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Several generic constructions for transforming one-way functions to asymmetric encryption schemes have been proposed. One-way functions only guarantee the weak secrecy of their arguments. That is, given the image by a one-way function of a random value, an adversary has only negligible probability to compute this random value. Encryption schemes must guarantee a stronger secrecy notion. They must be at least resistant against INDistinguishability-attacks under Chosen PlAintext text (IND-CPA). Most practical constructions have been proved in the random oracle model (ROM for short). Such computational proofs turn out to be complex and error prone. Bana et al. have introduced Formal Indistinguishability Relations (FIR), as an abstraction of computational indistinguishability.
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