This paper presents a procedure for calculating multiplicative inverses Modulo 2m, based on a novel mathematical approach. The procedure is suitable for software implementation on a general-purpose processor. When counting the total number of word-level processor multiplications, the computational effort involved in calculating a multiplicative inverse is 2/3 that of a single multiplication of m-bit values, in addition to a few word-level multiplications. For standard processor word sizes, the number of these additional multiplications does not exceed 12. This introduces a clear advantage of the proposed method when compared to other known methods presented in the literature.

Dynamic formation of node clusters is inherently embedded in a wide range of emerging wireless sensor network (WSN) applications. It is expected that security will play a key role in the design and successful deployment of these, as well as many other, applications. The ad-hoc nature and unique power-constraint characteristics of WSN suggest that a prerequisite for achieving security is the ability to encrypt and decrypt confidential data among an arbitrary set of sensor nodes. Consequently, the nodes are required to generate a joint secret key. Elliptic curve cryptography (ECC) has emerged as a suitable public key cryptographic foundation for WSN. This paper describes a pragmatic ECC-based methodology for self-certified group key generation in ad hoc clusters of sensor nodes. A novel load-balancing technique and chained data exchange yield reduced overall communications and facilitate an efficient distribution of the computational effort involved.

A novel binary number system, called Redundant Linear Coding (RLC), is presented. By eliminating the need for carry handling, a feasible tradeoff between speed and area yields short computation time for up/down counting and comparison operations. The scheme can efficiently be applied to a wide range of high-speed digital applications.