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Authentication in Quantum Key Distribution : Security Proof and Universal Hash Functions

Aysajan Abidin

Published Jan 1, 2013• 17 citations
OpenAlex

Abstract

Quantum Key Distribution (QKD) is a secret key agreement technique that consists of two parts: quantum transmission and measurement on a quantum channel, and classical post-processing on a public communication channel. It enjoys provable unconditional security provided that the public communication channel is immutable. Otherwise, QKD is vulnerable to a man-in-the-middle attack. Immutable public communication channels, however, do not exist in practice. So we need to use authentication that implements the properties of an immutable channel as well as possible. One scheme that serves this purpose well is the Wegman-Carter authentication (WCA), which is built upon Almost Strongly Universal2 (ASU2) hashing. This scheme uses a new key in each authentication attempt to select a hash function from an ASU2 family, which is then used to generate the authentication tag for a message. The main focus of this dissertation is on authentication in the context of QKD. We study ASU2 hash functions, security of QKD that employs a computationally secure authentication, and also security of authentication with a partially known key. Specifically, we study the following. First, Universal hash functions and their constructions are reviewed, and as well as a new construction of ASU2 hash functions is presented. Second, security of QKD that employs a specific computationally secure authentication is studied. We present detailed attacks on various practical implementations of QKD that employs this authentication. We also provide countermeasures and prove necessary and sufficient conditions for upgrading the security of the authentication to the level of unconditional security. Third, Universal hash function based multiple authentication is studied. This uses a fixed ASU2 hash function followed by one-time pad encryption, to keep the hash function secret. We show that the one-time pad is necessary in every round for the authentication to be unconditionally secure. Lastly, we study security of the WCA scheme, in the case of a partially known authentication key. Here we prove tight information-theoretic security bounds and also analyse security using witness indistinguishability as used in the Universal Composability framework.

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Quantum Key Distribution (QKD) is a secret key agreement technique that consists of two parts: quantum transmission and measurement on a quantum channel, and classical post-processing on a public communication channel. It enjoys provable unconditional security provided that the public communication channel is immutable. Otherwise, QKD is vulnerable to a man-in-the-middle attack. Immutable public communication channels, however, do not exist in practice. So we need to use authentication that implements the properties of an immutable channel as well as possible. One scheme that serves this purpose well is the Wegman-Carter authentication (WCA), which is built upon Almost Strongly Universal2 (ASU2) hashing. This scheme uses a new key in each authentication attempt to select a hash function from an ASU2 family, which is then used to generate the authentication tag for a message. The main focus of this dissertation is on authentication in the context of QKD. We study ASU2 hash functions, security of QKD that employs a computationally secure authentication, and also security of authentication with a partially known key. Specifically, we study the following. First, Universal hash functions and their constructions are reviewed, and as well as a new construction of ASU2 hash functions is presented. Second, security of QKD that employs a specific computationally secure authentication is studied. We present detailed attacks on various practical implementations of QKD that employs this authentication. We also provide countermeasures and prove necessary and sufficient conditions for upgrading the security of the authentication to the level of unconditional security. Third, Universal hash function based multiple authentication is studied. This uses a fixed ASU2 hash function followed by one-time pad encryption, to keep the hash function secret. We show that the one-time pad is necessary in every round for the authentication to be unconditionally secure. Lastly, we study security of the WCA scheme, in the case of a partially known authentication key. Here we prove tight information-theoretic security bounds and also analyse security using witness indistinguishability as used in the Universal Composability framework.
Authentication is an indispensable part of Quantum Cryptography, which is an unconditionally secure key distribution technique based on the laws of nature. Without proper authentication, Quantum Cryptography is vulnerable to “man-in-the-middle” attacks. Therefore, to guarantee unconditional security of any Quantum Cryptographic protocols, the authentication used must also be unconditionally secure. The standard in Quantum Cryptography is to use theWegman-Carter authentication, which is unconditionally secure and is based on the idea of universal hashing. In this thesis, we first investigate properties of a Strongly Universal hash function family to facilitate understanding the properties of (classical) authentication used in Quantum Cryptography. Then, we study vulnerabilities of a recently proposed authentication protocol intended to rule out a "man-in-the-middle" attack on Quantum Cryptography. Here, we point out that the proposed authentication primitive is not secure when used in a generic Quantum Cryptographic protocol. Lastly, we estimate the lifetime of authentication using encrypted tags when the encryption key is partially known. Under simplifying assumptions, we derive that the lifetime is linearly dependent on the length of the authentication key. Experimental results that support the theoretical results are also presented.
We study the security of a specific authentication procedure of interest in the context of Quantum Key Distribution (QKD). It works as follows: use a secret but fixed Strongly Universal2_22​ (SU2_22​) hash function and encrypt the output tag with a one-time pad (OTP). If the OTP is completely secret, the expected time for an adversary to create a tag for a chosen message is exponential in the tag length. If, however, the OTP is partially known in each authentication round, as is the case in practical QKD protocols, then the picture is different; the adversary's partial knowledge of the OTP in each authentication round gives partial information on the secret hash function, and this weakens the authentication in later rounds. The effect of this is that the lifetime of the system is linear in the length of the fixed key. This is supported by the composability theorem for QKD, that in this setting provides an upper bound to the security loss on the secret hash function, which is exponential in the number of authentication rounds. This needs to be taken into account when using the protocol, since the authentication gets weakened at each subsequent round and thus the QKD generated is key is not as strong as when the authentication is strong. Some countermeasures are discussed at the end of this paper.
Quantum Key Distribution (QKD - also referred to as Quantum Cryptography) is a technique for secret key agreement. It has been shown that QKD rigged with Information-Theoretic Secure (ITS) authentication (using secret key) of the classical messages transmitted during the key distribution protocol is also ITS. Note, QKD without any authentication can trivially be broken by man-in-the-middle attacks. Here, we study an authentication method that was originally proposed because of its low key consumption; a two-step authentication that uses a publicly known hash function, followed by a secret strongly universal2 hash function, which is exchanged each round. This two-step authentication is not information-theoretically secure but it was argued that nevertheless it does not compromise the security of QKD. In the current contribution we study intrinsic weaknesses of this approach under the common assumption that the QKD adversary has access to unlimited resources including quantum memories. We consider one implementation of Quantum Cryptographic protocols that use such authentication and demonstrate an attack that fully extract the secret key. Even including the final key from the protocol in the authentication does not rule out the possibility of these attacks. To rectify the situation, we propose a countermeasure that, while not information-theoretically secure, restores the need for very large computing power for the attack to work. Finally, we specify conditions that must be satisfied by the two-step authentication in order to restore information-theoretic security.
Abstract In addition to the quantum channel, an auxiliary classical authentic communication channel is required for quantum key distribution. To provide unconditional security in quantum cryptography, which based on the fundamental laws of quantum mechanics, information-theoretic authentication is required, and not authentication based on computational complexity. The paper provides a security proof of information-theoretic authentication in quantum cryptography using ɛ -ASU 2 hash functions. The internal structure of ɛ -ASU 2 hash functions is not used in the proof, so these hash functions can be implemented by a different composition of other hash functions, for example, including the composition ɛ -AXU 2 functions with a reused key and subsequent encryption of the tag with a one-time pad key, which is taken from the previous session of quantum key distribution. It is also shown that information-theoretic authentication preserves composable security of the keys. This authentication method can also be used for key agrrement in in networks with trusted nodes (Molotkov 2022 Laser Phys. Lett. 19 045201–9; Arbekov and Molotkov 2020 Laser Phys. Lett. 17 055202–8) and with quantum key distribution.
This work describes the using of Universal and Strongly Universal classes of hash functions for unconditionally secure message authentication in quantum cryptogra- phy. Different classes are compared and constructions of flexible e-Almost Strongly Universal classes are described. A new upper bound on the lifetime of a single hash function in one-time padded tags is introduced and optimisation on the final QKD key rate is shown for the QuAKE experiment, a B92 based QKD system. The public channel communication protocol of QuAKE is described, with special stress on the security issues
Quantum key distribution (QKD) enables unconditionally secure communication between distinct parties using a quantum channel and an authentic public channel. Reducing the portion of quantum-generated secret keys, that is consumed during the authentication procedure, is of significant importance for improving the performance of QKD systems. In the present work, we develop a lightweight authentication protocol for QKD based on a `ping-pong' scheme of authenticity check for QKD. An important feature of this scheme is that the only one authentication tag is generated and transmitted during each of the QKD post-processing rounds. For the tag generation purpose, we design an unconditionally secure procedure based on the concept of key recycling. The procedure is based on the combination of almost universal2polynomial hashing, XOR universal2Toeplitz hashing, and one-time pad (OTP) encryption. We demonstrate how to minimize both the length of the recycled key and the size of the authentication key, that is required for OTP encryption. As a result, in real case scenarios, the portion of quantum-generated secret keys that is consumed for the authentication purposes is below 1%. Finally, we provide a security analysis of the full quantum key growing process in the framework of universally composable security.