encryption entity equal equation example exists extension factor field finite field follows forger Frobenius function genus give given hash function Hence identity identity-based implementation input integer isogeny Lemma lift means methods modulo multiplication Note obtain operations oracle OUTPUT pairing parameters particular polynomial possible prime private key probability problem proof properties protocol public key queries random reduced requires result Return root runs satisfies scheme secret selective shows side-channel signature signature scheme simple solve standard step subgroup symmetric takes techniques Theorem trace
Pagina 267 - 95, pages 171-183, 1995.  P. Kocher, J. Jaffe, and B. Jun. Differential power analysis. In Proceedings of 19th International Advances in Cryptology Conference - CRYPTO '99, pages 388-397, 1999.  JJ. Quisquater and D. Samyde. Electromagnetic analysis (ema): Measures and counter-measures for smart cards.
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