Impact of the Hamming weight of the difference of two random variables on the probability of its preservation after addition and subtraction
We study how does the Hamming weight of the difference between two values influence the probability of this difference preservation after modulo addition and subtraction. By the difference between two random variables we mean the operation XOR which is standard for cryptanalysis. We prove that if th...
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| Veröffentlicht in: | Journal of applied and industrial mathematics 2014, Vol.8 (1), p.92-96 |
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| creator | Pestunov, A. I. |
| description | We study how does the Hamming weight of the difference between two values influence the probability of this difference preservation after modulo addition and subtraction. By the difference between two random variables we mean the operation XOR which is standard for cryptanalysis. We prove that if the most significant bit of the difference is equal to 0 (is equal to 1) then the probability of the difference preservation is equal to 2
−h
(equal to 2
−(
h
−1)
), where
h
is the Hamming weight of the difference. The theoretical results are confirmed experimentally. |
| doi_str_mv | 10.1134/S1990478914010104 |
| format | Article |
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−h
(equal to 2
−(
h
−1)
), where
h
is the Hamming weight of the difference. The theoretical results are confirmed experimentally.</description><identifier>ISSN: 1990-4789</identifier><identifier>EISSN: 1990-4797</identifier><identifier>DOI: 10.1134/S1990478914010104</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Applied mathematics ; Cryptography ; Equality ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Preservation ; Probability ; Random variables ; Studies ; Subtraction</subject><ispartof>Journal of applied and industrial mathematics, 2014, Vol.8 (1), p.92-96</ispartof><rights>Pleiades Publishing, Ltd. 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2164-684fa632a57d3a1613c343936dbe0b0332e8a3445a36cb323c8ede6b0d74660c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1990478914010104$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1990478914010104$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Pestunov, A. I.</creatorcontrib><title>Impact of the Hamming weight of the difference of two random variables on the probability of its preservation after addition and subtraction</title><title>Journal of applied and industrial mathematics</title><addtitle>J. Appl. Ind. Math</addtitle><description>We study how does the Hamming weight of the difference between two values influence the probability of this difference preservation after modulo addition and subtraction. By the difference between two random variables we mean the operation XOR which is standard for cryptanalysis. We prove that if the most significant bit of the difference is equal to 0 (is equal to 1) then the probability of the difference preservation is equal to 2
−h
(equal to 2
−(
h
−1)
), where
h
is the Hamming weight of the difference. 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−h
(equal to 2
−(
h
−1)
), where
h
is the Hamming weight of the difference. The theoretical results are confirmed experimentally.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1134/S1990478914010104</doi><tpages>5</tpages></addata></record> |
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| identifier | ISSN: 1990-4789 |
| ispartof | Journal of applied and industrial mathematics, 2014, Vol.8 (1), p.92-96 |
| issn | 1990-4789 1990-4797 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applied mathematics Cryptography Equality Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Preservation Probability Random variables Studies Subtraction |
| title | Impact of the Hamming weight of the difference of two random variables on the probability of its preservation after addition and subtraction |
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