The Role of Time in Cryptography: Play, Fast Forward, and Speed Up

Abstract

The primary objectives of the thesis work are to conduct in-depth research in the field of delay-based cryptography and to improve the efficiency of evaluating ideal class group action, which serves as a building block in this area. Delay-based cryptographic primitives, such as time-lock puzzles and verifiable delay functions, play a crucial role in many cryptographic protocols by ensuring that certain computations cannot be completed faster than a predetermined time, even in parallel. Our study of delay-based cryptography aims to formalize and implement new delay-based primitives that use time-delay functions to improve the security and functionality of various applications.

We start by introducing a class of trapdoor verifiable delay functions (trapdoor-VDFs), an extended notion of verifiable delay functions, and providing a formal definition of their security properties. Trapdoor-VDFs feature a large ensemble of trapdoors, allowing a client to randomly select a private trapdoor to generate a unique challenge. Without the trapdoor, a server must perform a predetermined number of sequential steps to solve the challenge, while any client can efficiently verify the server's solution without knowing the trapdoor. We also propose a construction of trapdoor-VDFs based on large smooth-degree supersingular isogenies with bilinear pairings for efficient public verification. Our construction is useful for time-sensitive applications that require guaranteed timely release with public verification, such as sealed voting and front-running attack prevention.

Then, we introduce the notion of ChronoCloak, an integrated solution designed to prevent premature access to digital content while preserving recipients' privacy. Specifically, ChronoCloak enables a sender to transmit a collection of secret data through a puzzle that requires a predetermined amount of time to be solved. Once the puzzle is solved, the receiver can only extract the chosen subset of the sender's secret data without the sender knowing which subset was chosen. With public verifiability, the puzzle-solving process can be securely outsourced while ensuring that only the receiver can extract the chosen secret subset. Additionally, we introduce an ideal functionality for ChronoCloak and propose a generic protocol that implements ChronoCloak's functionality in the random oracle model.

Finally, we propose a new batching strategy for computing a set of group actions within the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) framework, which is a crucial component for developing post-quantum cryptographic schemes like zero-knowledge proofs and signature schemes. Our work presents two variants of the batching strategy, each of which is suited to different security requirements. The first variant is for computing a public set of CSIDH group actions and aims to reduce the number of finite field arithmetic operations required. Our results show a roughly up to 14% reduction in computational cost. Toward our second variant, we first propose an efficient new constant-time CSIDH algorithm for evaluating a private group action based on state-of-the-art batching techniques from CTIDH. We then introduce a method for computing a private set of CSIDH group actions, which runs in constant time while reducing the overall number of finite field arithmetic operations needed. Combined with our constant-time algorithm, it shows a reduction in computational cost of roughly up to 8% compared to the current state-of-the-art constant-time CSIDH. Interestingly, the constant-time algorithm alone reduces computations by about 4%. Finally, we present a proof-of-concept implementation, showcasing the results of our work.