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This paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto–Naehrig elliptic curve. Our library is able to compute the optimal ate pairing over a 254-bit prime field Fp, in just 2.33 million of clock cycles on a single core of an Intel Core i7 2.8GHz processor, which implies that the pairing… (More)

This paper describes the design of a fast multi-core library for the cryptographic Tate pairing over supersingular elliptic curves. For the computation of the reduced modified Tate pairing over F 3 509 , we report calculation times of just 2.94 ms and 1.87 ms on the Intel Core2 and Intel Core i7 architectures, respectively. We also try to answer one… (More)

ÐField-programmable gate arrays (FPGAs) are large, fast integrated circuitsÐthat can be modified, or configured, almost at any point by the end user. Within the domain of configurable computing, we distinguish between two modes of configurability: staticÐwhere the configurable processor's configuration string is loaded once at the outset, after which it… (More)

— In this paper, we propose a modified ηT pairing algorithm in characteristic three which does not need any cube root extraction. We also discuss its implementation on a low cost platform which hosts an Altera Cyclone II FPGA device. Our pairing accelerator is ten times faster than previous known FPGA implementations in characteristic three.

Since their introduction in constructive cryptographic applications , pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we first study an accelerator for the ηT pairing over F3[x]/(x 97… (More)

In this article we propose a study of the modified Tate pairing in characteristics two and three. Starting from the ηT pairing introduced by Barreto et al. [1], we detail various algorithmic improvements in the case of characteristic two. As far as characteristic three is concerned, we refer to the survey by Beuchat et al. [4]. We then show how to get back… (More)

— Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware archi-tectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in… (More)

This paper presents integer multiplication and division operators dedicated to Virtex-II FPGAs from Xilinx. Those operators are based on small 18×18 multiplier blocks available in the Virtex-II device family. Various trade-offs are explored (computation decomposition, radix, digit sets. . .) using specific VHDL generators. The obtained operators lead to… (More)

This article presents a novel optimal pairing over supersin-gular genus-2 binary hyperelliptic curves. Starting from Vercauteren's work on optimal pairings, we describe how to exploit the action of the 2 3m-th power Verschiebung in order to further reduce the loop length of Miller's algorithm compared to the genus-2 ηT approach. As a proof of concept, we… (More)