Handbook of elliptic and hyperelliptic curve cryptography pdf

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handbook of elliptic and hyperelliptic curve cryptography pdf

Elliptic Curve Cryptography | SpringerLink

Du kanske gillar. Spara som favorit. Skickas inom vardagar specialorder. The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases.
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Elliptic Curve Diffie Hellman

Elliptic Curve Cryptography

Handbook of Information and Communication Security pp Cite as. Elliptic curve cryptography, in essence, entails using the group of points on an elliptic curve as the underlying number system for public key cryptography. There are two main reasons for using elliptic curves as a basis for public key cryptosystems. The first reason is that elliptic curve based cryptosystems appear to provide better security than traditional cryptosystems for a given key size. One can take advantage of this fact to increase security, or more often to increase performance by reducing the key size while keeping the same security. The second reason is that the additional structure on an elliptic curve can be exploited to construct cryptosystems with interesting features which are difficult or impossible to achieve in any other way. A notable example of this phenomenon is the development of identity-based encryption and the accompanying emergence of pairing-based cryptographic protocols.

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From the official CRC flyer: The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner.

Henri Cohen, Gerhard Frey, et al., Handbook of Elliptic and Hyperelliptic Curve Cryptography. Charles J. Colbourn and Jeffrey H. Dinitz, The CRC Handbook of.
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In the current work we propose two efficient formulas for computing the 5-fold 5 P of an elliptic curve point P. One formula is for curves over finite fields of even characteristic and the other is for curves over prime fields.

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