Pub Date : 2022-09-21DOI: 10.1080/01611194.2022.2109944
Stuart Boersma
{"title":"Elizebeth Smith Friedman’s recovery of the wiring of two rotors from an enigma D machine","authors":"Stuart Boersma","doi":"10.1080/01611194.2022.2109944","DOIUrl":"https://doi.org/10.1080/01611194.2022.2109944","url":null,"abstract":"","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48848084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-26DOI: 10.1080/01611194.2022.2105179
Chris Christensen
In 2021 Codebreaker Girls: A Secret Life at Bletchley Park, Jan Slimming’s first book about World War II codebreaking appeared. Slimming’s interest in codebreaking and, in particular, in Bletchley Park resulted from the fact that her mother Daisy Lawrence had served as a civilian codebreaker at Bletchley Park. What Slimming discovered of her mother’s service as a codebreaker is told in her first book. The first book also includes a bit of the story of her father Stanley Moore, who joined the Royal Army Service Corps, was taken prisoner by the Japanese during the fall of Singapore in 1942, and was a POW during the remainder of the war. Unfortunately Slimming tried to expand the story of her mother to include much of the cryptologic history of World War II, and in trying to do so she went badly wrong. Codebreaker Girls: A Secret Life at Bletchley Park is filled with errors and misunderstandings (Christensen 2022). This new Codebreaker Girls book is built upon the story of Janice Martin Benario, a US Navy codebreaker during World War II. Readers would be forgiven if, part way through Secret Life, they lose track of what would appear to be the focus of the book – the story of Janice Benario – because, like her first book, Slimming has attempted to go beyond the foundation of the book and tell a larger story – in this case seemingly the complete story of World War II codebreaking and more. Slimming has also filled this book with errors and misunderstandings. As with the review of A Secret Life at Bletchley Park, it unfortunately becomes necessary to provide evidence of Slimming’s errors and misunderstandings. Page ix: Problems begin with the second paragraph of the “Prologue.” Slimming locates the building that is designated Main Navy on Pennsylvania Avenue in Washington, DC. Main Navy was located on B Street, which is now Constitution Avenue. This might seem like a minor error, but such errors pop up throughout the book. Page 38: Referring to a delay in the receiving of a 6 December 1941 diplomatic message from President Roosevelt to the Japanese Emperor, Slimming explains that because the message was encoded with the less secure US diplomatic GRAY code US Ambassador to Japan Joseph Grew thought that it was possible that “Japanese militants had intercepted the message, solved its contents and deliberately delayed it to hinder any peace effort.” (37–38) Slimming then, referencing David Kahn’s The Codebreakers page 495, says: “The real reason, however, was not the code or the diplomats but a full embargo placed on all Japanese military incoming diplomatic messages.” (38) Much of what Slimming says about this event seems to be based on Kahn’s explanation. (Kahn
{"title":"Review of The Secret Life of an American Codebreaker: Codebreaker Girls by Jan Slimming","authors":"Chris Christensen","doi":"10.1080/01611194.2022.2105179","DOIUrl":"https://doi.org/10.1080/01611194.2022.2105179","url":null,"abstract":"In 2021 Codebreaker Girls: A Secret Life at Bletchley Park, Jan Slimming’s first book about World War II codebreaking appeared. Slimming’s interest in codebreaking and, in particular, in Bletchley Park resulted from the fact that her mother Daisy Lawrence had served as a civilian codebreaker at Bletchley Park. What Slimming discovered of her mother’s service as a codebreaker is told in her first book. The first book also includes a bit of the story of her father Stanley Moore, who joined the Royal Army Service Corps, was taken prisoner by the Japanese during the fall of Singapore in 1942, and was a POW during the remainder of the war. Unfortunately Slimming tried to expand the story of her mother to include much of the cryptologic history of World War II, and in trying to do so she went badly wrong. Codebreaker Girls: A Secret Life at Bletchley Park is filled with errors and misunderstandings (Christensen 2022). This new Codebreaker Girls book is built upon the story of Janice Martin Benario, a US Navy codebreaker during World War II. Readers would be forgiven if, part way through Secret Life, they lose track of what would appear to be the focus of the book – the story of Janice Benario – because, like her first book, Slimming has attempted to go beyond the foundation of the book and tell a larger story – in this case seemingly the complete story of World War II codebreaking and more. Slimming has also filled this book with errors and misunderstandings. As with the review of A Secret Life at Bletchley Park, it unfortunately becomes necessary to provide evidence of Slimming’s errors and misunderstandings. Page ix: Problems begin with the second paragraph of the “Prologue.” Slimming locates the building that is designated Main Navy on Pennsylvania Avenue in Washington, DC. Main Navy was located on B Street, which is now Constitution Avenue. This might seem like a minor error, but such errors pop up throughout the book. Page 38: Referring to a delay in the receiving of a 6 December 1941 diplomatic message from President Roosevelt to the Japanese Emperor, Slimming explains that because the message was encoded with the less secure US diplomatic GRAY code US Ambassador to Japan Joseph Grew thought that it was possible that “Japanese militants had intercepted the message, solved its contents and deliberately delayed it to hinder any peace effort.” (37–38) Slimming then, referencing David Kahn’s The Codebreakers page 495, says: “The real reason, however, was not the code or the diplomats but a full embargo placed on all Japanese military incoming diplomatic messages.” (38) Much of what Slimming says about this event seems to be based on Kahn’s explanation. (Kahn","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"584 - 587"},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44884937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-16DOI: 10.1080/01611194.2022.2064200
K. Bures
Abstract In 1940 the US Army’s Signal Intelligence Service (SIS) cracked PURPLE, the Japanese diplomatic cipher. Shortly after that accomplishment, William Friedman, legendary cryptographer and civilian head of SIS, wrote his Preliminary Historical Report on the Solution of the “B” Machine. In it he introduced the mysterious “Identification of Homologs” and stated there that it had been a crucial technology to the success of cracking PURPLE. Despite that dramatic assessment, the concept simply disappeared, ignored by all subsequent authors of PURPLE histories and technical analyses. So what exactly is the Identification of Homologs and what role did it play in the cryptanalysis of PURPLE? That is the subject of this paper. We give a complete technical description, as well as historical information, some newly uncovered, about how SIS collected PURPLE “data”.
{"title":"Cracking PURPLE: the identification of homologs in the cryptanalysis of the Angooki Taipu B cipher machine","authors":"K. Bures","doi":"10.1080/01611194.2022.2064200","DOIUrl":"https://doi.org/10.1080/01611194.2022.2064200","url":null,"abstract":"Abstract In 1940 the US Army’s Signal Intelligence Service (SIS) cracked PURPLE, the Japanese diplomatic cipher. Shortly after that accomplishment, William Friedman, legendary cryptographer and civilian head of SIS, wrote his Preliminary Historical Report on the Solution of the “B” Machine. In it he introduced the mysterious “Identification of Homologs” and stated there that it had been a crucial technology to the success of cracking PURPLE. Despite that dramatic assessment, the concept simply disappeared, ignored by all subsequent authors of PURPLE histories and technical analyses. So what exactly is the Identification of Homologs and what role did it play in the cryptanalysis of PURPLE? That is the subject of this paper. We give a complete technical description, as well as historical information, some newly uncovered, about how SIS collected PURPLE “data”.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"436 - 448"},"PeriodicalIF":0.6,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43116081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-10DOI: 10.1080/01611194.2022.2092916
S. Bingöl
Abstract In parallel with the change in the understanding of diplomacy during the reign of Selim III, the Ottoman Empire started to use diplomatic cryptography. However, the efforts which started in 1797 were interrupted to a great extent when the ambassadors were recalled to the state after 1811. In the following period, Chargé d’affaires took over their duties and continued to use cryptography. With the reassignment of ambassadors to European capitals after 1834, Ottoman diplomatic cryptography stepped into a new era. In this study, the process until 1877 is discussed in the light of encrypted documents found in Ottoman archives. Codes and coding/decoding methods of Ottoman diplomats throughout the period are also examined.
{"title":"The changes in Ottoman diplomatic cryptography and its methods during the 19th century (1811–1877)","authors":"S. Bingöl","doi":"10.1080/01611194.2022.2092916","DOIUrl":"https://doi.org/10.1080/01611194.2022.2092916","url":null,"abstract":"Abstract In parallel with the change in the understanding of diplomacy during the reign of Selim III, the Ottoman Empire started to use diplomatic cryptography. However, the efforts which started in 1797 were interrupted to a great extent when the ambassadors were recalled to the state after 1811. In the following period, Chargé d’affaires took over their duties and continued to use cryptography. With the reassignment of ambassadors to European capitals after 1834, Ottoman diplomatic cryptography stepped into a new era. In this study, the process until 1877 is discussed in the light of encrypted documents found in Ottoman archives. Codes and coding/decoding methods of Ottoman diplomats throughout the period are also examined.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"541 - 569"},"PeriodicalIF":0.6,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43023803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-04DOI: 10.1080/01611194.2022.2092784
Floe Foxon
Abstract The ‘Rilke Cryptogram’ is a possible cipher of German, WWII origin. This study summarises the text’s history, and examines explanations for its nature. Statistical techniques are applied to an updated transcription. The text consists of 18,760 characters in 3,305 unique groups of four, arranged into 670 rows by seven columns on 33 pages of an otherwise ordinary book. The distribution of these groups is not particularly Zipfian, suggesting the text is likely not a code or monoalphabetic substitution cipher. Its alphabet is longer than English and German (46 characters). Character and N-gram entropy analyses suggest the text is less ordered than English and German, but more ordered than random text. Machine-learning modelling suggests the text is a substitution cipher, but frequency and Kasiski-Kerckhoff analyses suggest otherwise. Sukhotin’s algorithm results for the text are somewhat consistent with results for German, though N-gram distributions do not strongly resemble English or German. Statistical analysis of physical typewriter key distances suggest the text’s groupings are highly unlikely to appear at random, and are consistent with intentional ‘lazy’ typing. The text is inconsistent with machine ciphers of its era (e.g., Enigma), and other features are not entirely consistent with non-cipher explanations. Further investigation is required.
{"title":"A treatise on the Rilke cryptogram","authors":"Floe Foxon","doi":"10.1080/01611194.2022.2092784","DOIUrl":"https://doi.org/10.1080/01611194.2022.2092784","url":null,"abstract":"Abstract The ‘Rilke Cryptogram’ is a possible cipher of German, WWII origin. This study summarises the text’s history, and examines explanations for its nature. Statistical techniques are applied to an updated transcription. The text consists of 18,760 characters in 3,305 unique groups of four, arranged into 670 rows by seven columns on 33 pages of an otherwise ordinary book. The distribution of these groups is not particularly Zipfian, suggesting the text is likely not a code or monoalphabetic substitution cipher. Its alphabet is longer than English and German (46 characters). Character and N-gram entropy analyses suggest the text is less ordered than English and German, but more ordered than random text. Machine-learning modelling suggests the text is a substitution cipher, but frequency and Kasiski-Kerckhoff analyses suggest otherwise. Sukhotin’s algorithm results for the text are somewhat consistent with results for German, though N-gram distributions do not strongly resemble English or German. Statistical analysis of physical typewriter key distances suggest the text’s groupings are highly unlikely to appear at random, and are consistent with intentional ‘lazy’ typing. The text is inconsistent with machine ciphers of its era (e.g., Enigma), and other features are not entirely consistent with non-cipher explanations. Further investigation is required.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"493 - 510"},"PeriodicalIF":0.6,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-26DOI: 10.1080/01611194.2022.2101404
Chris Christensen
William Friedman did his bit to keep Hitt’s name alive at the National Security Agency, but it was David Kahn who preserved Hitt’s legacy as a cryptologist with his book The Codebreakers. Kahn who expressed an interest in codes and ciphers at an early age, first wrote to Hitt in 1949, asking him to autograph his copy of Hitt’s Manual. In November 1963 Kahn contacted Hitt with some questions, and Parker suggested that he read Friedman’s Elements of Cryptanalysis, if he could find it. He also suggested that Kahn contact Friedman, “one of my prot eg es ... .” (200)
{"title":"Review of Parker Hitt: The Father of American Military Cryptology by Betsy Rohaly Smoot","authors":"Chris Christensen","doi":"10.1080/01611194.2022.2101404","DOIUrl":"https://doi.org/10.1080/01611194.2022.2101404","url":null,"abstract":"William Friedman did his bit to keep Hitt’s name alive at the National Security Agency, but it was David Kahn who preserved Hitt’s legacy as a cryptologist with his book The Codebreakers. Kahn who expressed an interest in codes and ciphers at an early age, first wrote to Hitt in 1949, asking him to autograph his copy of Hitt’s Manual. In November 1963 Kahn contacted Hitt with some questions, and Parker suggested that he read Friedman’s Elements of Cryptanalysis, if he could find it. He also suggested that Kahn contact Friedman, “one of my prot eg es ... .” (200)","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"489 - 492"},"PeriodicalIF":0.6,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43669221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.1080/01611194.2022.2078077
Joshua Holden
Abstract Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect quantum computers to make common forms of public-key cryptography obsolete in the near future. Fortunately, there are several systems being evaluated to replace RSA and the other systems we currently use. While some of the systems are too complicated to be good examples in introductory courses, others are either quite manageable or have simplified versions that are manageable. This article gives a tour of the main types of systems under consideration and the teaching resources available for instructors who want to teach them.
{"title":"Resource guide for teaching post-quantum cryptography","authors":"Joshua Holden","doi":"10.1080/01611194.2022.2078077","DOIUrl":"https://doi.org/10.1080/01611194.2022.2078077","url":null,"abstract":"Abstract Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect quantum computers to make common forms of public-key cryptography obsolete in the near future. Fortunately, there are several systems being evaluated to replace RSA and the other systems we currently use. While some of the systems are too complicated to be good examples in introductory courses, others are either quite manageable or have simplified versions that are manageable. This article gives a tour of the main types of systems under consideration and the teaching resources available for instructors who want to teach them.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"459 - 465"},"PeriodicalIF":0.6,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48517918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-20DOI: 10.1080/01611194.2022.2060052
C. Christensen
Abstract On 20 February 1939, a new Japanese diplomatic cipher machine that U.S. Army codebreakers would name PURPLE came into use. By 10 April 1939, the Army’s Signal Intelligence Service (SIS) had made startling progress. SIS codebreakers had discovered that, for no cryptographic reason, PURPLE maintained the split of the Roman alphabet into a set of 6 letters and a set of 20 letters—the sixes and the twenties—a split that had been observed in PURPLE’s predecessor RED. They had a familiar problem, and they were quickly able to recover the enciphering table for the sixes But 18 months later they were still puzzled by the enciphering of the twenties Then, on 20 September 1940, Genevieve Grotjan, an SIS codebreaker, made a discovery that opened the way for the recovery of the PURPLE machine. This paper explores the patterns for which Grotjan was searching and concludes with what she found.
{"title":"Genevieve Grotjan’s “great discovery”","authors":"C. Christensen","doi":"10.1080/01611194.2022.2060052","DOIUrl":"https://doi.org/10.1080/01611194.2022.2060052","url":null,"abstract":"Abstract On 20 February 1939, a new Japanese diplomatic cipher machine that U.S. Army codebreakers would name PURPLE came into use. By 10 April 1939, the Army’s Signal Intelligence Service (SIS) had made startling progress. SIS codebreakers had discovered that, for no cryptographic reason, PURPLE maintained the split of the Roman alphabet into a set of 6 letters and a set of 20 letters—the sixes and the twenties—a split that had been observed in PURPLE’s predecessor RED. They had a familiar problem, and they were quickly able to recover the enciphering table for the sixes But 18 months later they were still puzzled by the enciphering of the twenties Then, on 20 September 1940, Genevieve Grotjan, an SIS codebreaker, made a discovery that opened the way for the recovery of the PURPLE machine. This paper explores the patterns for which Grotjan was searching and concludes with what she found.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"302 - 317"},"PeriodicalIF":0.6,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44932212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-09DOI: 10.1080/01611194.2023.2174821
J. Gathen
Abstract In December 2020, David Oranchak, Jarl Van Eycke, and Sam Blake solved a 51-year old mystery: the Zodiac cipher of 340 symbols. The correctness of their solution has not been seriously doubted, and here we give a further argument in its favor: the unicity distance of the cipher’s system is at most 153.
摘要2020年12月，David Oranchak、Jarl Van Eycke和Sam Blake解开了一个51年前的谜团：340个符号的黄道带密码。他们的解决方案的正确性没有受到严重怀疑，在这里我们给出了一个有利于它的进一步论点：密码系统的唯一性距离最多为153。
{"title":"Unicity distance of the Zodiac-340 cipher","authors":"J. Gathen","doi":"10.1080/01611194.2023.2174821","DOIUrl":"https://doi.org/10.1080/01611194.2023.2174821","url":null,"abstract":"Abstract In December 2020, David Oranchak, Jarl Van Eycke, and Sam Blake solved a 51-year old mystery: the Zodiac cipher of 340 symbols. The correctness of their solution has not been seriously doubted, and here we give a further argument in its favor: the unicity distance of the cipher’s system is at most 153.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"474 - 488"},"PeriodicalIF":0.6,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42855744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-18DOI: 10.1080/01611194.2022.2046660
Arvind Kumar, P. Mishra, O. Ojjela
Abstract ‘Rotation and shift’ based diffusion functions are used in modern ciphers especially in ARX (Addition, Rotation, and XOR) based designs. They are preferred over other alternatives as they are efficient and lightweight. Usually, such diffusion functions map an n-bit block to another n-bit block. One of the requirements for an n-bit to n-bit diffusion function is that, it should be invertible. In this paper, we present mathematical models for different classes of ‘rotation and shift’ based diffusion functions and explore their invertibility. We derive sufficient conditions under which diffusion functions of these classes are invertible.
{"title":"Analysis of rotation and shift based diffusion functions","authors":"Arvind Kumar, P. Mishra, O. Ojjela","doi":"10.1080/01611194.2022.2046660","DOIUrl":"https://doi.org/10.1080/01611194.2022.2046660","url":null,"abstract":"Abstract ‘Rotation and shift’ based diffusion functions are used in modern ciphers especially in ARX (Addition, Rotation, and XOR) based designs. They are preferred over other alternatives as they are efficient and lightweight. Usually, such diffusion functions map an n-bit block to another n-bit block. One of the requirements for an n-bit to n-bit diffusion function is that, it should be invertible. In this paper, we present mathematical models for different classes of ‘rotation and shift’ based diffusion functions and explore their invertibility. We derive sufficient conditions under which diffusion functions of these classes are invertible.","PeriodicalId":55202,"journal":{"name":"Cryptologia","volume":"47 1","pages":"419 - 435"},"PeriodicalIF":0.6,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44929140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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