In this document, we provide a cryptographic treatment of the adjustable join protocol from CryptDB [5]. We also discuss how our scheme could be used outside of CryptDB because it provides a simple functionality that may be needed in other settings. Intuitively, it is a pseudorandom permutation where an external party not knowing the secret key can nonetheless adjust a ciphertext under one key ...

In this paper, we proposed a model for text encryption using elliptic curve cryptography (ECC) for secure transmission of text and by incorporating the Arithmetic/Huffman data compression technique for effective utilization of channel bandwidth and enhancing the security. In this model, every character of text message is transformed into the elliptic curve points 1 / 4

The main problem on caps, posed originally by Segre in the fifties, is to determine the values of k for which there exists a complete k-cap. In the present paper, we construct in PG(3, q), for odd prime q, a family of ~ (q2 + 7)-caps which have 2 points on a line external to an elliptic quadric E and the remaining points on E. We conjecture that they are complete.

We describe an equivalence between the notion of balanced twisted curve introduced by Abramovich and Vistoli, and a new notion of log twisted curve, which is a nodal curve equipped with some logarithmic data in the sense of Fontaine and Illusie. As applications of this equivalence, we construct a universal balanced twisted curve, prove that a balanced twisted curve over a general base scheme ad...

There are 26 possibilities for the torsion group of elliptic curves de ned over quadratic number elds. We present examples of high rank elliptic curves with given torsion group which give the current records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for Z/15Z, there exist an elliptic curve over some quadratic eld with this torsion ...

Elliptic curve cryptosystem protocols use two main operations, the scalar multiplication and the pairing computation. Both of them are done through a chain of basic operation on the curve. In this paper we present new formulas for supersingular elliptic curve in characteristic 2 and 3. We improve best known formulas by at least one multiplication in the field.

This paper analyzes the cost of breaking ECC under the following assumptions: (1) ECC is using a standardized elliptic curve that was actually chosen by an attacker; (2) the attacker is aware of a vulnerability in some curves that are not publicly known to be vulnerable. This cost includes the cost of exploiting the vulnerability, but also the initial cost of computing a curve suitable for sabo...

This is a summary of a three-part lecture series given at the meeting on “Explicit methods in number theory” that was held in Oberwolfach from July 12 to 18, 2009. The theme of this lecture series was the explicit construction of algebraic points on elliptic curves from cycles on modular varieties. Given a fixed elliptic curve E over Q, the goal is to better understand the group E(Q̄) of algebra...

We prove a generalization of both Pascal’s Theorem and its converse, the Braikenridge–Maclaurin Theorem: If two sets of k lines meet in k2 distinct points, and if dk of those points lie on an irreducible curve C of degree d , then the remaining k(k − d) points lie on a unique curve S of degree k − d. If S is a curve of degree k − d produced in this manner using a curve C of degree d , we say th...

— In the present paper, we prove the finiteness of the set of moderate rational points of a once-punctured elliptic curve over a number field. This finitenessmay be regarded as an analogue for a once-punctured elliptic curve of the well-known finiteness of the set of torsion rational points of an abelian variety over a number field. In order to obtain the finiteness, we discuss the center of th...