We obtain estimates for Eve's forgery probability, namely the probability that she is able to forge a message which Alice or Bob mistakenly accept over a noisy Quantum channel for generating a shared Quantum secret key. This probability is related to Eve's success probability obtained in a previous work due to Renner and Wolf, which was obtained from assumptions on the min-entropy for characterizing asymmetric security. To demonstrate that protocols over noisy Quantum channels are dependent upon a single, unified security threshold in comparison to multiple security parameters in the Renner-Wolf interactive authentication protocol framework we upper bound Eve's forgery probability with a Holevo-type quantity that can be made negligibly small. By leveraging estimates for Eve's false acceptance probability that have previously been obtained by the author, we obtain the desired security threshold by bounding the false acceptance probability with a suitably chosen two-universal function which serves as a counterpart to two-universal hashing functions that have previously been examined for cryptographic protocols in Quantum key distribution. As a result the protocol is not only $ε$-secure, for some $ε>0$, but also composable against forgery and key leakage.
Comments
Template (29 pages). Discussion of this work is at: https://www.youtube.com/watch?v=jgPXdD0iEms. Related topics of discussion: https://www.youtube.com/playlist?list=PL3rTBtU0TK_DYTpmZAHcAMFMBj9ov1oPf, https://www.youtube.com/playlist?list=PL3rTBtU0TK_Cy35rrbIBmeNiBsWkhfvCe, https://www.youtube.com/playlist?list=PL3rTBtU0TK_C05u3pbB8fOLI2XFwWPorX
We obtain estimates for Eve's forgery probability, namely the probability that she is able to forge a message which Alice or Bob mistakenly accept over a noisy Quantum channel for generating a shared Quantum secret key. This probability is related to Eve's success probability obtained in a previous work due to Renner and Wolf, which was obtained from assumptions on the min-entropy for characterizing asymmetric security. To demonstrate that protocols over noisy Quantum channels are dependent upon a single, unified security threshold in comparison to multiple security parameters in the Renner-Wolf interactive authentication protocol framework we upper bound Eve's forgery probability with a Holevo-type quantity that can be made negligibly small. By leveraging estimates for Eve's false acceptance probability that have previously been obtained by the author, we obtain the desired security threshold by bounding the false acceptance probability with a suitably chosen two-universal function which serves as a counterpart to two-universal hashing functions that have previously been examined for cryptographic protocols in Quantum key distribution. As a result the protocol is not only ε-secure, for some ε>0, but also composable against forgery and key leakage.
We model (interactive) resources that provide Alice with a string X and a guarantee that any Eve interacting with her interface of the resource obtains a (quantum) system E such that the conditional (smooth) min-entropy of X given E is lower bounded by some k. This (abstract) resource specification encompasses any setting that results in the honest players holding such a string (or aborting). For example, it could be constructed from, e.g., noisy channels, quantum key distribution (QKD), or a violation of Bell inequalities, which all may be used to derive bounds on the min-entropy of X. As a first application, we use this min-entropy resource to modularize key distribution (KD) schemes by dividing them in two parts, which may be analyzed separately. In the first part, a KD protocol constructs a min-entropy resource given the (physical) resources available in the specific setting considered. In the second, it distills secret key from the min-entropy resource---i.e., it constructs a secret key resource. We prove security for a generic key distillation protocol that may use any min-entropy resource. Since the notion of resource construction is composable---security of a composed protocol follows from the security of its parts--- this reduces proving security of a KD protocol (e.g., QKD) to proving that it constructs a min-entropy resource. As a second application, we provide a composable security proof for the recent Fehr-Salvail protocol [EUROCRYPT 2017] that authenticates classical messages with a quantum message authentication code (Q-MAC), and recycles all the key upon successfully verifying the authenticity of the message. This protocol uses (and recycles) a non-uniform key, which we model as consuming and constructing a min-entropy resource.
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for the bit transmission rate without the presence of significant noise over the channel shared by Alice and Bob for the purposes of encoding, decoding, transmission and authentication, the author suggests that upper bounding the bit transmission rate could be of use towards classifying paradoxical aspects of communication protocols, as well as constructing error correcting codes which are resilient to noise. The upper bound that is obtained in this work for the bit transmission rate, as a converse result, is dependent upon the natural logarithm of the size of each player's alphabet, as well as smaller alphabets, which can be leveraged for simultaneously realizing Quantum advantage for maximizing error correction and minimizing false acceptance. Crucially, the upper bound to the bit transmission rate is dependent upon a pruning procedure, which seeks to determine whether letters from player's alphabets can be removed so that prospective Quantum advantage, in order for Alice and Bob to implement error correction protocols with high probability, despite the fact that there is more noise over the channel between Alice and Bob in comparison to that between Bob and Eve.
We consider a setup in which the channel from Alice to Bob is less noisy than the channel from Eve to Bob. We show that there exist encoding and decoding which accomplish error correction and authentication simultaneously; that is, Bob is able to correctly decode a message coming from Alice and reject a message coming from Eve with high probability. The system does not require any secret key shared between Alice and Bob, provides information theoretic security, and can safely be composed with other protocols in an arbitrary context.
We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given research directions of interest previously identified in arXiv: 1804.01797, besides converse upper bounds on the bit transmission rate obtained by the author in recent work (arXiv: 2507.03035), additional possibilities remain, including: (1) determining whether aspects of QKD dependent protocols can be incorporated into steps of QKD independent protocols; (2) whether there would be any amplification to the Quantum-classical performance gap that Alice and Bob can exploit towards prospective Quantum advantage; (3) formulating the conditions under which secrecy and authentication can be simultaneously achieved. To characterize the conditions for which secrecy can be achieved with high probability, we argue that there not only exists suitable protocols which enable Alice and Bob to map into the authenticated space of bit codewords with high probability, but also that forward conceptual channels, through cascading, can significantly increase Eve's probability of false acceptance. Albeit the fact that secrecy, along with conceputalizations of the public broadcast channel, were initially discussed by Maurer for QKD dependent protocols, determining whether aspects of such protocols can be adapted for unconditional security without the use of a secret key is of great interest to explore. We demonstrate that Eve's error probability, through the cascading procedure, can be analyzed with the Holevo information under an optimal decoder. Furthermore, through post-processing of the outputs of a Completely Positive Trace Preserving (CPTP) map, we also demonstrate how to decrease Holevo sum quantities with data-processing and entropy-continuity bounds.
We consider the scenario in which Alice transmits private classical messages to Bob via a classical-quantum channel, part of whose output is intercepted by an eavesdropper Eve. We prove the existence of a universal coding scheme under which Alice's messages can be inferred correctly by Bob, and yet Eve learns nothing about them. The code is universal in the sense that it does not depend on specific knowledge of the channel. Prior knowledge of the probability distribution on the input alphabet of the channel, and bounds on the corresponding Holevo quantities of the output ensembles at Bob's and Eve's end suffice.
The security of quantum key distribution against undetected eavesdropping depends on the key-sharing parties (Alice and Bob) making a probabilistic estimate of the ignorance of a maximally adept eavesdropper (Eve) concerning sifted, error-free bits from which Alice and Bob distill a key. For individual attacks on the BB84 protocol, we show how to generalize the defense function and the defense frontier of Slutsky et al. to take advantage of Cachin’s analysis of Renyi entropy of arbitrary order R, here called R-entropy. For a special case of an attack uniform over all bits, an optimum defense frontier is displayed. Evidence is discussed for the conjecture that this defense frontier in terms of R-entropy holds good not just for uniform attacks but for all individual attacks on BB84. We also show how the entropy estimate fits in to the full suite of key-distillation protocols in a QKD system, in particular how it relates to privacy amplification. After privacy amplification, Eve will have, with high probability, no information about the remaining bits. By choosing the optimal Rényi order R, we can distill secure bits in the presence of a significantly higher error rate.