{"title":"Cryptanalysis of a Special Case of RSA Large Decryption Exponent Using Lattice Basis Reduction Method","authors":"Majid Mumtaz, Ping Luo","doi":"10.1109/ICCCS52626.2021.9449268","DOIUrl":null,"url":null,"abstract":"RSA public key cryptosystem is the “de-facto” standard, provides confidentiality and privacy security services over the internet. At Eurocrypt 1999, Boneh and Durfee proposed a polynomial time attacks on RSA small decryption key exponent. Their attacks worked by exploiting the lattice and sub lattice structure using lattice based Coppersmith's method to solve a modular polynomials, when $d < N^{0.284}$ and $d < N^{0.292}$ respectively. In this work, we propose a new attack on some special case of Boneh and Durfee's attack method with respect to large decryption exponent (i.e. $d=N^{\\epsilon} > e=N^{\\alpha}$, where $\\alpha$ and $\\epsilon$ are the encryption and decryption exponents respectively) for some $\\alpha\\leq\\epsilon$. The condition $d > \\phi(N)-N^{\\epsilon}$ satisfies our devised attack and the experimental outcome certifies that an RSA cryptosystem with large decryption exponent successfully revealed the weak keys through lattice basis reduction method.","PeriodicalId":376290,"journal":{"name":"2021 IEEE 6th International Conference on Computer and Communication Systems (ICCCS)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE 6th International Conference on Computer and Communication Systems (ICCCS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICCCS52626.2021.9449268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
RSA public key cryptosystem is the “de-facto” standard, provides confidentiality and privacy security services over the internet. At Eurocrypt 1999, Boneh and Durfee proposed a polynomial time attacks on RSA small decryption key exponent. Their attacks worked by exploiting the lattice and sub lattice structure using lattice based Coppersmith's method to solve a modular polynomials, when $d < N^{0.284}$ and $d < N^{0.292}$ respectively. In this work, we propose a new attack on some special case of Boneh and Durfee's attack method with respect to large decryption exponent (i.e. $d=N^{\epsilon} > e=N^{\alpha}$, where $\alpha$ and $\epsilon$ are the encryption and decryption exponents respectively) for some $\alpha\leq\epsilon$. The condition $d > \phi(N)-N^{\epsilon}$ satisfies our devised attack and the experimental outcome certifies that an RSA cryptosystem with large decryption exponent successfully revealed the weak keys through lattice basis reduction method.