Montgomery-form elliptic curves are widely used for efficient arithmetic calculations and immunity from timing attacks. Constructing hash function to hash messages into Montgomery-form elliptic curves is important, and this paper proposes four deterministic encoding algorithms to perform this transformation. One is based on finding a cube root, whereas the other three are based on finding square roots. We prove that the four algorithms are all hash functions. Moreover, we provide new functions indifferentiable from a random oracle based on our deterministic encodings.
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