We present the first known implementation of elliptic curve cryptography over F2 p for sensor networks based on the 8-bit, 7.3828-MHz MICA2 mote. Through instrumentation of UC Berkeley's TinySec module, we argue that, although secret-key cryptography has been tractable in this domain for some time, there has remained a need for an efficient, secure mechanism for distribution of secret keys among nodes. Although public-key infrastructure has been thought impractical, we argue, through analysis of our own implementation for TinyOS of multiplication of points on elliptic curves, that public-key infrastructure is, in fact, viable for TinySec keys' distribution, even on the MICA2. We demonstrate that public keys can be generated within 34 seconds, and that shared secrets can be distributed among nodes in a sensor network within the same, using just over 1 kilobyte of SRAM and 34 kilobytes of ROM.

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard, and was accepted in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard, and is under consideration for inclusion in some other ISO standards. Unlike the ordinary discrete logarithm problem and the integer factorization problem, no subexponential-time algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strength-per-key-bit is substantially greater in an algorithm that uses elliptic curves. This paper describes the ANSI X9.62 ECDSA, and discusses related security, implementation, and interoperability issues. Keywords: Signature schemes, elliptic curve cryptography, DSA, ECDSA.

We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel, and compare these methods to traditional algorithms that use point doubling. The performance advantage of halving methods is clearest in the case of point multiplication kP where P is not known in advance, and smaller field inversion to multiplication ratios generally favour halving. Although halving essentially operates on affine coordinate representations, we adapt an algorithm of Knuth to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.

The fundamental operation in elliptic curve cryptographic schemes is that of point multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves than previous such methods.

Abstract not found

For most of the time since they were proposed, it was widely believed that hyperelliptic curve cryptosystems (HECC) carry a substantial performance penalty compared to elliptic curve cryptosystems (ECC) and are, thus, not too attractive for practical applications. Only quite recently improvements have been made, mainly restricted to curves of genus 2. The work at hand advances the state-of-the-art considerably in several aspects. First, we generalize and improve the closed formulae for the group operation of genus 3 for HEC defined over fields of characteristic two. For certain curves we achieve over 50% complexity improvement compared to the best previously published results. Second, we introduce a new complexity metric for ECC and HECC defined over characteristic two fields which allow performance comparisons of practical relevance. It can be shown that the HECC performance is in the range of the performance of an ECC; for specific parameters HECC can even possess a lower complexity than an ECC at the same security level. Third, we describe the first implementation of a HEC cryptosystem on an embedded (ARM7) processor. Since HEC are particularly attractive for constrained environments, such a case study should be of relevance.

Abstract. This paper explains the design and implementation of a highsecurity elliptic-curve-Diffie-Hellman function achieving record-setting speeds: e.g., 832457 Pentium III cycles (with several side benefits: free key compression, free key validation, and state-of-the-art timing-attack protection), more than twice as fast as other authors ’ results at the same conjectured security level (with or without the side benefits). 1

Rights to individual papers remain with the author or the author's employer. Permission is granted for noncommercial reproduction of the work for educational or research purposes. This copyright notice must be included in the reproduced paper. USENIX acknowledges all trademarks herein.

In this paper we introduce NTRUSign, a new family of signature schemes based on solving the approximate closest vector problem (appr-CVP) in NTRU-type lattices. We explore the properties of general appr-CVP based signature schemes (e.g. GGH) and show that they are not immune to transcript attacks even in the random oracle model.

Elliptic curve cryptography (ECC) was introduced by Victor Miller and Neal Koblitz in 1985. ECC proposed as an alternative to established public-key systems such as DSA and RSA, have recently gained a lot attention in industry and academia. The main reason for the attractiveness of ECC is the fact that there is no sub-exponential algorithm known to solve the discrete logarithm problem on a properly chosen elliptic curve. This means that significantly smaller parameters can be used in ECC than in other competitive systems such RSA and DSA, but with equivalent levels of security. Some benefits of having smaller key sizes include faster computations, and reductions in processing power, storage space and bandwidth. This makes ECC ideal for constrained environments such as pagers, PDAs, cellular phones and smart cards. The implementation of ECC, on the other hand, requires several choices such as the type of the underlying finite field, algorithms for implementing the finite field arithmetic and so on. In this paper we give we presen an selective overview of the main methods.