Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Effective Privacy Amplification for Secure Classical Communications⋆

Horváth, T., Kish, L. B., Jacob Scheuer

Published Jan 1, 2011• 32 citations
OpenAlex

Abstract

We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10−8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.

Related papers

Effective privacy amplification for secure classical communications

T. Horváth, L. B. Kish, J. Scheuer

We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10 −8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.

arXiv:1101.4264•Europhysics Letters (EPL)•Apr 1, 2011•38 citations

Security Issues Associated With Error Correction And Privacy Amplification In Quantum Key Distribution

Horace P. Yuen

Privacy amplification is a necessary step in all quantum key distribution protocols, and error correction is needed in each except when signals of many photons are used in the key communication in quantum noise approach. No security analysis of error correcting code information leak to the attacker has ever been provided, while an ad hoc formula is currently employed to account for such leak in the key generation rate. It is also commonly believed that privacy amplification allows the users to at least establish a short key of arbitrarily close to perfect security. In this paper we show how the lack of rigorous error correction analysis makes the otherwise valid privacy amplification results invalid, and that there exists a limit on how close to perfect a generated key can be obtained from privacy amplification. In addition, there is a necessary tradeoff between key rate and security, and the best theoretical values from current theories would not generate enough near-uniform key bits to cover the message authentication key cost in disturbance-information tradeoff protocols of the BB84 variety.

arXiv:1411.2310•Nov 10, 2014•1 citation

Stream Privacy Amplification for Quantum Cryptography

Yizhi Huang, Xingjian Zhang, Xiongfeng Ma

Abstract Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated before privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy amplification scheme, which resembles the classical stream cipher, to solve the problems of final key generation delay and error spread. The stream scheme can also help to enhance the security of trusted-relay quantum networks. Inspired by the connection between stream ciphers and quantum error correction in our security analysis, we further develop a generic information-theoretic tool to study the security of classical encryption algorithms.

arXiv:2111.14108•PRX Quantum•Jun 10, 2022•11 citations

Privacy Amplification in Quantum Key Distribution: Pointwise Bound versus Average Bound

Gerald N. Gilbert, Michael Hamrick, F. Javier Thayer

In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.

arXiv:quant-ph/0108013•Aug 2, 2001•3 citations

Practical scheme to share a secret key through a quantum channel with a 27.6% bit error rate

H. F. Chau

A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due to eavesdropping or imperfect apparatus is low. Here, a practical quantum key distribution scheme by making use of an adaptive privacy amplification procedure with two-way classical communication is reported. Then, it is proven that the scheme generates a secret key whenever the bit error rate of the quantum channel is less than $0.5\ensuremath{-}0.1\sqrt{5}\ensuremath{\approx}27.6%,$ thereby making it the most error resistant scheme known to date.

Physical Review A•Dec 20, 2002•232 citations

Practical Scheme To Share A Secret Key Through An Up To 27.6% Bit Error Rate Quantum Channel

H. F. Chau

A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due to eavesdropping or imperfect apparatus is low. Here, I report a practical quantum key distribution scheme making use of an adaptive privacy amplification procedure with two-way classical communication. Then, I prove that the scheme generates a secret key whenever the bit error rate of the quantum channel is less than $0.5-0.1\sqrt{5} \approx 27.6%$, thereby making it the most error resistant scheme known to date.

arXiv:quant-ph/0205060•May 11, 2002•6 citations
We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10−8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.
We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10 −8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.
Privacy amplification is a necessary step in all quantum key distribution protocols, and error correction is needed in each except when signals of many photons are used in the key communication in quantum noise approach. No security analysis of error correcting code information leak to the attacker has ever been provided, while an ad hoc formula is currently employed to account for such leak in the key generation rate. It is also commonly believed that privacy amplification allows the users to at least establish a short key of arbitrarily close to perfect security. In this paper we show how the lack of rigorous error correction analysis makes the otherwise valid privacy amplification results invalid, and that there exists a limit on how close to perfect a generated key can be obtained from privacy amplification. In addition, there is a necessary tradeoff between key rate and security, and the best theoretical values from current theories would not generate enough near-uniform key bits to cover the message authentication key cost in disturbance-information tradeoff protocols of the BB84 variety.
Abstract Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated before privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy amplification scheme, which resembles the classical stream cipher, to solve the problems of final key generation delay and error spread. The stream scheme can also help to enhance the security of trusted-relay quantum networks. Inspired by the connection between stream ciphers and quantum error correction in our security analysis, we further develop a generic information-theoretic tool to study the security of classical encryption algorithms.
In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.
A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due to eavesdropping or imperfect apparatus is low. Here, a practical quantum key distribution scheme by making use of an adaptive privacy amplification procedure with two-way classical communication is reported. Then, it is proven that the scheme generates a secret key whenever the bit error rate of the quantum channel is less than $0.5\ensuremath{-}0.1\sqrt{5}\ensuremath{\approx}27.6%,$ thereby making it the most error resistant scheme known to date.
A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due to eavesdropping or imperfect apparatus is low. Here, I report a practical quantum key distribution scheme making use of an adaptive privacy amplification procedure with two-way classical communication. Then, I prove that the scheme generates a secret key whenever the bit error rate of the quantum channel is less than 0.5−0.15≈27.60.5-0.1\sqrt{5} \approx 27.6%0.5−0.15​≈27.6, thereby making it the most error resistant scheme known to date.