Pub Date : 2025-01-01Epub Date: 2025-08-13DOI: 10.1007/s12095-025-00825-3
Chris Brzuska, Geoffroy Couteau, Christoph Egger, Pihla Karanko, Pierre Meyer
We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), , which builds a PRF from a weak PRF via a public pre-processing random oracle . In applications to secure multiparty computation (MPC), only the low-complexity performs secret-depending operations. Our construction replaces by , where f is a non-adaptive PRF and the key is public and thus known to the distinguishing adversary. We show that, perhaps surprisingly, several existing weak PRF candidates are plausibly also secure when their inputs are generated by . Firstly, analogous cryptanalysis applies (because pseudorandomness of f implies good statistical properties) and/or secondly an attack against the weak PRF with such pseudorandom inputs generated by f would imply surprising results such as key agreement from the hardness of the high-noise version of the Learning Parity with Noise (LPN) when implementing both and f from this assumption. Our simple transformation of replacing public pre-processing by public pre-processing applies to the entire family of PRF-style functions. Specifically, we obtain results for oblivious PRFs, which are a core building block for password-based authenticated key exchange (PAKE) and private set intersection (PSI) protocols, and we also obtain results for pseudorandom correlation functions (PCF), which are a key tool for silent oblivious transfer (OT) extension.
{"title":"Instantiating the Hash-then-evaluate paradigm: Strengthening PRFs, PCFs, and OPRFs.","authors":"Chris Brzuska, Geoffroy Couteau, Christoph Egger, Pihla Karanko, Pierre Meyer","doi":"10.1007/s12095-025-00825-3","DOIUrl":"https://doi.org/10.1007/s12095-025-00825-3","url":null,"abstract":"<p><p>We instantiate the hash-then-evaluate paradigm for pseudorandom functions (PRFs), <math><mrow><mi>PRF</mi> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>x</mi> <mo>)</mo> <mo>:</mo> <mo>=</mo> <mi>wPRF</mi> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>RO</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo></mrow> </math> , which builds a PRF <math><mi>PRF</mi></math> from a weak PRF <math><mi>wPRF</mi></math> via a <i>public</i> pre-processing random oracle <math><mi>RO</mi></math> . In applications to secure multiparty computation (MPC), only the low-complexity <math><mi>wPRF</mi></math> performs secret-depending operations. Our construction replaces <math><mi>RO</mi></math> by <math><mrow><mi>f</mi> <mo>(</mo> <msub><mi>k</mi> <mi>H</mi></msub> <mo>,</mo> <mi>elf</mi> <mrow><mo>(</mo> <mi>x</mi> <mo>)</mo></mrow> <mo>)</mo></mrow> </math> , where <i>f</i> is a non-adaptive PRF and the key <math><msub><mi>k</mi> <mi>H</mi></msub> </math> is <i>public</i> and thus known to the distinguishing adversary. We show that, perhaps surprisingly, several existing weak PRF candidates are plausibly also secure when their inputs are generated by <math><mrow><mi>f</mi> <mo>(</mo> <msub><mi>k</mi> <mi>H</mi></msub> <mo>,</mo> <mi>elf</mi> <mrow><mo>(</mo> <mo>.</mo> <mo>)</mo></mrow> <mo>)</mo></mrow> </math> . Firstly, analogous cryptanalysis applies (because pseudorandomness of <i>f</i> implies good statistical properties) and/or secondly an attack against the weak PRF with such pseudorandom inputs generated by <i>f</i> would imply surprising results such as key agreement from the hardness of the high-noise version of the Learning Parity with Noise (LPN) when implementing both <math><mi>wPRF</mi></math> and <i>f</i> from this assumption. Our simple transformation of replacing <math><mrow><mi>RO</mi> <mo>(</mo> <mo>·</mo> <mo>)</mo></mrow> </math> public pre-processing by <math><mrow><mi>f</mi> <mo>(</mo> <msub><mi>k</mi> <mi>H</mi></msub> <mo>,</mo> <mi>elf</mi> <mrow><mo>(</mo> <mi>x</mi> <mo>)</mo></mrow> <mo>)</mo></mrow> </math> public pre-processing applies to the entire family of PRF-style functions. Specifically, we obtain results for oblivious PRFs, which are a core building block for password-based authenticated key exchange (PAKE) and private set intersection (PSI) protocols, and we also obtain results for pseudorandom correlation functions (PCF), which are a key tool for silent oblivious transfer (OT) extension.</p>","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":"17 5","pages":"1325-1366"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12474740/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145187094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01Epub Date: 2025-05-22DOI: 10.1007/s12095-025-00805-7
Ayça Çeşmelioğlu, Wilfried Meidl
Recently in Çeşmelioğlu, Meidl (Adv. Math. Commun.,18, 2024), the study of EA-equivalence and CCZ-equivalence for functions from to the cyclic group has been initiated, where denotes an n-dimensional vector space over . Amongst others it has been shown that there exist functions from to which are CCZ-equivalent but not EA-equivalent. We extend these results to larger classes of functions from to . We then discuss constructions of generalized bent functions from to , p odd or and n is even, which correspond to large affine spaces of bent functions. In particular we employ versions of the direct sum, the semi-direct sum and of a recent secondary bent function construction in Wang et. al., (IEEE Trans. Inform. Theory69, 2023), to generate large affine spaces of bent functions. Finally we present a solution for constructing generalized bent functions from to , n odd, from arbitrary generalized bent functions from to .
最近在Çeşmelioğlu， Meidl （Adv. Math）。Commun。， 18, 2024)，开始了从V n (p)到循环群Z p k的函数ea -等价和ccz -等价的研究，其中V n (p)表示F p上的n维向量空间。其中，已经证明存在从vn(2)到z4的函数是ccz等效的，但不是ea等效的。我们将这些结果推广到更大的函数类，从vn (p)到zkp。然后讨论了从V n (p)到Z p k， p奇数或p = 2和n为偶的广义弯曲函数的构造，它们对应于弯曲函数的大仿射空间。特别地，我们采用了直接和、半直接和和的版本，以及最近在Wang等人（IEEE Trans.）中的二次弯曲函数构造的版本。通知。理论69,2023)，以产生弯曲函数的大仿射空间。最后给出了从vn - 1(2)到z2k - 1的任意广义弯曲函数构造从vn(2)到z2k - 1的广义弯曲函数的解。
{"title":"Construction and equivalence for generalized boolean functions.","authors":"Ayça Çeşmelioğlu, Wilfried Meidl","doi":"10.1007/s12095-025-00805-7","DOIUrl":"https://doi.org/10.1007/s12095-025-00805-7","url":null,"abstract":"<p><p>Recently in Çeşmelioğlu, Meidl (<i>Adv. Math. Commun.,</i> <i>18</i>, 2024), the study of EA-equivalence and CCZ-equivalence for functions from <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>)</mo></mrow> </msubsup> </math> to the cyclic group <math><msub><mi>Z</mi> <msup><mi>p</mi> <mi>k</mi></msup> </msub> </math> has been initiated, where <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>)</mo></mrow> </msubsup> </math> denotes an <i>n</i>-dimensional vector space over <math><msub><mi>F</mi> <mi>p</mi></msub> </math> . Amongst others it has been shown that there exist functions from <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mn>2</mn> <mo>)</mo></mrow> </msubsup> </math> to <math><msub><mi>Z</mi> <mn>4</mn></msub> </math> which are CCZ-equivalent but not EA-equivalent. We extend these results to larger classes of functions from <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>)</mo></mrow> </msubsup> </math> to <math><msub><mi>Z</mi> <msup><mi>p</mi> <mi>k</mi></msup> </msub> </math> . We then discuss constructions of generalized bent functions from <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mi>p</mi> <mo>)</mo></mrow> </msubsup> </math> to <math><msub><mi>Z</mi> <msup><mi>p</mi> <mi>k</mi></msup> </msub> </math> , <i>p</i> odd or <math><mrow><mi>p</mi> <mo>=</mo> <mn>2</mn></mrow> </math> and <i>n</i> is even, which correspond to large affine spaces of bent functions. In particular we employ versions of the direct sum, the semi-direct sum and of a recent secondary bent function construction in Wang et. al., (<i>IEEE Trans. Inform. Theory</i> <i>69</i>, 2023), to generate large affine spaces of bent functions. Finally we present a solution for constructing generalized bent functions from <math><msubsup><mi>V</mi> <mi>n</mi> <mrow><mo>(</mo> <mn>2</mn> <mo>)</mo></mrow> </msubsup> </math> to <math><msub><mi>Z</mi> <msup><mn>2</mn> <mi>k</mi></msup> </msub> </math> , <i>n</i> odd, from arbitrary generalized bent functions from <math><msubsup><mi>V</mi> <mrow><mi>n</mi> <mo>-</mo> <mn>1</mn></mrow> <mrow><mo>(</mo> <mn>2</mn> <mo>)</mo></mrow> </msubsup> </math> to <math><msub><mi>Z</mi> <msup><mn>2</mn> <mrow><mi>k</mi> <mo>-</mo> <mn>1</mn></mrow> </msup> </msub> </math> .</p>","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":"17 6","pages":"1659-1682"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12537615/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145349486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-05DOI: 10.1007/s12095-023-00672-0
Changhui Chen, H.-B. Kan, Jie Peng, Lijing Zheng, Yanjun Li
{"title":"Three classes of permutation quadrinomials in odd characteristic","authors":"Changhui Chen, H.-B. Kan, Jie Peng, Lijing Zheng, Yanjun Li","doi":"10.1007/s12095-023-00672-0","DOIUrl":"https://doi.org/10.1007/s12095-023-00672-0","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43062328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-04DOI: 10.1007/s12095-023-00671-1
Xinxin Lv, Cuiling Fan, Yanyan Wang
{"title":"The cross-correlation spectrum of ternary perfect sequences and their decimations","authors":"Xinxin Lv, Cuiling Fan, Yanyan Wang","doi":"10.1007/s12095-023-00671-1","DOIUrl":"https://doi.org/10.1007/s12095-023-00671-1","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47095224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-21DOI: 10.1007/s12095-023-00663-1
Cheng Che, Tian Tian
{"title":"Further Results on Affine Sub-Families of NFSR Sequences","authors":"Cheng Che, Tian Tian","doi":"10.1007/s12095-023-00663-1","DOIUrl":"https://doi.org/10.1007/s12095-023-00663-1","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46560892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-15DOI: 10.1007/s12095-023-00661-3
M. Steiner
{"title":"A lower bound for differential uniformity by multiplicative complexity & bijective functions of multiplicative complexity 1 over finite fields","authors":"M. Steiner","doi":"10.1007/s12095-023-00661-3","DOIUrl":"https://doi.org/10.1007/s12095-023-00661-3","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44741373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1007/s12095-023-00665-z
A. Roy, S. Majhi
{"title":"Lower bounds on the maximum cross-correlations of 2-D quasi-complementary array sets","authors":"A. Roy, S. Majhi","doi":"10.1007/s12095-023-00665-z","DOIUrl":"https://doi.org/10.1007/s12095-023-00665-z","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44137590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-05DOI: 10.1007/s12095-023-00656-0
N. Zidarič, K. Mandal, G. Gong, M. Aagaard
{"title":"The welch-gong stream cipher - evolutionary path","authors":"N. Zidarič, K. Mandal, G. Gong, M. Aagaard","doi":"10.1007/s12095-023-00656-0","DOIUrl":"https://doi.org/10.1007/s12095-023-00656-0","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42223998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-02DOI: 10.1007/s12095-023-00664-0
Xianhong Xie, Ouyang Yi, Ming Mao
{"title":"Vectorial bent functions and linear codes from quadratic forms","authors":"Xianhong Xie, Ouyang Yi, Ming Mao","doi":"10.1007/s12095-023-00664-0","DOIUrl":"https://doi.org/10.1007/s12095-023-00664-0","url":null,"abstract":"","PeriodicalId":48936,"journal":{"name":"Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences","volume":"68 s277","pages":"1011 - 1029"},"PeriodicalIF":1.4,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41255443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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