An overview of the properties of three classes of curves in generalized Edwards form Ea, d
with two parameters is given. The known formulas for the odd degree isogenies on curves …

A multifunctional cryptosystem RCNIE on isogenies of non-supersingular Edwards curves is
proposed, which solves the problems of Diffie-Hellman secret sharing, digital signature, and …

An original key encapsulation scheme is proposed as a modification of the CSIDH algorithm
built on the isogenies of non-cyclic Edwards curves. The corresponding CSIKE algorithm …

For the PQC CSIDH and CSIKE algorithms, the advantages of two classes of quadratic and
twisted supersingular Edwards curves over complete Edwards curves are justified. These …

The properties of twisted and quadratic supersingular Edwards curves forming pairs of
quadratic torsion with the order p+ 1 over the simple field Fp are considered. A modification …

Розглянуто властивості скручених та квадратичних суперсингулярних кривих Едвардса,
що утворюють пари квадратичного кручення з порядком над простим полем. Наведено …

In one of the famous works, an incorrect formulation and an incorrect solution of the
implementation problem of the CSIDH algorithm on Edwards curves is discovered. A …

An original CSIKE post-quantum cryptography algorithm is proposed as a modification of the
CSIDH algorithm but with one public key instead of two. The conditions for its …

Incorrect formulation and incorrect solution of the problem of the CSIDH algorithm
implementation on Edwards curves was revealed in one of the famous works. The purpose …

The authors analyze the special properties of two classes of quadratic and twisted Edwards
curves over a prime field, which take into account their non-cyclic structure and the …