Goppa codes over Edwards curves

Given an Edwards curve, we determine a basis for the Riemann-Roch space of any divisor whose support does not contain any of the two singular points. This basis allows us to compute a generating matrix for an algebraic-geometric Goppa code over the Edwards curve.

MSB BASED IMAGE STEGANOGRAPHY USING MCELIECE CRYPTOSYSTEM

Steganography is the science of embedding secret data inside data so they can be sent to destination security. Encryption algorithms used to save information from sly activities when sent from one device to another over the wireless network. In this paper McEliece will be used to text encryption by Goppa code, where McEliece cryptosystem is a public-key cryptosystem based on error-correcting codes; then embedding the ciphertext as steganography image by MSB method. This lead to save information from attackers.

Group Signature with Verifier-Local Revocation Based on Coding Theory

Group signature with verifier-local revocation (VLR-GS) is a special variant of revocable group signature that not only allows a user to anonymously sign messages but also only requires the verifiers to possess some up-to-date revocation information. To date, a number of VLR-GS schemes have been proposed under bilinear groups and lattices, while they have not yet been instantiated based on coding theory. In this paper, we present a code-based VLR-GS scheme in the random oracle model, which is the first construction to the best of our knowledge. Concretely, our VLR-GS scheme does not rely on the traditional paradigm which utilizes an encryption scheme as a building block and achieves logarithmic-size group signature. To obtain the scheme, we first introduce a new code-based Stern-like interactive zero-knowledge protocol with member revocation mechanism based on syndrome decoding problem. Moreover, we employ the binary Goppa code embedded for our scheme with efficiency and security analysis.

EXTENDED SUBCLASS OF CYCLIC SEPARABLE GOPPA CODES

In 2013[4]a new subclass of cyclic Goppa code with Goppa polynomial of degree 2 is presented by Bezzateev and Shekhunova. They proved that this subclass contains all cyclic codes of considered length. In the present work we consider a Goppa polynomial of degree three and proved that the subclass generated by this polynomial represent a cyclic, reversible and separable Goppa code.

Counting Irreducible Polynomials of Degree r over Fqn and Generating Goppa Codes Using the Lattice of Subfields of Fqnr

The problem of finding the number of irreducible monic polynomials of degree r over Fqn is considered in this paper. By considering the fact that an irreducible polynomial of degree r over Fqn has a root in a subfield Fqs of Fqnr if and only if (nr/s,r)=1, we show that Gauss’s formula for the number of monic irreducible polynomials can be derived by merely considering the lattice of subfields of Fqnr . We also use the lattice of subfields of Fqnr to determine if it is possible to generate a Goppa code using an element lying in a proper subfield of Fqnr.