Abstract. Cryptographic hash functions are an important tool in cryptography for applications such as digital fingerprinting of messages, message authentication, and key derivation. During the last five years, several fast software hash functions have been proposed; most of them are based on the design principles of Ron Rivest's MD4. One such proposal was RIPEMD, which was developed in the framework of the EU project RIPE (Race Integrity Primitives Evaluation). Because of recent progress in the cryptanalysis of these hash functions, we propose a new version of RIPEMD with a 160-bit result, as well as a plug-in substitute for RIPEMD with a 128-bit result. We also compare the software performance of several MD4-based algorithms, which is of independent interest.

Abstract. We present a software implementation of arithmetic operations in a finite field GF(2~), based on an alternative representation of the field elements. An important application is in elliptic curve cryptosystems. Whereas previously reported implementations of elliptic curve cryptosystems use a standard basis or an optimal normal basis to perform field operations, we represent the field elements as polynomials with coefficients in the smaller field GF(216). Calculations in this smaller field are carried out using pre-calculated lookup tables. This results in rather simple routines matching the structure of computer memory very well. The use of an irreducible trinomial as the field polynomial, as was proposed at Crypto'95 by R. Schroeppel et al., can be extended to this representation. In our implementation, the resulting routines are slightly faster than standard basis routines.

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Three modular reduction algorithms for large integers are compared with respect to their performance in portable aoftware: the classical aIgorithm, Barrett'e algorithm and Montgomery's algorithm. These algorithms are a time critical step in the implementation of the modular exponentiation operation. For each of these aIgorithxm their a g plication in the modular exponentiation operation is considered. Modular exponentiation constitutes the basis of many well known and widely used public key cryptosystems. A fast and portable modular exponentiation will considerably enhance the speed and applicability of these systems.

With the advent of the Pentium processor parallelization finally bccarne available to Intel based computer systems. One of the design principles of the MD4-family of hash functions (MD4, MD5, SHA-1, FLIPEMD-160) is to be fast on the 32-bit Intel processors. This paper shows that carefully coded implementations of these hash functions are able to exploit the Pentium's superscalar architecture to its maximum effect: the performance with respect to execution on a non-parallel architecture increases by about 60%. This is an important result in view of the recent claims on the limited data bandwidth of these hash functions. Moreover, it is conjectured that these implementations are very close to optimal. It will also be shown that t,he performance penalty incurred by non-cached data and endianness conversion is limited, and in the order of 10% of running time.