The ideal class groups of hyperelliptic curves (HECs) can be used in cryptosystems based on the discrete logarithm problem. Recent developments of computational technologies for scalar multiplications of divisor classes have shown that the performance of hyperelliptic curve cryptosystems (HECC) is compatible to that of elliptic curve cryptosystems. Especially, due to short operand sizes, genus 3 HECC are well suited for all kinds of embedded processor architectures, where resources such as storage, time or power are constrained. In the paper, the acceleration of the divisor class doubling for genus 3 HECs over binary fields is investigated and the number of field operations needed is analysed. By constructing birational transformations of variables, four types of curves which can lead to much faster divisor class doubling are found and the corresponding explicit formulae are given. In particular, for special genus 3 HECs over binary fields with h(X)=1, the fastest explicit doubling formula published so far which only requires one field inversion, ten field multiplications and eleven field squarings, is obtained. Furthermore, comparisons with the known results in terms of field operations and implementations of genus 3 HECC over three different binary fields on a Pentium-4 processor are provided.

Digit serial multipliers are used extensively in hardware implementations of elliptic and hyperelliptic curve cryptography. This contribution shows different architectural enhancements in least significant digit (LSD) multiplier for binary fields GF(2m). We propose two different architectures, the double accumulator multiplier (DAM) and N-accumulator multiplier (NAM), which are both faster compared to traditional LSD multipliers. Our evaluation of the multipliers for different digit sizes gives optimum choices and shows that currently used digit sizes are the worst possible choices. Hence, one of the most important results of this contribution is that digit sizes of the form 2l- 1, where l is an integer, are preferable for the digit multipliers. Furthermore, one should always use the NAM architecture to get the best timings. Considering the time area product DAM or NAM gives the best performance depending on the digit size

Hyperelliptic curves (HEC) look promising for cryptographic applications, because of their short operand size compared to other public-key schemes. The operand sizes seem well suited for small processor architectures, where memory and speed are constrained. However, the group operation has been believed to be too complex and, thus, HEC have not been used in this context so far. In recent years, a lot of effort has been made to speed up group operation of genus-2 HEC. In this paper, we increase the efficiency of the genus-2 and genus-3 hyperelliptic curve cryptosystems (HECC). For certain genus-3 curves, we can gain almost 80 percent performance for a group doubling. This work not only improves Gaudry and Harley's algorithm, but also improves the original algorithm introduced by Cantor [1987]. Contrary to common belief, we show that it is also practical for certain curves to use Cantor's algorithm to obtain the highest efficiency for the group operation. In addition, we introduce a general reduction method for polynomials according to Karatsuba. We implemented our most efficient group operations on Pentium and ARM microprocessors.

In the last decade, it has become apparent that embedded systems are integral parts of our every day lives. The wireless nature of many embedded applications as well as their omnipresence has made the need for security and privacy preserving mechanisms particularly important. Thus, as field programmable gate arrays (FPGAs) become integral parts of embedded systems, it is imperative to consider their security as a whole. This contribution provides a state-of-the-art description of security issues on FPGAs, both from the system and implementation perspectives. We discuss the advantages of reconfigurable hardware for cryptographic applications, show potential security problems of FPGAs, and provide a list of open research problems. Moreover, we summarize both public and symmetric-key algorithm implementations on FPGAs.

It is widely recognized that data security will play a central role in future IT systems. Providing public-key cryptographic primitives, which are the core tools for security, is often difficult on embedded processor due to computational, memory, and power constraints. This contribution appears to be the first thorough comparison of two public-key families, namely elliptic curve (ECC) and hyperelliptic curve cryptosystems on a wide range of embedded processor types (ARM, ColdFire, PowerPC). We investigated the influence of the processor type, resources, and architecture regarding throughput. Further, we improved previously known HECC algorithms resulting in a more efficient arithmetic.