{"id":14821,"date":"2022-05-28T20:34:06","date_gmt":"2022-05-29T00:34:06","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14821"},"modified":"2026-06-09T10:22:56","modified_gmt":"2026-06-09T14:22:56","slug":"tr-182-breaking-substitution-cyphers-using-stochastic-automata","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/tr-182-breaking-substitution-cyphers-using-stochastic-automata\/","title":{"rendered":"TR-182: Breaking Substitution Cyphers using Stochastic Automata"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-182: Breaking Substitution Cyphers using Stochastic Automata\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/\">Technical Report<\/a>&nbsp;<strong>TR-182<\/strong><br>October 1990<\/p>\n\n\n\n<h2 id=\"breaking-substitution-cyphers-using-stochastic-automata\" class=\"wp-block-heading\">Breaking Substitution Cyphers using Stochastic Automata<\/h2>\n\n\n\n<p>B.J. Oommen &amp; J.R. Zgierski<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>Let A be a finite plaintext alphabet, and V be a cypher alphabet with the same cardinality as A. In all one-to-one substitution cyphers there exists the property that each element in A maps onto exactly one element in V. This mapping of V onto A is represented by a function T\u201d\u2018 which maps any v e V onto some A. e A (i.e., T*(v) = A). In this paper we consider the problem of learning the mapping T\u201d\u2018 (or its inverse (T\u201d\u2018)-1) by processing a sequence of cypher text. Traditional methods which break the cypher utilize the statistical information contained in the unigrams, and bigrams of the language from which the plaintext has been derived. A fast and more elegant method which uses trigrams of the language from which the plaintext has been derived is the one due to Peleg et. al. which utilizes the concept of relaxation [8,9]. In this paper we present a new learning automaton approach to break the cypher. A new finite state learning machine called the Cypher Learning Automaton (CLA) has been proposed which sequentially processes the cyphertext and a finite dictionary which is used as a model for the language from which the plaintext has been derived. This method is fast and the advantages of the scheme in terms of time and space requirements over the relaxation method [8,9] have been listed. The paper contains various simulation results comparing both the cypher breaking techniques.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-182.pdf\">TR-182.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-182October 1990 Breaking Substitution Cyphers using Stochastic Automata B.J. Oommen &amp; J.R. Zgierski Abstract Let A be a finite plaintext alphabet, and V be a cypher alphabet with the same cardinality as A. In all one-to-one substitution cyphers there exists the property that each element in A maps onto exactly one element in [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11906,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-14821","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14821","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14821"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14821\/revisions"}],"predecessor-version":[{"id":24525,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14821\/revisions\/24525"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11906"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14821"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}