Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. With software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the T pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over IF 3 m. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field IF 3 97 given by IF 3 ½x=ðx 97 þ x 12 þ 2Þ, which compares favorably with other solutions described in the open literature.

In this paper, we propose a modified η T 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.

Abstract. Signcryption is a cryptographic primitive that fulfills both the functions of digital signature and public key encryption simultaneously, at a cost significantly lower than that required by the traditional signature-then-encryption approach. In this paper, we address a question whether it is possible to construct a hybrid signcryption scheme in the certificateless setting. This question seems to have never been addressed in the literature. We answer the question positively in this paper. In particular, we extend the concept of signcryption tag-KEM to the certificateless setting. We show how to construct a certificateless signcryption scheme using certificateless signcryption tag-KEM. We also give an example of certificateless signcryption tag-KEM.

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