Showing papers by "Christof Paar published in 2002"

Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes

Abstract: This contribution is concerned with a generalization of Itoh and Tsujii's algorithm for inversion in extension fields GF(q^m). Unlike the original algorithm, the method introduced here uses a standard (or polynomial) basis representation. The inversion method is generalized for standard basis representation and relevant complexity expressions are established, consisting of the number of extension field multiplications and exponentiations. As the main contribution, for three important classes of fields we show that the Frobenius map can be explored to perform the exponentiations required for the inversion algorithm efficiently. As an important consequence, Itoh and Tsujii's inversion method shows almost the same practical complexity for standard basis as for normal basis representation for the field classes considered.

Reconfigurable computing for symmetric-key algorithms

Abstract: Efficient implementation of block ciphers is critical towards achieving both high security and high speed processing. Numerous block ciphers have been proposed and implemented, covering a wide and varied range of functional operations. As a result, it has become increasingly more difficult to develop a hardware architecture that allows the efficient and fast realization of a wide variety of block ciphers. In an effort to achieve such a hardware architecture, a study of a wide range of block ciphers was undertaken to develop an understanding of the functional requirements of each algorithm. This study led to the development of COBRA, a programmable and configurable architecture for the efficient implementation of a wide variety of block ciphers. A detailed discussion of the top level architecture, interconnection scheme, and underlying elements of the architecture will be provided. System configuration and on-the-fly reconfiguration will be analyzed, and from this analysis it will be demonstrated that the COBRA architecture satisfies the requirements for achieving efficient implementation of a wide range of block ciphers.

Hardware architectures proposed for cryptosystems based on hyperelliptic curves

Abstract: Security issues play an important role in almost all modern communication and computer networks. The foundations of security are cryptographic systems, such as hyperelliptic curve cryptosystems (HECC). The advantage of HECC is that they allow encryption with shorter operands and at the same time provide the same level of security as other public-key cryptosystems, based on the integer factorization problem (e.g. RSA) or the discrete logarithm problem in finite fields or elliptic curves. Shorter operands appear promising for applications in constrained environments. This work describes hardware architectures for HECC. We present efficient architectures to implement the necessary field operations and polynomial arithmetic in hardware, including architectures for polynomial division and calculation of the extended Euclidean algorithm in the polynomial ring. All architectures are speed and area optimized. To our knowledge, this is the first work that presents hardware architectures for the implementation of a HECC.

Area efficient GF(p) architectures for GF(p/sup m/) multipliers

Abstract: This contribution describes new GF(p) multipliers, for p>2, specially suited for GF(p/sup m/) multiplication. We construct truth tables whose inputs are the bits of the multiplicand and multiplier and whose output are the bits that represent the modular product. However, contrary to previous approaches, we do not represent the elements of GF(p) in the normal binary positional system. Rather, we choose a representation which minimizes the resulting Boolean function. We obtain improvements of up to 35% in area when compared to previous approaches for small odd prime fields. We report transistor counts for all multipliers with p<2/sup 5/ which we obtained through the SIS sequential circuit synthesis program.