A group law on the projective plane with applications in Public Key Cryptography

10 Jun 2019 Díaz R. Durán Martínez V. Gayoso Encinas L. Hernández Masqué J. Muñoz

We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered... (read more)

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