International Association
for Cryptologic Research

In this work, we study the cryptographic primitive called time-lock encryption (TLE). The concept of TLE involves a party initiating the encryption of a message that one can only decrypt after a certain amount of time has elapsed. Following the universal composability (UC) paradigm introduced by Canetti [IEEE FOCS 2001], we formally abstract the concept of TLE into an ideal functionality in a flexible way. In addition, we provide a standalone definition for secure TLE schemes in a game-based style and we devise a hybrid protocol that relies on such a secure TLE scheme. We show that if the underlying TLE scheme satisfies the standalone game-based security definition, then our hybrid protocol UC realises the TLE functionality in the random oracle model. Finally, we present \emph{Astrolabous}, a TLE construction that satisfies our security definition, leading to the first UC realization of the TLE functionality. Interestingly, it is hard to prove UC secure any of the TLE construction proposed in the literature. The reason behind this difficulty relates to the UC framework itself. Intuitively, to capture semantic security, no information should be leaked regarding the plaintext in the ideal world, thus the ciphertext should not contain any information relating to the message. On the other hand, all ciphertexts will eventually open, resulting in a trivial distinction of the real from the ideal world in the standard model. We overcome this limitation by extending any secure TLE construction adopting the techniques of Nielsen [CRYPTO 2002] in the random oracle model. Specifically, the description of the extended TLE algorithms includes calls to the random oracle, allowing our simulator to equivocate. This extension can be applied to any TLE algorithm that satisfies our standalone game-based security definition, and in particular to Astrolabous.