Privacy-Preserving Matching Protocols for Attributes and Strings
In this technical report we present two new privacy-preserving matching protocols for singular attributes and strings, respectively. The first one is used for matching of common attributes without revealing unmatched ones to each other. The second protocol is used to discover the longest common sub-string of two input strings in a privacy-preserving manner. Compared with previous work, our solutions are efficient and suitable to implement for many different applications, e.g., discovery of common worm signatures, computation of similarity of IP payloads.
Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves
Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose the idea of effective polynomial families for finding the curves through different kinds of Pell equations or special forms of D(x)V^2(x). In addition, we discover some efficient families which can be used to build pairing-friendly elliptic curves over extension fields, e.g. Fp^2 and Fp^4.
Special Polynomial Families for Generating More Suitable Elliptic Curves for Pairing-Based Cryptosystems
Constructing non-supersingular elliptic curves for pairing-based cryptosystems have attracted much attention in recent years. The best previous technique builds curves with p = lg(q)/lg(r) = 1 (k = 12) and p = lg(q)/lg(r) = 1.25 (k = 24). When k > 12, most of the previous works address the question by representing r(x) as a cyclotomic polynomial. In this paper, we propose a new method to find more pairing-friendly elliptic curves with arbitrary embedding degree k by certain special polynomial families. The new method generates curves with lg(q)/lg(r) = 1 (k > 48) by random forms of r(x). Different representations of r(x) allow us to obtain many new families of pairing-friendly elliptic curves. In addition, we propose a equation to illustrate how to obtain small values of p by choosing appropriate forms of discriminant D and trace t. Numerous parameters of certain pairing-friendly elliptic curves are presented with support for the theoretical conclusions.