Aggelos Kiayias

Proactive secret-sharing (PSS) offers security for shared secrets in a setting of a {\em mobile} adversary which, over time, may corrupt the whole shareholder set. This remarkable property is achieved by having parties proactively and in a coordinated manner refresh their shares on a regular basis, while it assumes that the adversary never manages to corrupt more than a threshold number of parties between two consecutive share refresh operations. A common assumption for achieving PSS is the ability of parties to securely erase their private state once they have performed the refresh operation. Motivated by the difficulty in the real world to ensure secure erasure, we investigate whether it is possible to achieve PSS without erasures. As in the classic model of computation it can be easily shown that PSS without erasures is impossible, we hence ask whether it is possible to achieve PSS via quantum computation, while still requiring only classical communication. We answer the question in the affirmative by utilizing one-shot signatures and post-quantum classical witness encryption. In the process of developing our result, we define and construct threshold one-shot decryption and make connections to quantum money with classical communication both of which may be of independent interest. Finally, we show how, by combining post-quantum secure witness functional encryption with our PSS, it is possible for the secret to be used without explicitly being reconstructed, something that paves the way towards proactively secure threshold cryptography without erasures.

Bitcoin and its underlying blockchain protocol have received recently significant attention in the context of building distributed systems as well as from the perspective of the foundations of the consensus problem. At the same time, the rapid development of quantum technologies brings the possibility of quantum computing devices from a theoretical concept to an emerging technology. Motivated by this, in this work we revisit the formal security of the core of the Bitcoin protocol, called the Bitcoin backbone, in the presence of an adversary that has access to a scalable quantum computer. We prove that the protocol’s essential properties stand in the post-quantum setting assuming a general quantum adversary with suitably bounded number of queries in the Quantum Random Oracle (QRO) model. In order to achieve this, we investigate and bound the quantum complexity of a Chain-of-Proofs-of-Work search problem which is at the core of the blockchain protocol. Our results imply that security can be shown by bounding the quantum queries so that each quantum query is worth O(p^{−1/2}) classical ones and that the wait time for safe settlement is expanded by a multiplicative factor of O(p^{−1/6}), where p is the probability of success of a single classical query to the protocol’s underlying hash function.