How to compute an isogeny on the extended Jacobi quartic curves?

Computing isogenies between elliptic curves is a significantpart of post-quantum cryptography with many practicalapplications (for example, in SIDH, SIKE, B-SIDH, or CSIDHalgorithms). Comparing to other post-quantum algorithms, themain advantages of these protocols are smaller keys, the similaridea as in the ECDH, and a large basis of expertise aboutelliptic curves. The main disadvantage of the isogeny-basedcryptosystems is their computational efficiency - they are slowerthan other post-quantum algorithms (e.g., lattice-based). That iswhy so much effort has been put into improving the hithertoknown methods of computing isogenies between elliptic curves.In this paper, we present new formulas for computing isogeniesbetween elliptic curves in the extended Jacobi quartic formwith two methods: by transforming such curves into the shortWeierstrass model, computing an isogeny in this form and thentransforming back into an initial model or by computing anisogeny directly between two extended Jacobi quartics

SIDH hybrid schemes with a classical component based on the discrete logarithm problem over finite field extension

The concept of a hybrid scheme with connection of SIDH and ECDH is nowadays very popular. In hardware implementations it is convenient to use a classical key exchange algorithm, which is based on the same finite field as SIDH. Most frequently used hybrid scheme is SIDH-ECDH. On the other hand, using the same field as in SIDH, one can construct schemes over \Fpn, like Diffie-Hellman or XTR scheme, whose security is based on the discrete logarithm problem. In this paper, idea of such schemes will be presented. The security of schemes, which are based on the discrete logarithm problem over fields \Fp, \Fpd, \Fpc, \Fps and \Fpo, for primes $p$ used in SIDH, will be analyzed. At the end, the propositions of practical applications of these schemes will be presented

SIDH Hybrid Schemes with Classical Component Based on the Discrete Logarithm Problem over Finite Field Extension

The concept of a hybrid scheme with connection of SIDH and ECDH is nowadays very popular. In hardware implementations it is convenient to use a classical key exchange algorithm, which is based on the same finite field as SIDH. Most frequently used hybrid scheme is SIDH-ECDH. On the other hand, using the same field as in SIDH, one can construct schemes over Fpn, like Diffie-Hellman or XTR scheme, whose security is based on the discrete logarithm problem. In this paper, idea of such schemes will be presented. The security of schemes, which are based on the discrete logarithm problem over fields Fp; Fp2 ; Fp4 ; Fp6 and Fp8 , for primes p used in SIDH, will be analyzed. At the end, the propositions of practical applications of these schemes will be presented