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Direct proof of security of Wegman-Carter authentication with partially known key
Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1082-8325
2014 (English)In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 13, no 10, 2155-2170 p.Article in journal (Refereed) Published
Abstract [en]

Information-theoretically secure (ITS) authentication is needed in Quantum Key Distribution (QKD). In this paper, we study security of an ITS authentication scheme proposed by Wegman& Carter, in the case of partially known authentication key. This scheme uses a new authentication key in each authentication attempt, to select a hash function from an Almost Strongly Universal2 hash function family. The partial knowledge of the attacker is measured as the trace distance between the authentication key distribution and the uniform distribution; this is the usual measure in QKD. We provide direct proofs of security of the scheme, when using partially known key, first in the information-theoretic setting and then in terms of witness indistinguishability as used in the Universal Composability (UC) framework. We find that if the authentication procedure has a failure probability ε and the authentication key has an ε´ trace distance to the uniform, then under ITS, the adversary’s success probability conditioned on an authentic message-tag pair is only bounded by ε +|Ƭ|ε´, where |Ƭ| is the size of the set of tags. Furthermore, the trace distance between the authentication key distribution and the uniform increases to |Ƭ|ε´ after having seen an authentic message-tag pair. Despite this, we are able to prove directly that the authenticated channel is indistinguishable from an (ideal) authentic channel (the desired functionality), except with probability less than ε + ε´. This proves that the scheme is (ε + ε´)-UC-secure, without using the composability theorem.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 13, no 10, 2155-2170 p.
Keyword [en]
Authentication, Strongly Universal hash functions, Partially known key, Trace distance, Universal Composability, Quantum Key Distribution.
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:liu:diva-91264DOI: 10.1007/s11128-013-0641-6ISI: 000341842000002OAI: oai:DiVA.org:liu-91264DiVA: diva2:616699
Projects
ICG QC
Available from: 2013-04-18 Created: 2013-04-18 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Authentication in Quantum Key Distribution: Security Proof and Universal Hash Functions
Open this publication in new window or tab >>Authentication in Quantum Key Distribution: Security Proof and Universal Hash Functions
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. 55 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1517
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-91265 (URN)978-91-7519-625-1 (ISBN)
Public defence
2013-05-17, Visionen, B-huset, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Projects
ICG QC
Available from: 2013-04-18 Created: 2013-04-18 Last updated: 2016-08-31Bibliographically approved

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Abidin, AysajanLarsson, Jan-Åke

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