Handbook of Elliptic and Hyperelliptic Curve Cryptography~tqw~ darksiderg

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  Handbook of Elliptic and Hyperelliptic Curve Cryptography~tqw~ darksiderg
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  *******************************************************************************<br /> Handbook of Elliptic and Hyperelliptic Curve Cryptography <br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 6,913,834 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> The discrete logarithm problem based on elliptic and hyperelliptic curves has <br /> gained a lot of popularity as a cryptographic primitive. The main reason is that <br /> no subexponential algorithm for computing discrete logarithms on small genus <br /> curves is currently available, except in very special cases. Therefore curve-<br /> based cryptosystems require much smaller key sizes than RSA to attain the same <br /> security level. This makes them particularly attractive for implementations on <br /> memory-restricted devices like smart cards and in high-security applications.<br /> <br /> Table of Contents<br /> 1 Introduction to public-key cryptography 1<br /> I Mathematical background <br /> 2 Algebraic background 19<br /> 3 Background on p-adic numbers 39<br /> 4 Background on curves and Jacobians 45<br /> 5 Varieties over special fields 87<br /> 6 Background on pairings 115<br /> 7 Background on Weil descent 125<br /> 8 Cohomological background on point counting 133<br /> II Elementary arithmetic <br /> 9 Exponentiation 145<br /> 10 Integer arithmetic 169<br /> 11 Finite field arithmetic 201<br /> 12 Arithmetic of p-adic numbers 239<br /> III Arithmetic of curves <br /> 13 Arithmetic of elliptic curves 267<br /> 14 Arithmetic of hyperelliptic curves 303<br /> 15 Arithmetic of special curves 355<br /> 16 Implementation of pairings 389<br /> IV Point counting <br /> 17 Point counting on elliptic and hyperelliptic curves 407<br /> 18 Complex multiplication 455<br /> V Computation of discrete logarithms <br /> 19 Generic algorithms for computing discrete logarithms 477<br /> 20 Index calculus 495<br /> 21 Index calculus for hyperelliptic curves 511<br /> 22 Transfer of discrete logarithms 529<br /> VI Applications <br /> 23 Algebraic realizations of DL systems 547<br /> 24 Pairing-based cryptography 573<br /> 25 Compositeness and primality testing - factoring 591<br /> VII Realization of discrete logarithm systems <br /> 26 Fast arithmetic in hardware 617<br /> 27 Smart cards 647<br /> 28 Practical attacks on smart cards 669<br /> 29 Mathematical countermeasures against side-channel attacks 687<br /> 30 Random numbers - generation and testing 715<br /> <br /> Product Details<br /> <br /> * ISBN: 1584885181<br /> * ISBN-13: 9781584885184<br /> * Format: Hardcover, 808pp<br /> * Publisher: CRC Press<br /> * Pub. Date: July 2005<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader<br />
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