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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SUMMARYPairing-based cryptography provides us many novel cryptographic applications such as ID-based cryptosystems and efficient broadcast encryptions. The security problems in ubiquitous sensor networks have been discussed in many papers, and pairing-based cryptography is a crucial technique to solve them. Due to the limited resources in the current sensor node, it is challenged to optimize the implementation of pairings on sensor nodes. In this paper we present an efficient implementation of pairing over MICAz, which is widely used as a sensor node for ubiquitous sensor network. We improved the speed of η T pairing by using a new efficient multiplication specialized for ATmega128L, called the block comb method and several optimization techniques to save the number of data load/store operations. The timing of η T pairing over GF(2 239 ) achieves about 1.93 sec, which is the fastest implementation of pairing over MICAz to the best of our knowledge. From our dramatic improvement, we now have much high possibility to make pairing-based cryptography for ubiquitous sensor networks practical.

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Abstract. Pairings on elliptic curves in finite fields are crucial material for constructions of various cryptographic schemes. The ηT pairing on supersingular curves over GF(3 n ) is in particular popular since it is efficiently implementable. Taking into account of the MOV attack, the discrete logarithm problems (DLP) in GF(3 6n ) becomes concerned to the security of cryptosystems using ηT pairings in this case. In 2006, Joux and Lercier proposed a new variant of the function field sieve in the medium prime case, named JL06-FFS. We have, however, not found any practical implementations on JL06-FFS over GF(3 6n ) up to now. Therefore, we have firstly fulfilled such an implementation and successfully set a new record for solving the DLP in GF(3 6n ), the DLP in GF(3 6·71 ) of 676-bit size. We conclude that n = 97 case, where there are many implementations of the ηT pairing, is not recommended in practical use. In addition, we also conduct comparisons between JL06-FFS and an earlier version, named JL02-FFS, by practical experiments. Our results confirm that the former is faster several times than the latter under certain conditions.