The monoidal nature of the Feistel-Toffoli construction

IF 0.6 4区 数学 Q3 MATHEMATICS Quaestiones Mathematicae Pub Date : 2023-11-01 DOI:10.2989/16073606.2023.2247730
Hans-E. Porst
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引用次数: 0

Abstract

AbstractThe Feistel-Toffoli construction of a bijective Boolean function out of an arbitrary one, a fundamental tool in reversible computing and in cryptography, has recently been analyzed (see [12]) to be a special instance of the construction of a monoid homomorphism from the X -fold cartesian power of a monoid M into the endomorphism monoid of the free M -set over the set X . It is the purpose of this note to show that this construction itself is in fact a genuine monoidal one. The generalization of the Feistel-Toffoli construction to internal categories in arbitrary finitely complete categories of [12] then becomes a special instance of this monoidal description.Mathematics Subject Classification (2020): 18M0518D4068Q09Key words: Convolution monoids and Hopf monoids in monoidal categoriesinternal categoryKleisli categoryspansFeistel schemeToffoli gate
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Feistel-Toffoli结构的单一性
摘要任意双射布尔函数的Feistel-Toffoli构造是可逆计算和密码学中的一个基本工具,最近被分析(见[12]),它是由单似群M的X倍笛卡儿幂构造为集合X上自由M集的自同态单似群的一个特殊实例。这篇笔记的目的是表明这个结构本身实际上是一个真正的单轴结构。将Feistel-Toffoli构造推广到任意有限完备范畴[12]中的内范畴,就成为这种一元描述的一个特殊实例。数学学科分类(2020):18m0518d4068q09关键字:一元类中的卷积一元和Hopf一元;内范畴;kleisli范畴
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来源期刊
Quaestiones Mathematicae
Quaestiones Mathematicae 数学-数学
CiteScore
1.70
自引率
0.00%
发文量
121
审稿时长
>12 weeks
期刊介绍: Quaestiones Mathematicae is devoted to research articles from a wide range of mathematical areas. Longer expository papers of exceptional quality are also considered. Published in English, the journal receives contributions from authors around the globe and serves as an important reference source for anyone interested in mathematics.
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