We introduce two new Kirchhoff-law-Johnson-noise (KLJN) secure key distribution schemes which are generalizations of the original KLJN scheme. The first of these, the Random-Resistor (RR-) KLJN scheme, uses random resistors with values chosen from a quasi-continuum set. It is well-known since the creation of the KLJN concept that such a system could work in cryptography, because Alice and Bob can calculate the unknown resistance value from measurements, but the RR-KLJN system has not been addressed in prior publications since it was considered impractical. The reason for discussing it now is the second scheme, the Random-Resistor-Random-Temperature (RRRT-) KLJN key exchange, inspired by a recent paper of Vadai, Mingesz and Gingl, wherein security was shown to be maintained at non-zero power flow. In the RRRT-KLJN secure key exchange scheme, both the resistances and their temperatures are continuum random variables. We prove that the security of the RRRT-KLJN scheme can prevail at non-zero power flow, and thus the physical law guaranteeing security is not the Second Law of Thermodynamics but the Fluctuation-Dissipation Theorem. Alice and Bob know their own resistances and temperatures and can calculate the resistance and temperature values at the other end of the communication channel from measured voltage, current and power-flow data in the wire. However, Eve cannot determine these values because, for her, there are four unknown quantities while she can set up only three equations. The RRRT-KLJN scheme has several advantages and makes all former attacks on the KLJN scheme invalid or incomplete.
{"title":"Random-resistor-random-temperature Kirchhoff-law-Johnson-noise (RRRT-KLJN) key exchange","authors":"L. Kish, C. Granqvist","doi":"10.1515/mms-2016-0007","DOIUrl":"https://doi.org/10.1515/mms-2016-0007","url":null,"abstract":"We introduce two new Kirchhoff-law-Johnson-noise (KLJN) secure key distribution schemes which are generalizations of the original KLJN scheme. The first of these, the Random-Resistor (RR-) KLJN scheme, uses random resistors with values chosen from a quasi-continuum set. It is well-known since the creation of the KLJN concept that such a system could work in cryptography, because Alice and Bob can calculate the unknown resistance value from measurements, but the RR-KLJN system has not been addressed in prior publications since it was considered impractical. The reason for discussing it now is the second scheme, the Random-Resistor-Random-Temperature (RRRT-) KLJN key exchange, inspired by a recent paper of Vadai, Mingesz and Gingl, wherein security was shown to be maintained at non-zero power flow. In the RRRT-KLJN secure key exchange scheme, both the resistances and their temperatures are continuum random variables. We prove that the security of the RRRT-KLJN scheme can prevail at non-zero power flow, and thus the physical law guaranteeing security is not the Second Law of Thermodynamics but the Fluctuation-Dissipation Theorem. Alice and Bob know their own resistances and temperatures and can calculate the resistance and temperature values at the other end of the communication channel from measured voltage, current and power-flow data in the wire. However, Eve cannot determine these values because, for her, there are four unknown quantities while she can set up only three equations. The RRRT-KLJN scheme has several advantages and makes all former attacks on the KLJN scheme invalid or incomplete.","PeriodicalId":124480,"journal":{"name":"arXiv: Emerging Technologies","volume":"101 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120813340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper discusses the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The Shannon gate complexity function $L(n, q)$ for a reversible circuit, implementing a Boolean transformation $fcolon mathbb Z_2^n to mathbb Z_2^n$, is defined as a function of $n$ and the number of additional inputs $q$. The general lower bound $L(n,q) geq frac{2^n(n-2)}{3log_2(n+q)} - frac{n}{3}$ for the gate complexity of a reversible circuit is proved. An upper bound $L(n,0) leqslant 3n2^{n+4}(1+o(1)) mathop / log_2n$ for the gate complexity of a reversible circuit without additional inputs is proved. An upper bound $L(n,q_0) lesssim 2^n$ for the gate complexity of a reversible circuit with $q_0 sim n2^{n-o(n)}$ additional inputs is proved.
{"title":"О сложности обратимых схем,состоящих из функциональных элементов NOT, CNOT и 2-CNOT@@@","authors":"Дмитрий Владимирович Закаблуков, D. V. Zakablukov","doi":"10.4213/DM1365","DOIUrl":"https://doi.org/10.4213/DM1365","url":null,"abstract":"The paper discusses the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The Shannon gate complexity function $L(n, q)$ for a reversible circuit, implementing a Boolean transformation $fcolon mathbb Z_2^n to mathbb Z_2^n$, is defined as a function of $n$ and the number of additional inputs $q$. The general lower bound $L(n,q) geq frac{2^n(n-2)}{3log_2(n+q)} - frac{n}{3}$ for the gate complexity of a reversible circuit is proved. An upper bound $L(n,0) leqslant 3n2^{n+4}(1+o(1)) mathop / log_2n$ for the gate complexity of a reversible circuit without additional inputs is proved. An upper bound $L(n,q_0) lesssim 2^n$ for the gate complexity of a reversible circuit with $q_0 sim n2^{n-o(n)}$ additional inputs is proved.","PeriodicalId":124480,"journal":{"name":"arXiv: Emerging Technologies","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122113762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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