Variations of the McEliece Cryptosystem

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed

Some Results on the Known Classes of Quadratic APN Functions

In this paper, we determine the Walsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Gölo\u glu is affine equivalent to Gold functions

Reducing the Key Size of McEliece Cryptosystem from Automorphism-induced Goppa Codes via Permutations

In this paper, we propose a new general construction to reduce the public key size of McEliece cryptosystems constructed from automorphism-induced Goppa codes. In particular, we generalize the ideas of automorphism-induced Goppa codes by considering nontrivial subsets of automorphism groups to construct Goppa codes with a nice block structure. By considering additive and multiplicative automorphism subgroups, we provide explicit constructions to demonstrate our technique. We show that our technique can be applied to automorphism-induced Goppa codes based cryptosystems to further reduce their key sizes

Hyperplane sections of fermat varieties in P³ in char. 2 and some applications to cyclic codes

We consider the cyclic codes C₃⁽ᵗ⁾ of length 2³−1 generated by m₁(X)mnt(X) where mᵢ(X) is the minimal polynomial of a primitive element of GF(2³), and ask when these codes have minimum distance ≥ 5. Words of weight ≤ 4 in these codes are directly related to rational points in GF(2³) on the curves corresponding to the polynomials Xᵗ+Yᵗ+Zᵗ+(X+Y+Z)ᵗ over the algebraic closure of GF(2). Study of the singularities and absolutely irreducible components of these polynomials leads to results on the minimum distance of the codes