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

IEEE International Symposium on Information Theory (ISIT)

Precise evaluation of leaked information with universal2 privacy amplification in the presence of quantum attacker

Masahito Hayashi

Published Jul 1, 2012• 7 citations
Publisher

Abstract

We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner's, which are based on quantum conditional Rényi entropy of order 1 + s. Using those theorems, we derive an exponential decreasing rate for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.

DOI
10.1109/isit.2012.6284690

Related papers

Exponential Decreasing Rate of Leaked Information in Universal Random Privacy Amplification

Masahito Hayashi

We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett 's bound based on the Rényi entropy of order 2 because the bound obtained here uses the Rényi entropy of order 1+sfors∈ [0,1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi 's exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.

arXiv:0904.0308•IEEE Transactions on Information Theory•May 25, 2011•269 citations

Exponential secrecy against unbounded adversary using joint encryption and privacy amplification

Yahya S. Khiabani, Shuangqing Wei

In this paper without tailoring to any presumed condition on communication channel or any restriction on adversary's resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. A key extractor based on a sampler and a Rényi extractor derives secret keys with the required entropy from this source. A general cipher uses this key to ensure the required equivocation for the plaintext and to establish the first layer of secrecy. Using privacy amplification on top of this cipher based on inverse universal2hashing constitutes the second layer of secrecy for highly confidential message transmission with information leakage that is exponentially decreasing. We provide exponent analysis and optimization to minimize information leakage in terms of Eve's distinguishability based on L1norm distance from uniformity. The required key rate is characterized for different source entropies in order to guarantee the secrecy that is demanded in terms of secrecy exponent for the second layer and Eve's error rate for the first layer.

IEEE Conference on Communications and Network Security•Oct 1, 2013•1 citation

Rethinking quantum smooth entropies: Tight one-shot analysis of quantum privacy amplification

Bartosz Regula, Marco Tomamichel

We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic constraints. Our main tool is a new class of smooth conditional entropies defined by lifting classical smooth divergences through measurements. A key role is played by the measured smooth Rényi relative entropy of order 2, which we show to admit an equivalent variational form: it can be understood as allowing for smoothing over not only states, but also non-positive Hermitian operators. Building on this, we establish a tightened leftover hash lemma, significantly improving over all known smooth min-entropy bounds on extractable randomness and recovering the sharpest classical achievability results. We extend these methods to decoupling, the coherent analogue of privacy amplification, obtaining a corresponding improved one-shot bound. Relaxing our smooth entropy bounds leads to one-shot achievability results in terms of measured Rényi divergences, tightening the bounds of [Dupuis, arXiv:2105.05342] and recovering state-of-the-art asymptotic i.i.d. error exponents. We show an approximate optimality of our results by giving a matching one-shot converse bound up to additive logarithmic terms. This yields an optimal second-order asymptotic expansion of privacy amplification under trace distance, establishing a significantly tighter one-shot achievability result than previously shown in [Shen et al., arXiv:2202.11590] and proving its optimality for all hash functions.

quant-pharXiv:2603.04493•Mar 6, 2026•0 citations

An end-to-end exponentially secure secrecy scheme against an unbounded adversary

Yahya S. Khiabani, Shuangqing Wei

In this paper without tailoring to any physical channel condition or any restriction on adversary's computational resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only advantage for legitimate users over eavesdropper is existence of a key source that is partially known by Eve. A key extractor based on a sampler and a Renyi extractor derives secret keys with the required entropy from this source. Encryption using this key with a general cipher maps Eve's uncertainty about the key to uncertainty about the plaintext that can also be interpreted as degradation in her channel. Using privacy amplification on top of this cipher based on inverse universal2 hashing results in information leakage with decreasing exponent that can be optimized to guarantee a higher level of secrecy.

Conference on Information Sciences and Systems•Mar 1, 2013•2 citations

Classical and quantum security analysis via smoothing of Renyi entropy of order 2

Masahito Hayashi

It is known that the security evaluation can be done by smoothing of Renyi entropy of order 2 in the classical ans quantum settings when we apply universal2 hash functions. This fact can be extended to the case when we apply ǫ-almost dual universal2 hash functions. Demonstrating the smoothing of Renyi entropy of order 2, we derived security bounds for universal composability and mutual information criterion under the condition in the classical and quantum setting. Further, we apply this analysis to the secret key generation with error correction.

•Feb 1, 2012•5 citations

Large Deviation Analysis for Quantum Security via Smoothing of Rényi Entropy of Order 2

Masahito Hayashi

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decreasing rates. These results are extended to the case when we apply ε-almost dual universal2hash functions. Furthermore, we apply this analysis to the secret key generation with error correction.

arXiv:1202.0322•IEEE Transactions on Information Theory•Aug 6, 2014•35 citations
We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner's, which are based on quantum conditional Rényi entropy of order 1 + s. Using those theorems, we derive an exponential decreasing rate for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.
We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett 's bound based on the Rényi entropy of order 2 because the bound obtained here uses the Rényi entropy of order 1+sfors∈ [0,1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi 's exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.
In this paper without tailoring to any presumed condition on communication channel or any restriction on adversary's resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. A key extractor based on a sampler and a Rényi extractor derives secret keys with the required entropy from this source. A general cipher uses this key to ensure the required equivocation for the plaintext and to establish the first layer of secrecy. Using privacy amplification on top of this cipher based on inverse universal2hashing constitutes the second layer of secrecy for highly confidential message transmission with information leakage that is exponentially decreasing. We provide exponent analysis and optimization to minimize information leakage in terms of Eve's distinguishability based on L1norm distance from uniformity. The required key rate is characterized for different source entropies in order to guarantee the secrecy that is demanded in terms of secrecy exponent for the second layer and Eve's error rate for the first layer.
We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic constraints. Our main tool is a new class of smooth conditional entropies defined by lifting classical smooth divergences through measurements. A key role is played by the measured smooth Rényi relative entropy of order 2, which we show to admit an equivalent variational form: it can be understood as allowing for smoothing over not only states, but also non-positive Hermitian operators. Building on this, we establish a tightened leftover hash lemma, significantly improving over all known smooth min-entropy bounds on extractable randomness and recovering the sharpest classical achievability results. We extend these methods to decoupling, the coherent analogue of privacy amplification, obtaining a corresponding improved one-shot bound. Relaxing our smooth entropy bounds leads to one-shot achievability results in terms of measured Rényi divergences, tightening the bounds of [Dupuis, arXiv:2105.05342] and recovering state-of-the-art asymptotic i.i.d. error exponents. We show an approximate optimality of our results by giving a matching one-shot converse bound up to additive logarithmic terms. This yields an optimal second-order asymptotic expansion of privacy amplification under trace distance, establishing a significantly tighter one-shot achievability result than previously shown in [Shen et al., arXiv:2202.11590] and proving its optimality for all hash functions.
In this paper without tailoring to any physical channel condition or any restriction on adversary's computational resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only advantage for legitimate users over eavesdropper is existence of a key source that is partially known by Eve. A key extractor based on a sampler and a Renyi extractor derives secret keys with the required entropy from this source. Encryption using this key with a general cipher maps Eve's uncertainty about the key to uncertainty about the plaintext that can also be interpreted as degradation in her channel. Using privacy amplification on top of this cipher based on inverse universal2 hashing results in information leakage with decreasing exponent that can be optimized to guarantee a higher level of secrecy.
It is known that the security evaluation can be done by smoothing of Renyi entropy of order 2 in the classical ans quantum settings when we apply universal2 hash functions. This fact can be extended to the case when we apply ǫ-almost dual universal2 hash functions. Demonstrating the smoothing of Renyi entropy of order 2, we derived security bounds for universal composability and mutual information criterion under the condition in the classical and quantum setting. Further, we apply this analysis to the secret key generation with error correction.
It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decreasing rates. These results are extended to the case when we apply ε-almost dual universal2hash functions. Furthermore, we apply this analysis to the secret key generation with error correction.