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 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 …

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 analysis of the 2-isogeny existence conditions of generalized Edwards form curves over
a prime field, including complete, quadratic, and twisted Edwards curves, is presented. An …

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 …

An analysis of existence conditions of supersingular twisted Edwards curves over a prime
field is given. Theorems on the conditions of existence of supersingular curves with j …

Theorems on the conditions for the existence of supersingular Edwards curves over a prime
field with the j-invariant equal to 66 3 and with other values of j-invariants are formulated and …

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 …