Handbook of elliptic and hyperelliptic curve cryptography download pdfIn 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. Using the proposed point quintupling formulas one can use 2, 5 and 3, 5 besides 2, 3 as bases of the double base number system. In the current work we propose a scalar multiplication algorithm, which uses a representation of the scalar using three bases 2, 3 and 5 and computes the scalar multiplication very efficiently. The proposed scheme is faster than all sequential scalar multiplication algorithms reported in literature. Unable to display preview.
Cohen H., Frey G. (eds.) Handbook of Elliptic and Hyperelliptic 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.
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. 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.