Efficient Squaring Algorithm for Xate Pairing with Freeman Curve
نویسندگان
چکیده
Recently, pairing–based cryptographies have attracted much attention. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field should be efficient. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper proposes an efficient squaring algorithm in extension field for Freeman curve.
منابع مشابه
Extension Field for Xate Pairing with Freeman Curve
In recent years, pairing-based cryptographies such as ID-based cryptography [1] and group signature [2] have been studied. For their implementations, pairings such as Weil pairing [1], Tate pairing, Ate pairing [3] and Xate pairing [4] have been used. In order to implement these pairings, several kinds of ordinary pairing-friendly curves such as Miyaji-Nakabayashi-Takano (MNT) curve [5], Barret...
متن کاملPairing-Friendly Elliptic Curves with Small Security Loss by Cheon's Algorithm
Pairing based cryptography is a new public key cryptographic scheme. An elliptic curve suitable for pairing based cryptography is called a “pairing-friendly” elliptic curve. After Mitsunari, Sakai and Kasahara’s traitor tracing scheme and Boneh and Boyen’s short signature scheme, many protocols based on pairing-related problems such as the q-weak Diffie-Hellman problem have been proposed. In Eu...
متن کاملAccelerating Twisted Ate Pairing with Frobenius Map, Small Scalar Multiplication, and Multi-pairing
In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of (1/4) log2 r . On the other hand, the twisted Ate pairing requires (3/4) log2 r loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted ...
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملTripling Formulae of Elliptic Curve over Binary Field in Lopez-dahab Model
In elliptic curve cryptosystem (ECC), scalar multiplication is the major and most costly operation. Scalar multiplication involves with point operations such as point addition, point doubling, and point tripling. Scalar multiplication can be improved by using efficient point operations. This research focuses on point tripling operation for elliptic curves over the binary field in Lopez-Dahab (L...
متن کامل