Random Oracles in a Quantum World

The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore post-quantum secure. We conclude with a rich set of open problems in this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a related paper by Boneh and Zhandr

Lossy Trapdoor Permutations with Improved Lossiness

Lossy trapdoor functions (Peikert and Waters, STOC 2008 and SIAM J. Computing 2011) imply, via black-box transformations, a number of interesting cryptographic primitives, including chosen-ciphertext secure public-key encryption. Kiltz, O\u27Neill, and Smith (CRYPTO 2010) showed that the RSA trapdoor permutation is lossy under the Phi-hiding assumption, but syntactically it is not a lossy trapdoor function since it acts on Z_N and not on strings. Using a domain extension technique by Freeman et al. (PKC 2010 and J. Cryptology 2013) it can be extended to a lossy trapdoor permutation, but with considerably reduced lossiness. In this work we give new constructions of lossy trapdoor permutations from the Phi-hiding assumption, the quadratic residuosity assumption, and the decisional composite residuosity assumption, all with improved lossiness. Furthermore, we propose the first all-but-one lossy trapdoor permutation from the Phi-hiding assumption. A technical vehicle used for achieving this is a novel transform that converts trapdoor functions with index-dependent domain into trapdoor functions with fixed domain

Proofs of Replicated Storage Without Timing Assumptions

In this paper we provide a formal treatment of proof of replicated storage, a novel cryptographic primitive recently proposed in the context of a novel cryptocurrency, namely Filecoin. In a nutshell, proofs of replicated storage is a solution to the following problem: A user stores a file $m$ on $n$ different servers to ensure that the file will be available even if some of the servers fail. Using proof of retrievability, the user could check that every server is indeed storing the file. However, what if the servers collude and, in order to save on resources, decide to only store one copy of the file? A proof of replicated storage guarantees that, unless the server is indeed reserving the space necessary to store $n$ copies of the file, the user will not accept the proof. While some candidate proofs of replicated storage have already been proposed, their soundness relies on timing assumptions i.e., the user must reject the proof if the prover does not reply within a certain time-bound. In this paper we provide the first construction of a proof of replication which does not rely on any timing assumptions

Virtual Smart Cards: How to Sign with a Password and a Server

An important shortcoming of client-side cryptography on consumer devices is the poor protection of secret keys. Encrypting the keys under a human-memorizable password hardly offers any protection when the device is stolen. Trusted hardware tokens such as smart cards can provide strong protection of keys but are cumbersome to use. We consider the case where secret keys are used for digital signatures and propose a password-authenticated server-aided signature Pass2Sign protocol, where signatures are collaboratively generated by a device and a server, while the user authenticates to the server with a (low-entropy) password. Neither the server nor the device store enough information to create a signature by itself or to perform an offline attack on the password. The signed message remains hidden from the server. We argue that our protocol offers comparable security to trusted hardware, but without its inconveniences. We prove it secure in the universal composability (UC) framework in a very strong adaptive corruption model where, unlike standard UC, the adversary does not obtain past inputs and outputs upon corrupting a party. This is crucial to hide previously entered passwords and messages from the adversary when the device gets corrupted. The protocol itself is surprisingly simple: it is round-optimal, efficient, and relies exclusively on standard primitives such as hash functions and RSA. The security proof involves a novel random-oracle programming technique that may be of independent interest