Towards Quantum One-Time Memories from Stateless Hardware

A central tenet of theoretical cryptography is the study of the minimal assumptions re- quired to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework. We prove stand-alone security against a malicious sender, but leave open the question of composable security against a malicious sender, as well as security against a malicious receiver making a polynomial number of adaptive queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the “prepare-and-measure” type. We also show our scheme is “tight” according to two scenarios

Towards Quantum One-Time Memories from Stateless Hardware

A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also show our scheme is "tight" according to two scenarios

Unclonable Secret Keys

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting. In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only is unclonable, but also is restricted to signing only one message even in the paradoxical scenario where it is generated dishonestly. We propose a construction relative to a classical oracle and prove its unconditional security. Moreover, we provide numerous applications including a signature scheme where an adversary can sign as many messages as it wants and yet it cannot generate two signing keys for the same public key. We show that one-shot signatures are sufficient to build a proof-of-work-based decentralized cryptocurrency with several ideal properties: it does not make use of a blockchain, it allows sending money over insecure classical channels and it admits several smart contracts. Moreover, we demonstrate that a weaker version of one-shot signatures, namely privately verifiable tokens for signatures, are sufficient to reduce any classically queried stateful oracle to a stateless one. This effectively eliminates, in a provable manner, resetting attacks to hardware devices (modeled as oracles). In the encryption setting, we study different forms of unclonable decryption keys. We give constructions that vary on their security guarantees and their flexibility. We start with the simplest setting of secret key encryption with honestly generated keys and show that it exists in the quantum random oracle model. We provide a range of extensions, such as public key encryption with dishonestly generated keys, predicate encryption, broadcast encryption and more