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.