A Birthday Attack on the Birthday Problem.
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| Title: | A Birthday Attack on the Birthday Problem. |
|---|---|
| Authors: | Harrison, Michael1 (AUTHOR) mah5044@gmail.com, Morrison, Travis2 (AUTHOR) |
| Source: | Mathematics Magazine. Apr2026, Vol. 99 Issue 2, p156-165. 10p. |
| Subject Terms: | *Algorithms, *Computer simulation, Cryptography, Factorization |
| Abstract: | The article focuses on applying Pollard’s ρ-method, a birthday attack algorithm inspired by the birthday paradox, to efficiently find collisions in functions representing birthday assignments. It explains how the birthday paradox implies that collisions (shared birthdays) are likely in surprisingly small groups and demonstrates a simulation of the ρ-method using minimal storage to detect such collisions in large populations. The authors explore adapting this method to smaller groups by composing the birthday function with a surjective hash function and using random permutations to increase the likelihood of detecting true birthday collisions rather than false positives caused by hash collisions. They provide probabilistic analyses and simulation results on the expected number of iterations (shufflings) and rounds needed to find collisions, highlighting the method’s potential for classroom demonstrations and cryptographic applications such as integer factorization and hash collision detection. [Extracted from the article] |
| Copyright of Mathematics Magazine is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 193710546 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Birthday Attack on the Birthday Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Harrison%2C+Michael%22">Harrison, Michael</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mah5044@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Morrison%2C+Travis%22">Morrison, Travis</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+Magazine%22">Mathematics Magazine</searchLink>. Apr2026, Vol. 99 Issue 2, p156-165. 10p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br />*<searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptography%22">Cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The article focuses on applying Pollard’s ρ-method, a birthday attack algorithm inspired by the birthday paradox, to efficiently find collisions in functions representing birthday assignments. It explains how the birthday paradox implies that collisions (shared birthdays) are likely in surprisingly small groups and demonstrates a simulation of the ρ-method using minimal storage to detect such collisions in large populations. The authors explore adapting this method to smaller groups by composing the birthday function with a surjective hash function and using random permutations to increase the likelihood of detecting true birthday collisions rather than false positives caused by hash collisions. They provide probabilistic analyses and simulation results on the expected number of iterations (shufflings) and rounds needed to find collisions, highlighting the method’s potential for classroom demonstrations and cryptographic applications such as integer factorization and hash collision detection. [Extracted from the article] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics Magazine is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=193710546 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/0025570X.2025.2509470 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 156 Subjects: – SubjectFull: Algorithms Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Cryptography Type: general – SubjectFull: Factorization Type: general Titles: – TitleFull: A Birthday Attack on the Birthday Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Harrison, Michael – PersonEntity: Name: NameFull: Morrison, Travis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0025570X Numbering: – Type: volume Value: 99 – Type: issue Value: 2 Titles: – TitleFull: Mathematics Magazine Type: main |
| ResultId | 1 |
