From Bi-Linear Maps to Searchable Encryption. Theoretical research into pairings-based cryptography has been a well-researched area over the last few years, this cryptography scheme is based on the mapping of two cryptographical groups which allows for a new cryptographical scheme based on a trapdoor permutation between the groups with some interesting complexity properties. Mostly all constructions of pairings-based cryptosystems use bilinear maps, for this we consider two groups.

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