Encapsulating Secrets Using Lockable Obfuscation and a RMERS-Based Public Key Encryption

Lockable obfuscation, a new primitive that occurs in cryptography, makes it possible to execute arbitrary polynomial-sized functions and recover a secret under specific equality conditions. More concretely, if the function executed over a specific input produces an output that matches an expected target value, here denoted by a , some secret string of bits s is exposed. Written in algebraic terms, if f : X → A has the property that for some x , f ( x ) = a , s is revealed. This work explores the possibility for safely decrypting ciphertexts, and based on the recovered plaintext’s equality to a stored message, to reveal some secret. Concretely, this work provides a review of existing, well-known public key encryption schemes and argues for the efficiency of a new one relying on the ratio Mersenne hypothesis (RMERS), which is to be used in conjunction with a lockable obfuscator. This work explores the advantage conferred by this scheme, especially in the minimization of the branching program’s number of levels that need to be obfuscated. The drawbacks of such schemes are also pointed out, given that they currently require the LWE evaluations level-per-level, one output bit at a time.