© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Symmetry

Privacy Amplification Strategies in Sequential Secret Key Distillation Protocols Based on Machine Learning

Jelica Radomirović, Milan Milosavljević, Branko D. Kovačević, Miloš Jovanović

Published Sep 27, 2022• 6 citations

Abstract

It is well known that Renyi’s entropy of order 2 determines the maximum possible length of the distilled secret keys in sequential secret key distillation protocols so that no information is leaked to the eavesdropper. There have been no attempts to estimate this key quantity based on information available to the legitimate parties to this protocol in the literature. We propose a new machine learning system, which estimates the lower bound of conditional Renyi entropy with high accuracy, based on 13 characteristics locally measured on the side of legitimate participants. The system is based on a prediction intervals deep neural network, trained for a given source of common randomness. We experimentally evaluated this result for two different sources, namely 14 and 6-dimensional EEG signals, of 50 participants, with varying advantage distillation and information reconciliation strategies with and without additional lossless compression block. Across all proposed systems and analyzed sources on average, the best machine learning strategy, called the hybrid strategy, increases the quantity of generated keys 2.77 times compared to the classical strategy. By introducing the Huffman lossless coder before the PA block, the loss of potential source randomness was reduced from 68.48% to a negligible 0.75%, while the leakage rate per one bit remains in the order of magnitude 10−4.

DOI: 10.3390/sym14102028

Related papers

Secret Key Distillation with Speech Input and Deep Neural Network-Controlled Privacy Amplification

Jelica Radomirović, Milan Milosavljević, Zoran Banjac +1 more

We propose a new high-speed secret key distillation system via public discussion based on the common randomness contained in the speech signal of the protocol participants. The proposed system consists of subsystems for quantization, advantage distillation, information reconciliation, an estimator for predicting conditional Renyi entropy, and universal hashing. The parameters of the system are optimized in order to achieve the maximum key distillation rate. By introducing a deep neural block for the prediction of conditional Renyi entropy, the lengths of the distilled secret keys are adaptively determined. The optimized system gives a key rate of over 11% and negligible information leakage to the eavesdropper, while NIST tests show the high cryptographic quality of produced secret keys. For a sampling rate of 16 kHz and quantization of input speech signals with 16 bits per sample, the system provides secret keys at a rate of 28 kb/s. This speed opens the possibility of wider application of this technology in the field of contemporary information security.

Mathematics•Mar 21, 2023•6 citations

One-way rate-limited sequential key-distillation

Rémi A. Chou, Matthieu R. Bloch

We study the problem of key-distillation for a source model, with a one-way and rate-limited public communication between two legitimate users. Although, the secret-key capacity is already known, we provide an alternative achievability scheme, that directly translates into practical designs. We consider a sequential key-distillation strategy, which consists of a reconciliation phase followed by a privacy amplification phase performed with extractors. We determine the reconciliation capacity and show that, for a degraded source, such a sequential strategy leads to an optimal key-distillation strategy that achieves the secret-key capacity. We illustrate our results in the case of a binary source model.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•3 citations

Amplifying Privacy in Privacy Amplification.

Divesh Aggarwal, Yevgeniy Dodis, Zahra Jafargholi +2 more

We study the classical problem of privacy amplification, where two parties Alice and Bob share a weak secret X of min-entropy k, and wish to agree on secret key R of length m over a public communication channel completely controlled by a computationally unbounded attacker Eve. Despite being extensively studied in the literature, the problem of designing “optimal ” efficient privacy amplification protocols is still open, because there are several optimization goals. The first of them is (1) minimizing the entropy loss L = k−m (it is known that the optimal value for L = O(λ), where ε = 2−λ is the desired security of the protocol). Other important considerations include (2) minimizing the number of communication rounds, (3) maintaining security even after the secret key is used (this is called post-application robustness), and (4) ensuring that the protocol P does not leak some “useful information ” about the source X (this is called source privacy). Additionally, when dealing with a very long source X, as happens in the so-called Bounded Retrieval Model (BRM), extracting as long a key as possible is no longer the goal. Instead, the goals are (5) to touch as little of X as possible (for efficiency), and (6) to be able to run the protocol many times on the same X, extracting multiple secure keys.

•Jan 1, 2013•0 citations

Length of the unconditionally secure secret key distilled by public discussion

Liu Sheng

This paper discusses how to distill the secret key by public discussion using unconditionally secure secret key agreement protocols. The relation between the length of the distilled secret key and the information reconciliation privacy amplification in the protocol is shown with the help of Universal Hash and Renyi entropy.

Jounal of Xidian University•Jan 1, 1999•0 citations

Privacy Amplification in Quantum Key Distribution with Machine Learning

Nipun Agarwal

The Quantum Key Distribution (QKD) method leverages the principles of quantum mechanics to securely create and distribute private keys using quantum systems and an authenticated public classical channel. Despite offering informationtheoretical security, its physical implementations often suffer from unintended information leakage, known as side channels, which eavesdroppers can exploit to obtain the private key. This study introduces a classical-side-channel attack on the privacyamplification step of a general QKD protocol based on matrix hashing, utilizing machine-learning techniques to analyze powerconsumption leakage. Through multiple simulated scenarios, the study found that the gradient-boosting machine consistently outperformed other models, recovering the entire private key for high measuring-instrument sampling rates, regardless of the hashing matrix size and noise level tested. Additionally, the study proposes a strategy based on analyzing the confusion matrices of the model to facilitate a brute-force search for the critical feasible in the case of a non-perfect model. Furthermore, the study discusses countermeasures such as noise insertion, masking, and randomization techniques, potentially restoring the QKD protocol's information-theoretical security. This work demonstrates that machine-learning techniques can effectively characterize the leakages in a QKD implementation and create potent attacks.

•Jul 15, 2024•0 citations

Information Reconciliation for Quantum Key Distribution

David Elkouss, Jesús Martínez-Mateo, Vicente Martín Ayuso +1 more

Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.

•Oct 1, 2010•31 citations

It is well known that Renyi’s entropy of order 2 determines the maximum possible length of the distilled secret keys in sequential secret key distillation protocols so that no information is leaked to the eavesdropper. There have been no attempts to estimate this key quantity based on information available to the legitimate parties to this protocol in the literature. We propose a new machine learning system, which estimates the lower bound of conditional Renyi entropy with high accuracy, based on 13 characteristics locally measured on the side of legitimate participants. The system is based on a prediction intervals deep neural network, trained for a given source of common randomness. We experimentally evaluated this result for two different sources, namely 14 and 6-dimensional EEG signals, of 50 participants, with varying advantage distillation and information reconciliation strategies with and without additional lossless compression block. Across all proposed systems and analyzed sources on average, the best machine learning strategy, called the hybrid strategy, increases the quantity of generated keys 2.77 times compared to the classical strategy. By introducing the Huffman lossless coder before the PA block, the loss of potential source randomness was reduced from 68.48% to a negligible 0.75%, while the leakage rate per one bit remains in the order of magnitude 10−4.

We propose a new high-speed secret key distillation system via public discussion based on the common randomness contained in the speech signal of the protocol participants. The proposed system consists of subsystems for quantization, advantage distillation, information reconciliation, an estimator for predicting conditional Renyi entropy, and universal hashing. The parameters of the system are optimized in order to achieve the maximum key distillation rate. By introducing a deep neural block for the prediction of conditional Renyi entropy, the lengths of the distilled secret keys are adaptively determined. The optimized system gives a key rate of over 11% and negligible information leakage to the eavesdropper, while NIST tests show the high cryptographic quality of produced secret keys. For a sampling rate of 16 kHz and quantization of input speech signals with 16 bits per sample, the system provides secret keys at a rate of 28 kb/s. This speed opens the possibility of wider application of this technology in the field of contemporary information security.

We study the problem of key-distillation for a source model, with a one-way and rate-limited public communication between two legitimate users. Although, the secret-key capacity is already known, we provide an alternative achievability scheme, that directly translates into practical designs. We consider a sequential key-distillation strategy, which consists of a reconciliation phase followed by a privacy amplification phase performed with extractors. We determine the reconciliation capacity and show that, for a degraded source, such a sequential strategy leads to an optimal key-distillation strategy that achieves the secret-key capacity. We illustrate our results in the case of a binary source model.

We study the classical problem of privacy amplification, where two parties Alice and Bob share a weak secret X of min-entropy k, and wish to agree on secret key R of length m over a public communication channel completely controlled by a computationally unbounded attacker Eve. Despite being extensively studied in the literature, the problem of designing “optimal ” efficient privacy amplification protocols is still open, because there are several optimization goals. The first of them is (1) minimizing the entropy loss L = k−m (it is known that the optimal value for L = O(λ), where ε = 2−λ is the desired security of the protocol). Other important considerations include (2) minimizing the number of communication rounds, (3) maintaining security even after the secret key is used (this is called post-application robustness), and (4) ensuring that the protocol P does not leak some “useful information ” about the source X (this is called source privacy). Additionally, when dealing with a very long source X, as happens in the so-called Bounded Retrieval Model (BRM), extracting as long a key as possible is no longer the goal. Instead, the goals are (5) to touch as little of X as possible (for efficiency), and (6) to be able to run the protocol many times on the same X, extracting multiple secure keys.

The Quantum Key Distribution (QKD) method leverages the principles of quantum mechanics to securely create and distribute private keys using quantum systems and an authenticated public classical channel. Despite offering informationtheoretical security, its physical implementations often suffer from unintended information leakage, known as side channels, which eavesdroppers can exploit to obtain the private key. This study introduces a classical-side-channel attack on the privacyamplification step of a general QKD protocol based on matrix hashing, utilizing machine-learning techniques to analyze powerconsumption leakage. Through multiple simulated scenarios, the study found that the gradient-boosting machine consistently outperformed other models, recovering the entire private key for high measuring-instrument sampling rates, regardless of the hashing matrix size and noise level tested. Additionally, the study proposes a strategy based on analyzing the confusion matrices of the model to facilitate a brute-force search for the critical feasible in the case of a non-perfect model. Furthermore, the study discusses countermeasures such as noise insertion, masking, and randomization techniques, potentially restoring the QKD protocol's information-theoretical security. This work demonstrates that machine-learning techniques can effectively characterize the leakages in a QKD implementation and create potent attacks.

Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.