1,614 research outputs found
Practical product proofs for lattice commitments
We construct a practical lattice-based zero-knowledge argument for proving multiplicative relations between committed values. The underlying commitment scheme that we use is the currently most efficient one of Baum et al. (SCN 2018), and the size of our multiplicative proof (9Â KB) is only slightly larger than the 7Â KB required for just proving knowledge of the committed values. We additionally expand on the work of Lyubashevsky and Seiler (Eurocrypt 2018) by showing that the above-mentioned result can also apply when working over rings Zq[X]/(Xd+1) where Xd+1 splits into low-degree factors, which is a desirable property for many applications (e.g. range proofs, multiplications over
Lattice-Based proof of a shuffle
In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft
On the efficiency of revocation in RSA-based anonymous systems
© 2016 IEEEThe problem of revocation in anonymous authentication systems is subtle and has motivated a lot of work. One of the preferable solutions consists in maintaining either a whitelist L-W of non-revoked users or a blacklist L-B of revoked users, and then requiring users to additionally prove, when authenticating themselves, that they are in L-W (membership proof) or that they are not in L-B (non-membership proof). Of course, these additional proofs must not break the anonymity properties of the system, so they must be zero-knowledge proofs, revealing nothing about the identity of the users. In this paper, we focus on the RSA-based setting, and we consider the case of non-membership proofs to blacklists L = L-B. The existing solutions for this setting rely on the use of universal dynamic accumulators; the underlying zero-knowledge proofs are bit complicated, and thus their efficiency; although being independent from the size of the blacklist L, seems to be improvable. Peng and Bao already tried to propose simpler and more efficient zero-knowledge proofs for this setting, but we prove in this paper that their protocol is not secure. We fix the problem by designing a new protocol, and formally proving its security properties. We then compare the efficiency of the new zero-knowledge non-membership protocol with that of the protocol, when they are integrated with anonymous authentication systems based on RSA (notably, the IBM product Idemix for anonymous credentials). We discuss for which values of the size k of the blacklist L, one protocol is preferable to the other one, and we propose different ways to combine and implement the two protocols.Postprint (author's final draft
Towards Realising Post-Quantum Secure ElectionGuard
ElectionGuard is a toolkit used to enable end-to-end verification of elections. Since
ElectionGuard uses exponential ElGamal, it is vulnerable to later vote decryption when
faced with quantum adversaries. Therefore, to avoid influences on voter behaviour, a
post-quantum adaption of ElectionGuard is needed to make the toolkits usage secure for
the foreseeable future.
In this work, we present cryptographic components that can be used to construct a
post-quantum version of ElectionGuard. We use the homomorphic encryption scheme
BGV and the commitment scheme BDLOP in a lattice setting. Applying existing and
new zero knowledge proofs, we construct the elements needed to show that votes are
well-formed and later aggregated correctly. As a final step, we show how to verifiably
decrypt the resulting tally.
In this paper, we lay the foundation for realising post-quantum secure ElectionGuard.
We provide the components for post-quantum vote encryption, aggregation, tallying and
verifiable decryption. Our work can be extended by distributed key generation and the
components for end-to-end verification
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
Quantum Lightning Never Strikes the Same State Twice
Public key quantum money can be seen as a version of the quantum no-cloning
theorem that holds even when the quantum states can be verified by the
adversary. In this work, investigate quantum lightning, a formalization of
"collision-free quantum money" defined by Lutomirski et al. [ICS'10], where
no-cloning holds even when the adversary herself generates the quantum state to
be cloned. We then study quantum money and quantum lightning, showing the
following results:
- We demonstrate the usefulness of quantum lightning by showing several
potential applications, such as generating random strings with a proof of
entropy, to completely decentralized cryptocurrency without a block-chain,
where transactions is instant and local.
- We give win-win results for quantum money/lightning, showing that either
signatures/hash functions/commitment schemes meet very strong recently proposed
notions of security, or they yield quantum money or lightning.
- We construct quantum lightning under the assumed multi-collision resistance
of random degree-2 systems of polynomials.
- We show that instantiating the quantum money scheme of Aaronson and
Christiano [STOC'12] with indistinguishability obfuscation that is secure
against quantum computers yields a secure quantum money schem
Computational Indistinguishability between Quantum States and Its Cryptographic Application
We introduce a computational problem of distinguishing between two specific
quantum states as a new cryptographic problem to design a quantum cryptographic
scheme that is "secure" against any polynomial-time quantum adversary. Our
problem, QSCDff, is to distinguish between two types of random coset states
with a hidden permutation over the symmetric group of finite degree. This
naturally generalizes the commonly-used distinction problem between two
probability distributions in computational cryptography. As our major
contribution, we show that QSCDff has three properties of cryptographic
interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff
coincides with its worst-case hardness; and (iii) QSCDff is computationally at
least as hard as the graph automorphism problem in the worst case. These
cryptographic properties enable us to construct a quantum public-key
cryptosystem, which is likely to withstand any chosen plaintext attack of a
polynomial-time quantum adversary. We further discuss a generalization of
QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies
on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail
proofs and follow-up of recent wor
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