The principal topic of this article is to extend Shanks' infrastructure ideas in real quadratic number elds to the case of real quadratic congruence function elds. In this view, this paper is intended as a \low-brow" approach to the theory of ideals and operations in the ideal class group. We summarize some basic properties of ideals and provide elementary proofs of the main results. For the pu...

The Weil and Tate pairings are defined for elliptic curves over fields, including finite fields. These definitions extend naturally to elliptic curves over Z/NZ , for any positive integer N , or more generally to elliptic curves over any finite commutative ring, and even the reduced Tate pairing makes sense in this more general setting. This paper discusses a number of issues which arise if one...

If A is a finite set of cardinality n ≥ 1, 2 is the set of all subsets of A, and S is a nonempty subset of 2, we say that S has the odd-intersection property if there exists a subset N of A such that the cardinality of N ∩S is odd for each S ∈ S. Let OIP (n) denote the set of all subsets of 2 with the odd-intersection property. A nonempty set S of nonempty subsets of A is an obstruction (to the...

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plücker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Moutard transformation, it is constructed the discrete analog of the W–congruences...

In 1997, Lin [1] proposed a dynamic key management scheme using user hierarchical structure. After that, Lee [2] brought to two comments on Lin’s method. In 2002, Lin [3] proposed a more efficient hierarchical key management scheme based on Elliptic Curve. Lin’s efficient scheme solves the weaknesses appearing in Lee’s scheme in [1]. In this paper, we further use Quadratic Residues (Q.R.) theor...

We introduce the first universally anonymous, thus key-private, IBE whose security is based on the standard quadratic residuosity assumption. Our scheme is a variant of Cocks IBE (which is not anonymous) and is efficient and highly parallelizable.

This paper proposes an algebraic decoding algorithm for the (41, 21, 9) quadratic residue code via Lagrange interpolation formula to determine error check and error locator polynomials. Programs written in C++ language have been executed to check every possible error pattern of this quadratic residue code.

We present a method for maximumlikelihood decoding of the (48; 24; 12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the code does ...