Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Subcarrier pairing and relay assignment with improved user fairness in a multi-user cooperative OFDM system

We consider a joint relay selection and subcarrier allocation problem that minimizes the total system power for a multi-user, multi-relay and single source cooperative OFDM based two hop system. The system is constrained to all users having a specific subcarrier requirement (user fairness). However no specific fairness constraints for relays are considered. To ensure the optimum power allocation, the subcarriers in two hops are paired with each other. We obtain an optimal subcarrier allocation for the single user case using a similar method to what is described in [1] and modify the algorithm for multiuser scenario. Although the optimality is not achieved in multiuser case the probability of all users being served fairly is improved significantly with a relatively low cost trade off.

Philanthropy and sociology : a logical pairing

In philanthropic studies we hear about a growing academic discipline of ‘philanthropic psychology’ but arguably there is an equal role for ‘philanthropic sociology’, both from a research and a teaching perspective. This commentary begins by noting the early links between philanthropy and sociology. It then introduces a few Australian studies that show how sociology is enriching an understanding of philanthropy, its institutions and its place in society.

Analysis of bilinear pairing-based accumulator for identity escrowing

An accumulator based on bilinear pairings was proposed at CT-RSA'05. Here, it is first demonstrated that the security model proposed by Lan Nguyen does lead to a cryptographic accumulator that is not collision resistant. Secondly, it is shown that collision-resistance can be provided by updating the adversary model appropriately. Finally, an improvement on Nguyen's identity escrow scheme, with membership revocation based on the accumulator, by removing the trusted third party is proposed.

Pairing technology and meals: A contextual enquiry in the family household

Recent research about technology during mealtime has been mostly concerned with developing technology rather than creating a deeper understanding of the context of family mealtimes and associated practices. In this paper, we present a two-phase study discussing how the temporal, social, and food related features are intertwined with technology use during mealtimes. Our findings show how people differentiate technology usage during weekday meals, weekend meals, and among different meals of the day. We identify and analyse prototypical situations ranging from the use of arbitrary technologies while eating solitary, to idiosyncratic family norms and practices associated with shared technologies. We discuss the use of mealtime technology to create appropriate ambience for meals with guests and demonstrate how technology can be used to complement food in everyday meals and special occasions. Our findings make recommendation about the need for HCI research to recognize the contextual nature of technology usage during family mealtimes and to adopt appropriate design strategies.