Download e-book for iPad: Handbook of Elliptic and Hyperelliptic Curve Cryptography by Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe

By Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren

ISBN-10: 1584885181

ISBN-13: 9781584885184

The discrete logarithm challenge in accordance with elliptic and hyperelliptic curves has received loads of acceptance as a cryptographic primitive. the most cause is that no subexponential set of rules for computing discrete logarithms on small genus curves is at the moment on hand, other than in very detailed situations. hence curve-based cryptosystems require a lot smaller key sizes than RSA to realize an analogous defense point. This makes them rather beautiful for implementations on memory-restricted units like clever playing cards and in high-security functions.

The instruction manual of Elliptic and Hyperelliptic Curve Cryptography introduces the idea and algorithms excited about curve-based cryptography. After a really particular exposition of the mathematical historical past, it offers ready-to-implement algorithms for the gang operations and computation of pairings. It explores tools for element counting and developing curves with the complicated multiplication approach and gives the algorithms in an particular demeanour. It additionally surveys wide-spread the right way to compute discrete logarithms and info index calculus tools for hyperelliptic curves. For a few certain curves the discrete logarithm challenge could be transferred to a neater one; the results are defined and proposals for strong offerings are given. The authors current functions to protocols for discrete-logarithm-based platforms (including bilinear constructions) and clarify using elliptic and hyperelliptic curves in factorization and primality proving. chapters discover their layout and effective implementations in clever playing cards. useful and theoretical facets of side-channel assaults and countermeasures and a bankruptcy dedicated to (pseudo-)random quantity iteration around off the exposition.

The huge assurance of all- vital components makes this booklet an entire guide of elliptic and hyperelliptic curve cryptography and a useful connection with a person drawn to this intriguing field.

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Handbook of Elliptic and Hyperelliptic Curve Cryptography (Discrete Mathematics and Its Applications) by Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren


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