An All-But-One Entropic Uncertainty Relation, and Application to Password-based Identification

Entropic uncertainty relations are quantitative characterizations of Heisenberg's uncertainty principle, which make use of an entropy measure to quantify uncertainty. In quantum cryptography, they are often used as convenient tools in security proofs. We propose a new entropic uncertainty relation. It is the first such uncertainty relation that lower bounds the uncertainty in the measurement outcome for all but one choice for the measurement from an arbitrarily large (but specifically chosen) set of possible measurements, and, at the same time, uses the min-entropy as entropy measure, rather than the Shannon entropy. This makes it especially suited for quantum cryptography. As application, we propose a new quantum identification scheme in the bounded quantum storage model. It makes use of our new uncertainty relation at the core of its security proof. In contrast to the original quantum identification scheme proposed by Damg{\aa}rd et al., our new scheme also offers some security in case the bounded quantum storage assumption fails hold. Specifically, our scheme remains secure against an adversary that has unbounded storage capabilities but is restricted to non-adaptive single-qubit operations. The scheme by Damg{\aa}rd et al., on the other hand, completely breaks down under such an attack.Comment: 33 pages, v

Unconditional security from noisy quantum storage

We consider the implementation of two-party cryptographic primitives based on the sole assumption that no large-scale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the so-called bounded-storage model which is a special case of our setting. Our protocols can be implemented with present-day hardware used for quantum key distribution. In particular, no quantum storage is required for the honest parties.Comment: 25 pages (IEEE two column), 13 figures, v4: published version (to appear in IEEE Transactions on Information Theory), including bit wise min-entropy sampling. however, for experimental purposes block sampling can be much more convenient, please see v3 arxiv version if needed. See arXiv:0911.2302 for a companion paper addressing aspects of a practical implementation using block samplin

Experimental implementation of bit commitment in the noisy-storage model

Fundamental primitives such as bit commitment and oblivious transfer serve as building blocks for many other two-party protocols. Hence, the secure implementation of such primitives are important in modern cryptography. In this work, we present a bit commitment protocol which is secure as long as the attacker's quantum memory device is imperfect. The latter assumption is known as the noisy-storage model. We experimentally executed this protocol by performing measurements on polarization-entangled photon pairs. Our work includes a full security analysis, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of two-party protocols in this model using real-world quantum devices. Finally, we provide a general analysis of our bit commitment protocol for a range of experimental parameters.Comment: 21 pages (7 main text +14 appendix), 6+3 figures. New version changed author's name from Huei Ying Nelly Ng to Nelly Huei Ying Ng, for consistency with other publication

Maintaining secrecy when information leakage is unavoidable

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 109-115).(cont.) We apply the framework to get new results, creating (a) encryption schemes with very short keys, and (b) hash functions that leak no information about their input, yet-paradoxically-allow testing if a candidate vector is close to the input. One of the technical contributions of this research is to provide new, cryptographic uses of mathematical tools from complexity theory known as randomness extractors.Sharing and maintaining long, random keys is one of the central problems in cryptography. This thesis provides about ensuring the security of a cryptographic key when partial information about it has been, or must be, leaked to an adversary. We consider two basic approaches: 1. Extracting a new, shorter, secret key from one that has been partially compromised. Specifically, we study the use of noisy data, such as biometrics and personal information, as cryptographic keys. Such data can vary drastically from one measurement to the next. We would like to store enough information to handle these variations, without having to rely on any secure storage-in particular, without storing the key itself in the clear. We solve the problem by casting it in terms of key extraction. We give a precise definition of what "security" should mean in this setting, and design practical, general solutions with rigorous analyses. Prior to this work, no solutions were known with satisfactory provable security guarantees. 2. Ensuring that whatever is revealed is not actually useful. This is most relevant when the key itself is sensitive-for example when it is based on a person's iris scan or Social Security Number. This second approach requires the user to have some control over exactly what information is revealed, but this is often the case: for example, if the user must reveal enough information to allow another user to correct errors in a corrupted key. How can the user ensure that whatever information the adversary learns is not useful to her? We answer by developing a theoretical framework for separating leaked information from useful information. Our definition strengthens the notion of entropic security, considered before in a few different contexts.by Adam Davison Smith.Ph.D