A QKD Protocol Extendable to Support Entanglement and Reduce Unauthorized Information Gain by Randomizing the Bases Lists with Key Values and Invalidate Explicit Privacy Amplification
C. Sanjeevakumar, M. Kasi Rajan, L. Sudarsan, Venkatesh, R., Srinivasan, N.
This paper suggests an improvement to the BB84 scheme in Quantum key distribution. The original scheme has its weakness in letting quantifiably more information gain to an eavesdropper during public announcement of unencrypted bases lists. The security of the secret key comes at the expense of the final key length. We aim at exploiting the randomness of preparation (measurement) basis and the bit values encoded (observed), so as to randomize the bases lists before they are communicated over the public channel. A proof of security is given for our scheme and proven that our protocol results in lesser information gain by Eve in comparison with BB84 and its other extensions. Moreover, an analysis is made on the feasibility of our proposal as such and to support entanglement based QKD. The performance of our protocol is compared in terms of the upper and lower bounds on the tolerable bit error rate. We also quantify the information gain (by Eve) mathematically using the familiar approach of the concept of Shannon entropy. The paper models the attack by Eve in terms of interference in a multi-access quantum channel. Besides, this paper also hints at the invalidation of a separate privacy amplification step in the "prepare-and-measure" protocols in general.
This paper suggests an improvement to the BB84 scheme in Quantum key distribution. The original scheme has its weakness in letting quantifiably more information gain to an eavesdropper during public announcement of unencrypted bases lists. The security of the secret key comes at the expense of the final key length. We aim at exploiting the randomness of preparation (measurement) basis and the bit values encoded (observed), so as to randomize the bases lists before they are communicated over the public channel. A proof of security is given for our scheme and proven that our protocol results in lesser information gain by Eve in comparison with BB84 and its other extensions. Moreover, an analysis is made on the feasibility of our proposal as such and to support entanglement based QKD. The performance of our protocol is compared in terms of the upper and lower bounds on the tolerable bit error rate. We also quantify the information gain (by Eve) mathematically using the familiar approach of the concept of Shannon entropy. The paper models the attack by Eve in terms of interference in a multi-access quantum channel. Besides, this paper also hints at the invalidation of a separate privacy amplification step in the "prepare-and-measure" protocols in general.
The prepare-and-measure quantum key distribution (QKD) has the merits of fast speed, high key generation rate, and easy implementation. However, the detector side channel attacks greatly undermine the security of the key bits. The eavesdropper, Eve, exploits the flaws of the detectors to obtain illegal information without violating quantum principles. It means that she can intervene in the communication without being detected. A prepare-and-measure Bell test protocol will be proposed. By randomly carrying out Bell test at the side of the information receiver, Bob, Eve's illegal information gain within the detector side channel attack can be well bounded. This protocol does not require any improvement on the detectors used in available prepare-and-measure QKD. Though we only illustrate its application in the BB84 protocol, it is applicable for any prepare-and-measure QKD.
We suggest that the randomness of the choices of measurement basis by Alice and Bob provides an additional important resource for quantum cryptography. As a specific application, we present a novel protocol for quantum key distribution (QKD) which enhances the BB84 scheme by encrypting the information sent over the classical channel during key sifting. We show that, in the limit of long keys, this process prevents an eavesdropper from reproducing the sifting process carried out by the legitimate users. The inability of the eavesdropper to sift the information gathered by tapping the quantum channel reduces the amount of information that an eavesdropper can gain on the sifted key. We further show that the protocol proposed is self sustaining, and thus allows the growing of a secret key.
Quantum key distribution (QKD) is a method that enables secure communication between two parties by applying the ideas of quantum physics. By minimizing information leakage that can happen during the key generation process, privacy amplification is a technique used to improve the security of QKD. The technique involves processing the raw key obtained from QKD through a randomization procedure to remove any residual information that may have been leaked during the quantum transmission. While privacy amplification can significantly improve the security of QKD, the effectiveness of the technique is limited by the quality of the initial raw key. The BB84 QKD protocol has been improved with the proposed En-BB84 protocol, which includes built-in authentication and integrity checks. The En-BB84 protocol ensures secure distribution of secret keys and protects against tampering by attackers. Key distillation and error correction techniques are employed to extract a shorter, more secure shared secret key and correct errors introduced during qubit transmission. The protocol utilizes a four-state QKD approach, expanding on the traditional two-state scheme of BB84. A simulation of the En-BB84 protocol is demonstrated using a quantum circuit implemented with Qiskit in Python. The circuit employs various gates and operations, including Hadamard, CX, controlled swap, and RZ gates, to achieve encoding and error correction. Furthermore, we have designed a better protocol with improved error rates by incorporating improvisations on the BB84 protocol. Experimental results indicate the successful integration of the B92 error correction scheme into the modified BB84 protocol, enhancing the security and performance of QKD systems.
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.
We introduce list privacy amplification (LPA), a relaxation of the final step of quantum key distribution (QKD) in which Alice and Bob extract a list of L candidate keys from a raw string correlated with an eavesdropper Eve, with the guarantee that at least one key is perfectly secret while Eve cannot identify which. This parallels list decoding in error-correcting codes: relaxing unique decoding to list decoding increases the decoding radius; analogously, list extraction increases achievable key length beyond the standard quantum leftover hash lemma (QLHL). Within the abstract cryptography framework, we formalise LPA and prove the \emph{Quantum List Leftover Hash Lemma} (QLLHL): an L-list of ℓ-bit keys can be extracted from an n-bit source with smooth min-entropy k iff ℓ≤k+logL−2log(1/ε)−3, yielding a tight additive logL gain over QLHL. This gain arises because the index of the secure key is chosen after hashing and hidden from Eve, effectively contributing logL bits of entropy. Applying QLLHL to BB84-type QKD, a list size L=2αn′ increases the tolerable phase-error threshold from h−1(1−h(eb)) to h−1(1−h(eb)+α), exceeding the standard ≈11% bound for any α>0. We prove tightness via a matching intercept-resend attack, establish composability with Wegman--Carter authentication, and present two constructions: a polynomial inner-product hash over F2m and a Toeplitz-based variant, running in O(nL) and O(nLlogn) time.
Quantum Key Distribution (QKD) protocols typically involve two separate steps of error-verification and privacy amplification. Both steps involve the application of a hash function sampled from a suitable hash family to classical data. A potentially simpler alternative is to implement a single-step hashing procedure, announce and compare a fixed number of bits of its output for error-verification, and retain the remaining bits as the final output key. This reduces the complexity of classical postprocessing, the amount of classical communication, and the amount of randomness needed in the protocol. While this construction has appeared in the literature, a suitable mathematical justification is lacking. In this work, we show that the security of such protocols, under certain simple conditions, follows from a slightly modified notion of secrecy of the protocol without the final error-verification step. In particular, we show that for most entropy-based proofs, the combined protocol can be implemented with no change to the key rate, and a minor change to the security parameter.