CSKH-02.2017 - (Abstract)—Extending Harold Edwards’s study of a new normal form of elliptic curves, Bernstein et al. generalized a family of curves, called the twisted Edwards curve, defined over a non-binary field k given by an equation ax^2+y^2=1+dx^2 y^2, where a,d∈k\{0},a≠d. The authors focused on the construction of efficient formulae of point adding on these curves in order to use them in the secure cryptographic schemes. Theoretically, the authors showed how to parameteries Edwards curves having torsion subgroup Z/12Z or Z/2Z×Z/8Z over the rational field Q. In the main result of this paper, we use the method which Bersntein et al. suggested to parameterise Edwards curves with the given torsion subgroups which are Z/4Z, Z/8Z, or Z/2Z×Z/4Z over Q.

CSKH-02.2017 - (Abstract) In this paper, the iterative scheme, namely the -scheme, is proposed constructing block ciphers. Then, the pseudorandomness and superpseudorandomness of this scheme are evaluated by using the Patarin’s H-coefficient technique. In particular, the pseudorandomness of -scheme is achieved in the case that the number of round is at least 3, and -scheme is superpseudorandomness in the case that the number of round is greater than or equal 5. However, we have not yet evaluated superpseudorandomness of this scheme when the round is 4.