Alberto Will attend ECC2011 (summer school and workshop http://ecc2011.loria.fr/ ) in Nancy in September, anybody will be there too ? :D
Alberto is having a great time in Dhulikhel (Nepal) at "CIMPA School of Number Theory in Cryptography and Its Applications" !!! :)
Alberto is having a great time in Dhulikhel (Nepal) at "CIMPA School of Number Theory in Cryptography and Its Applications" !!! :)
University of Naples "Federico II"
Graduate Student, Mathematics and Applications
University of Naples "Federico II"
Thesis Title: Il problema del logaritmo discreto sulle curve ellittiche e relazioni con la crittografia (Elliptc curves discrete logarithm problem and relations with cryptography).
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Aldo De Luca
Maurizio Laporta |
About
A short summary of my thesis work:
My thesis is split in four chapters:
Chapter 1: An introduction on elliptic curves on R on Q and on finite fields; some computational aspects related to elliptic curves on finite fields (with details on Hasse's Theorem and Deuring's Theorem).
Chapter 2: Elliptic curves discrete logarithm problem (ECDLP); Applications of ECDLP in cryptography: Diffie-Hellman key exchange, Massey-Omura encryption, ElGamal public key encryption, ElGamal digital signature, Elliptic Curves Digital Signature Algorithm (ECDSA), Elliptic Curve Integrated Encryption Scheme (ECIES); How to embed plain text into points of an elliptic curve.
Chapter 3: Generic methods for discrete logarithm problem resolution: Baby-step Giant step,Rho-Pollard (with details on iterating function and collision detection), Lambda-Pollard, Pohlig-Hellman, Index calculus; Isomorphisms-based methods for ECDLP resolution: Menezes-Okamoto-Vanstone (with details on Weil Pairing and Miller's algorithm to compute Weil pairing), Frey-Rück, Semaev/Satoh-Araki-Smart.
Chapter 4: In this chapter is described an implementation of Pollard's Rho algorithm for NVidia CUDA architecture using some recent results and some specific optimization for CUDA of modular arithmetic functions.
