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Cryptanalysis of 'Less Short' RSA Secret Exponents

Eric R. Verheul, Henk C. A. van Tilborg
<span title="1997-07-10">1997</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lnpibodwo5cpnp3qbzbnlmdepu" style="color: black;">Applicable Algebra in Engineering, Communication and Computing</a> </i> &nbsp;
In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [?]  ...  , describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a 'short' secret exponent. Let n = p · q be the modulus of the system.  ...  In some applications of RSA, it is desirable to have a short secret exponent d, as this reduces the execution times.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s002000050082">doi:10.1007/s002000050082</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kbnmmoou5nfefbvenk2i5p4xbi">fatcat:kbnmmoou5nfefbvenk2i5p4xbi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070824041111/http://www.cs.ru.nl/E.Verheul/papers/AiE1997/AiE1997.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/50/9550dcf315c55cae94701a193291f13eece8f7bf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s002000050082"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Cryptanalysis of RSA with a Small Parameter [chapter]

Xianmeng Meng, Xuexin Zheng
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper investigates the security of RSA system with short exponents. Let N = pq be an RSA modulus with balanced primes p and q. Denote the public exponent by e and the private exponent by d.  ...  As an application of our new attacks, we present the cryptanalysis on an RSA-type scheme proposed by Sun et al.  ...  The public key is then (N, e) and the secret key is (p, q, d) . The security of RSA is based on the hardness of factorization.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31448-3_9">doi:10.1007/978-3-642-31448-3_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6sgoquh7tzetbon5axygs4i5fm">fatcat:6sgoquh7tzetbon5axygs4i5fm</a> </span>
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Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization

Santosh Kumar.R, Narasimham.C Narasimham.C, Pallam Setty.S
<span title="2013-01-18">2013</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
In 2002, de Weger showed that choosing an RSA modulus with a small difference of primes improves the attack given by Boneh-Durfee.  ...  Adleman," A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", Communications of the ACM, vol.21, No.2, pp.120-126,1978. [2] Wiener, M.: Cryptanalysis of short RSA secret exponents,  ...  IEEE Transactions on Information Theory 36, 553-558 (1990). [3] Boneh, D., Durfee, G.: Cryptanalysis of RSA with Private Key d Less Than , Advances in Cryptology-EUROCRYPT99, Lecture Notes in Computer  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/9907-4499">doi:10.5120/9907-4499</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fj4qnvo6z5dsdmqgqhczncjjym">fatcat:fj4qnvo6z5dsdmqgqhczncjjym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180602151426/https://research.ijcaonline.org/volume61/number3/pxc3884499.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d0/e1/d0e1c6e9f6f2fb5eb52576947bdf18101bf34ada.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/9907-4499"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

ANOTHER PROOF OF WIENER'S SHORT SECRET EXPONENT

Muhammad Asyraf Asbullah, Muhammad Rezal Kamel Ariffin
<span title="2019-02-28">2019</span> <i title="Univ. of Malaya"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wmngegoijzfe3i42mmcaqih45e" style="color: black;">Malaysian Journal of Science</a> </i> &nbsp;
Wiener's short secret exponent attack is a well-known crypt-analytical result upon the RSA cryptosystem using a Diophantine's method called continued fractions.  ...  We recall that Wiener's attack works efficiently on RSA with the condition that the secret exponent d < 1 3 N 1 4 . Later, the upper bound was improved satisfying < √ 6√2 6 1 4 .  ...  In this work, we present another proof to Wiener's short secret exponent satisfying < 1 2 1 4 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22452/mjs.sp2019no1.6">doi:10.22452/mjs.sp2019no1.6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nbpoxu5ebvburbzt7wdsoz7uuu">fatcat:nbpoxu5ebvburbzt7wdsoz7uuu</a> </span>
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Cryptanalysis of short RSA secret exponents

M.J. Wiener
<span title="">1990</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
A cryptanalytic attack on the use of short RSA secret exponents is described.  ...  This attack poses no threat to the normal case of RSA where the secret exponent is approximately the same size as the modulus.  ...  There are various attacks on RSA that require, among other conditions, either the public or secret exponent to be short.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/18.54902">doi:10.1109/18.54902</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v3tmlgppbfcnjdzpi3daalokv4">fatcat:v3tmlgppbfcnjdzpi3daalokv4</a> </span>
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Checking before output may not be enough against fault-based cryptanalysis

Sung-Ming Yen, M. Joye
<span title="">2000</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5jlmyrayyrdazh5awdlsoec77q" style="color: black;">IEEE transactions on computers</a> </i> &nbsp;
In rsa, the secret exponent d and the public exponent e satisfy ed ≡ 1 (mod φ(N )), where φ is the Euler's totient function; or equivalently, there exists an integer k such that ed − kφ(N ) = 1.  ...  an adversary is to find the secret value of exponent d involved in the evaluation of M d mod N .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/12.869328">doi:10.1109/12.869328</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lwioe5ptrzazhmlegg4k2murve">fatcat:lwioe5ptrzazhmlegg4k2murve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809065844/http://joye.site88.net/papers/YJ00chkb.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/e3/5be314fb30d315d7e85229c9a4fe6794508bd040.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/12.869328"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Survey and Analysis of Security Issues on RSA Algorithm

Kunal Gagneja, K. John Singh
<span title="2015-11-15">2015</span> <i title="Maxwell Scientific Publication Corp."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/itifugluyrhulokjxf64yqrfey" style="color: black;">Research Journal of Applied Sciences Engineering and Technology</a> </i> &nbsp;
In this study, problems are identified based upon mathematical architecture of RSA and same observations are used in removal of defects.  ...  According to NIST key management guidelines, 15360 bit RSA is equivalent to 256-bit symmetric key in terms of strength. In case of small messages, even key would be longer than the message.  ...  Partial Key exposure attacks are also possible in RSA. They are based on knowledge of some bits of secret decryption exponent d (Wenbo, 2003) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.19026/rjaset.11.2094">doi:10.19026/rjaset.11.2094</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6dmjyumljavnjlfvzwjtjpm4u">fatcat:i6dmjyumljavnjlfvzwjtjpm4u</a> </span>
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Lattice based Attacks on Small Private Exponent of RSA: A Survey

R. SantoshKumar, C. Narasimham, S. Pallam Setty
<span title="2012-07-31">2012</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
In this paper we present several lattice based attacks on low private exponent of RSA.  ...  Lattice basis reduction algorithms have contributed a lot to cryptanalysis of RSA crypto system.  ...  It is an open problem for RSA, if secret exponent is greater than 0.292 without having the partial knowledge of any parameter.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/7878-1187">doi:10.5120/7878-1187</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/okjr6cll4zdhlbgmwan56n77bq">fatcat:okjr6cll4zdhlbgmwan56n77bq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180602232713/https://research.ijcaonline.org/volume49/number19/pxc3881187.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1b/85/1b85d3101f861093d82768189bb6ac454de35574.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/7878-1187"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Cryptanalysis of the RSA Schemes with Short Secret Exponent from Asiacrypt '99 [chapter]

Glenn Durfee, Phong Q. Nguyen
<span title="">2000</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
attack on RSA with short secret exponent.  ...  At Asiacrypt '99, Sun, Yang and Laih proposed three RSA variants with short secret exponent that resisted all known attacks, including the recent Boneh-Durfee attack from Eurocrypt '99 that improved Wiener's  ...  Acknowledgements Part of this work was done while the second author was visiting Stanford University, whose hospitality is gratefully acknowledged.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-44448-3_2">doi:10.1007/3-540-44448-3_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fddpupa7xbcyhfpy6hp47owprq">fatcat:fddpupa7xbcyhfpy6hp47owprq</a> </span>
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Minkowski Sum Based Lattice Construction for Multivariate Simultaneous Coppersmith's Technique and Applications to RSA [chapter]

Yoshinori Aono
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
As applications, we consider (i) a new RSA cryptanalysis for multiple short secret exponents, (ii) its partial key exposure situation, and (iii) investigating the hardness of finding a certain amount of  ...  LSBs of the RSA secret exponent.  ...  Cryptanalysis of RSA with short secret exponents As an application of our Minkowski sum lattice construction, we analyze the RSA with multiple short secret exponents with a common modulus.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-39059-3_7">doi:10.1007/978-3-642-39059-3_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wluvbcljibajhcidwkzcyf4t34">fatcat:wluvbcljibajhcidwkzcyf4t34</a> </span>
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Page 5416 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(NL-EIND; Eindhoven) Cryptanalysis ofless shortRSA secret exponents. (English summary) Appl. Algebra Engrg. Comm. Comput. 8 (1997), no. 5, 425-435.  ...  Summary: “In some applications of RSA, it is desirable to have a short secret exponent d. M. J. Wiener [IEEE Trans. Inform.  ... 
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Study of RSA and Proposed Variant against Wiener's Attack

Justin Jose, Siddharth Raina, Sushant Pawar, Shriket Pai
<span title="2010-02-25">2010</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
The chances of a short secret exponent attack are very much less in this variant because • If the attacker is successful in getting the private key 'd' using the Wiener's attack on short secret exponent  ...  Once r 2 − r 1 is discovered, we may use a result of Franklin and Reiter [9] Wiener's Attack on Short Secret Exponent To speed up RSA decryption and signing, it is tempting to use a small secret  ...  'x' is the randomly generated number 6. f(b,x) is the selected function which is to be applied on the RSA ciphertext. ENCRYPTION ALGORITHM. 1. Compute the values of the public key and private key. 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/369-556">doi:10.5120/369-556</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3f326nndwrc7vloqbbnp3x5sbe">fatcat:3f326nndwrc7vloqbbnp3x5sbe</a> </span>
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Page 9496 of Mathematical Reviews Vol. , Issue 2004k [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Annegret Weng (D-MNZ; Mainz) 2004k:94050 94A60 Chen, Chien-Yuan; Ku, Cheng-Yuan (RC-CHNG-IMG; Chia-Yi); Yen, David C. (1-MMOH-DSIS; Oxford, OH) Cryptanalysis of short secret exponents modulo RSA primes  ...  Summary: “In this manuscript, one way to attack on the short secret exponent d, modulo a larger RSA prime q is presented. When d, < (72)? and e <(pq)'/?  ... 
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CRYPTANALYSIS OF RSA WITH CONSTRAINED KEYS

ABDERRAHMANE NITAJ
<span title="">2009</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bpuytztbmzbm5injnbiypfctpa" style="color: black;">International Journal of Number Theory</a> </i> &nbsp;
Let n = pq be an RSA modulus with unknown prime factors of equal bit-size.  ...  Let e be the public exponent and d be the secret exponent satisfying ed ≡ 1 (mod φ(n)) where φ(n) is the Euler totient function.  ...  In Section 2 we review former continued fraction attacks on RSA with short secret exponents.  ... 
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Cryptography and Steganography

I.Venkata Sai Manoj
<span title="2010-02-25">2010</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
in the modern world of the ruler "security".  ...  Everyone in the entire scenario now emphasizes the need for cryptography and steganography codegroup utility which encodes and decodes binary files into fiveletter code groups just like secret agents use  ...  Some of the Finer Details of RSA Public Key Cryptography Unlike Diffie-Hellman, RSA can be used for key exchange as well as digital signatures and the encryption of small blocks of data.  ... 
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