One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes

This paper introduces a class of symmetric ciphering systems with a finite secret key, which provides ideal secrecy, autonomy in key generation and distribution, and robustness against the probabilistic structure of messages (the Ideally Secret Autonomous Robust (ISAR) system). The ISAR system is ba...

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Main Authors: Milan Milosavljević, Jelica Radomirović, Tomislav Unkašević, Boško Božilović
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/23/3724
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author Milan Milosavljević
Jelica Radomirović
Tomislav Unkašević
Boško Božilović
author_facet Milan Milosavljević
Jelica Radomirović
Tomislav Unkašević
Boško Božilović
author_sort Milan Milosavljević
collection DOAJ
description This paper introduces a class of symmetric ciphering systems with a finite secret key, which provides ideal secrecy, autonomy in key generation and distribution, and robustness against the probabilistic structure of messages (the Ideally Secret Autonomous Robust (ISAR) system). The ISAR system is based on wiretap polar codes constructed over an artificial wiretap channel with a maximum secrecy capacity of 0.5. The system autonomously maintains a minimum level of key equivocation by continuously refreshing secret keys without additional key generation and distribution infrastructure. Moreover, it can transform any stream ciphering system with a finite secret key of known length into an ISAR system without knowing and/or changing its algorithm. Therefore, this class of system strongly supports privacy, a critical requirement for contemporary security systems. The ISAR system’s reliance on wiretap polar coding for strong secrecy ensures resistance to passive known plaintext attacks. Furthermore, resistance to passive attacks on generated refreshing keys follows directly from ideal secrecy and autonomy. The results presented offer an efficient methodology for synthesizing this class of systems with predetermined security margins and a complexity of the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo>⁡</mo><mrow><mi>n</mi></mrow></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi></mrow></semantics></math></inline-formula> is the block length of the applied polar code.
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spelling doaj-art-501f8a63e57a4136a01ad2ccfd6edaef2025-08-20T02:50:38ZengMDPI AGMathematics2227-73902024-11-011223372410.3390/math12233724One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar CodesMilan Milosavljević0Jelica Radomirović1Tomislav Unkašević2Boško Božilović3Vlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, SerbiaVlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, SerbiaVlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, SerbiaVlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, SerbiaThis paper introduces a class of symmetric ciphering systems with a finite secret key, which provides ideal secrecy, autonomy in key generation and distribution, and robustness against the probabilistic structure of messages (the Ideally Secret Autonomous Robust (ISAR) system). The ISAR system is based on wiretap polar codes constructed over an artificial wiretap channel with a maximum secrecy capacity of 0.5. The system autonomously maintains a minimum level of key equivocation by continuously refreshing secret keys without additional key generation and distribution infrastructure. Moreover, it can transform any stream ciphering system with a finite secret key of known length into an ISAR system without knowing and/or changing its algorithm. Therefore, this class of system strongly supports privacy, a critical requirement for contemporary security systems. The ISAR system’s reliance on wiretap polar coding for strong secrecy ensures resistance to passive known plaintext attacks. Furthermore, resistance to passive attacks on generated refreshing keys follows directly from ideal secrecy and autonomy. The results presented offer an efficient methodology for synthesizing this class of systems with predetermined security margins and a complexity of the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mrow><mrow><mi mathvariant="normal">log</mi></mrow><mo>⁡</mo><mrow><mi>n</mi></mrow></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi></mrow></semantics></math></inline-formula> is the block length of the applied polar code.https://www.mdpi.com/2227-7390/12/23/3724cryptographyideal secrecypolar codingwiretap channelkey equivocationprivacy amplification
spellingShingle Milan Milosavljević
Jelica Radomirović
Tomislav Unkašević
Boško Božilović
One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
Mathematics
cryptography
ideal secrecy
polar coding
wiretap channel
key equivocation
privacy amplification
title One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
title_full One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
title_fullStr One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
title_full_unstemmed One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
title_short One Class of Ideally Secret Autonomous Symmetric Ciphering Systems Based on Wiretap Polar Codes
title_sort one class of ideally secret autonomous symmetric ciphering systems based on wiretap polar codes
topic cryptography
ideal secrecy
polar coding
wiretap channel
key equivocation
privacy amplification
url https://www.mdpi.com/2227-7390/12/23/3724
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AT tomislavunkasevic oneclassofideallysecretautonomoussymmetriccipheringsystemsbasedonwiretappolarcodes
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