International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Tim Kerins

Publications

Year
Venue
Title
2006
EPRINT
An Elliptic Curve Processor Suitable For RFID-Tags
RFID-Tags are small devices used for identification purposes in many applications nowadays. It is expected that they will enable many new applications and link the physical and the virtual world in the near future. Since the processing power of these devices is low, they are often in the line of fire when their security and privacy is concerned. It is widely believed that devices with such constrained resources can not carry out sufficient cryptographic operations to guarantee security in new applications. In this paper, we show that identification of RFID-Tags can reach high security levels. In particular, we show how secure identification protocols based on the DL problem on elliptic curves are implemented on a constrained device such as an RFID-Tag requiring between 8500 and 14000 gates, depending on the implementation characteristics. We investigate the case of elliptic curves over $F_{2^p}$ with p prime and over composite fields $F_{2^{2p}}$. The implementations in this paper make RFID-Tags suitable for anti-counterfeiting purposes even in the off-line setting.
2006
EPRINT
Hardware Implementation of the $\eta_T$ Pairing in Characteristic 3
Recently, there have been many proposals for secure and novel cryptographic protocols that are built on bilinear pairings. The $\eta_T$ pairing is one such pairing and is closely related to the Tate pairing. In this paper we consider the efficient hardware implementation of this pairing in characteristic 3. All characteristic 3 operations required to compute the pairing are outlined in detail. An efficient, flexible and reconfigurable processor for the $\eta_T$ pairing in characteristic 3 is presented and discussed. The processor can easily be tailored for a low area implementation, for a high throughput implementation, or for a balance between the two. Results are provided for various configurations of the processor when implemented over the field $\mathbb{F}_{3^{97}}$ on an FPGA. As far as we are aware, the processor returns the first characteristic 3 $\eta_T$ pairing in hardware that includes a final exponentiation to a unique value.
2005
CHES
2005
EPRINT
Efficient hardware for the Tate pairing calculation in characteristic three
In this paper the benefits of implementation of the Tate pairing computation in dedicated hardware are discussed. The main observation lies in the fact that arithmetic architectures in the extension field $GF(3^{6m})$ are good candidates for parallelization, leading to a similar calculation time in hardware as for operations over the base field $GF(3^m)$. Using this approach an architecture for the hardware implementation of the Tate pairing calculation based on a modified Duursma-Lee algorithm is proposed.
2005
EPRINT
A Dedicated Processor for the eta Pairing
The $\eta$ pairing is an efficient computation technique based on a generalization of the Duursma Lee method for calculating the Tate pairing. The pairing can be computed very efficiently on genus 2 hyperelliptic curves. In this paper it is demonstrated that this pairing operation is well suited to a dedicated parallel hardware implementation. An $\eta$ pairing processor is described in detail and the architectures required for such a system are discussed. Prototype implementation results are presented over a base field of $\mathbb{F}_{2^{103}}$ and the advantages of implementing the pairing on the dedicated processor are discussed.