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Mathematics

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

Jelica Radomirović, Milan Milosavljević, Zoran Banjac, Miloš Jovanović

Published Mar 21, 2023• 6 citations
Publisher

Abstract

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.

DOI
10.3390/math11061524

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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.
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.
This paper presents a system for secure digital voice signal transmission over the GSM mobile network (Global System for Mobile Communication). The cryptographic part of the system is based on Vernam cipher, which requires the same speed of generating secret symmetric keys as the basic information flow in the main channel. The system for generating and distributing secret keys for Vernam cipher is realized based on the correlation properties of the locally synthesized speech signal of the transmitter and the corresponding receiving speech signal. By applying the method of sequential distillation of secret keys (SKD) on the mentioned source of common randomness, the generation speed of up to 34 kb/s is ensured, which is more than enough to maintain the absolute secrecy of Vernam cipher. The price that needs to be paid is the necessity of having an additional authenticated public channel through which the SKD protocol is performed. The privacy amplification block, as a necessary part of the SKD protocol, was implemented using machine learning methods, in order to reliably estimate the conditional Renyi entropy of the second order. According to our knowledge, this is the first autonomous, perfectly secret system for voice transmission over the GSM network without explicit prior generation and distribution of secret keys.
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.
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.