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Workshop Talk
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How to Encrypt with Random Reversible Circuits: Functional, Homomorphic and CCA-secure

We revisit a natural paradigm for public-key encryption, whereby the public key is an obfuscated block cipher,  and the ciphertext is the result of applying the cipher directly to the message along with a short random nonce.  We show that if the block cipher is a permutable pseudorandom permutation [Shmueli--Zhandry, Crypto~'25] and the obfuscator is indistinguishability-secure, then the resulting  scheme is CCA2 secure.  Further, augmenting the scheme with the capability to generate obfuscated decrypt-then-apply-f circuits (for any given function f), yields a functional encryption scheme that is simulation-secure against adaptive chosen-ciphertext attacks. Even further, for any length-preserving function g, augmenting the public key with an obfuscated decrypt-apply-g-reencrypt circuit allows anyone to homomorphically apply g to encrypted data, for an unbounded number of times, while preventing any other homomorphisms or malleability. (This part relies on subexponential security.)

Formulating this powerful combination of controlled homomorphism, functional decryption, and CCA2 security within a single encryption scheme requires some care and may be of independent interest. Our definition extends that of Prabhakaran and Rosulek (PKC'08).

We finally  show, under the Split-Circuit Pseudorandomness assumption of  (Canetti, Chamon, Mucciolo, Ruckenstein, TCC '24), that an obfuscated version of a random reversible circuit is a permutable pseudorandom permutation, along with a reversible-circuit-only version of the obfuscation process leading to the actual encryption scheme. Combined with the heuristic obfuscation scheme of Canetti et al,  this suggests a potential avenue to realistic instantiations of this general template for public-key encryption. 

Joint work with Ran Canetti  and Yiding Zhang.