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The XTR Public Key System [chapter]

Arjen K. Lenstra, Eric R. Verheul
<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;
This paper introduces the XTR public key system. XTR is based on a new method to represent elements of a subgroup of a multiplicative group of a finite field.  ...  Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security.  ...  This makes it easily feasible for all users of XTR to have public keys that are not shared with others, unlike ECC where a large part of the public key is often shared between all users of the system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-44598-6_1">doi:10.1007/3-540-44598-6_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fw6umabhqvazpj67gfon6htnt4">fatcat:fw6umabhqvazpj67gfon6htnt4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110912131103/http://infoscience.epfl.ch/record/149712/files/EPFL-CONF-149712.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/e5/33/e533be003f8b70d772932eead3bce3a9f927dbb0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-44598-6_1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

An overview of the XTR public key system [chapter]

Arjen K. Lenstra, Eric R. Verheul
<i title="DE GRUYTER"> Public-Key Cryptography and Computational Number Theory </i> &nbsp;
This paper describes and explains the techniques and properties that are relevant for the XTR cryptosystem and its implementation. It is based on the material from [10, ?,?,?].  ...  XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field.  ...  Combined with its very easy programmability, this makes XTR an excellent public key system for a very wide variety of environments, ranging from smart cards to web servers, without the need to share system  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110881035.151">doi:10.1515/9783110881035.151</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4sqoz5witbf6bboxf2u4hqv5wa">fatcat:4sqoz5witbf6bboxf2u4hqv5wa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20041205173829/http://www.win.tue.nl:80/~klenstra/xtrsurvey.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/c5/aa/c5aa96a331059de4abd1333759116681ae53cf2f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110881035.151"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> degruyter.com </button> </a>

Page 8753 of Mathematical Reviews Vol. , Issue 2002K [page]

<span title="">2002</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;
The paper introduces the XTR public key system.  ...  The XTR public key system. (English summary) Advances in cryptology—CRYPTO 2000 (Santa Barbara, CA), 1-19, Lecture Notes in Comput. Sci., 1880, Springer, Berlin, 2000.  ... 
<span class="external-identifiers"> </span>
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XTR Cryptosystem for SMS Security

Ashok Kumar Nanda, Lalit Kumar Awasthi
<span title="">2012</span> <i title="IACSIT Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3zatj3ngx5g7ho7ki6fvv35s7m" style="color: black;">International Journal of Engineering and Technology</a> </i> &nbsp;
So this enhanced scheme will increase the current security level and fastest speed with respect to key generation, encryption decryption with small key size.  ...  We have plan to implement XTR cryptosystem with XTR -NR message recovery signature scheme.  ...  The authors would like to thank the anonymous reviewers for their insightful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7763/ijet.2012.v4.495">doi:10.7763/ijet.2012.v4.495</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n3mncz47knf47eojhovkdgh2fy">fatcat:n3mncz47knf47eojhovkdgh2fy</a> </span>
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Side Channel Cryptanalysis on XTR Public Key Cryptosystem

D.-G. HAN
<span title="2005-05-01">2005</span> <i title="Institute of Electronics, Information and Communications Engineers (IEICE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x2mklbxoqjfvjdjrdybgo53sdm" style="color: black;">IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences</a> </i> &nbsp;
The XTR public key cryptosystem was introduced in 2000. XTR is suitable for a variety of environments including low-end smart cards, and is regarded as an excellent alternative to RSA and ECC.  ...  From our implementation results, if we compare XTR with ECC with countermeasures against "SCAs," we think XTR is as suitable to smart cards as ECC. key words: XTR public key cryptosystem, side channel  ...  Acknowledgments This work was done while the first author visited in Kyushu Univ. and was supported by the Korea Science and Engineering Foundation (KOSEF).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/ietfec/e88-a.5.1214">doi:10.1093/ietfec/e88-a.5.1214</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wea6ecstynhmtm3p34hj2gsiye">fatcat:wea6ecstynhmtm3p34hj2gsiye</a> </span>
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A More Compact Representation of XTR Cryptosystem

M. SHIRASE, D.-G. HAN, Y. HIBINO, H. KIM, T. TAKAGI
<span title="2008-10-01">2008</span> <i title="Institute of Electronics, Information and Communications Engineers (IEICE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x2mklbxoqjfvjdjrdybgo53sdm" style="color: black;">IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences</a> </i> &nbsp;
XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext.  ...  Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.  ...  Acknowledgements The work reported in this paper was supported by the IT R&D program of MIC/IITA. [2005-S088-04, Development of Security technology for Secure RFID/USN Service].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/ietfec/e91-a.10.2843">doi:10.1093/ietfec/e91-a.10.2843</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o57gxgybprcphbfr26hekydt44">fatcat:o57gxgybprcphbfr26hekydt44</a> </span>
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New (k,l,m)-verifiable multi-secret sharing schemes based on XTR public key system [article]

Jing Yang, Fang-Wei Fu
<span title="2020-11-17">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our new schemes are based on XTR public key system, and can realize GF(p^6) security by computations in GF(p^2) without explicit constructions of GF(p^6), where p is a prime.  ...  Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, our schemes can achieve the same security level with shorter parameters by using trace function  ...  Further, XTR public key system can be considered as a special case of the optimization of LFSR public key cryptosystem .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.08648v1">arXiv:2011.08648v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cwy4pyfr6bfxjjg63ogmhvcfte">fatcat:cwy4pyfr6bfxjjg63ogmhvcfte</a> </span>
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Unbelievable Security Matching AES Security Using Public Key Systems [chapter]

Arjen K. Lenstra
<span title="">2001</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;
Despite the conclusions, this paper should not be interpreted as an endorsement of any particular public key system in favor of any other.  ...  Given a desired level of security for the AES, this paper discusses matching public key sizes for RSA and the ElGamal family of protocols.  ...  The author thanks Eric Verheul and Mike Wiener for their many insightful comments on earlier versions of this paper and Martijn Stam for his assistance with Figure 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45682-1_5">doi:10.1007/3-540-45682-1_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2uc5yj5upncjbol6clxsdsygsm">fatcat:2uc5yj5upncjbol6clxsdsygsm</a> </span>
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An XTR-Based Constant Round Key Agreement Scheme

Silan Zhang, Jianhua Chen, Jingbo Xia, Xiaochuan Ai
<span title="">2013</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wpareqynwbgqdfodcyhh36aqaq" style="color: black;">Mathematical Problems in Engineering</a> </i> &nbsp;
Furthermore, the computation framework of XTR-based key agreement scheme is introduced, and security of the scheme is proven under the formal model.  ...  A new XTR-based key agreement scheme with constant rounds is presented. Three theorems are formulated to reveal the logarithmic computational complexity of this scheme.  ...  fundamental research funds for the central universities.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2013/596868">doi:10.1155/2013/596868</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ysfvkbl7ivcrjm35inhlaqnspa">fatcat:ysfvkbl7ivcrjm35inhlaqnspa</a> </span>
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Optimal Extension Fields for XTR [chapter]

Dong-Guk Han, Ki Soon Yoon, Young-Ho Park, Chang Han Kim, Jongin Lim
<span title="">2003</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;
of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.  ...  XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF (p 6 ) and it can be generalized to the field GF (p 6m ) [6, 9] .  ...  The XTR public key system was introduced at Crypto 2000 [6] . From a security point of view XTR is a traditional subgroup discrete logarithm system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36492-7_24">doi:10.1007/3-540-36492-7_24</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qn2xh5z3h5fs7bjgk4pgd3u3uu">fatcat:qn2xh5z3h5fs7bjgk4pgd3u3uu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190504110847/https://link.springer.com/content/pdf/10.1007%2F3-540-36492-7_24.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/9a/fa/9afa084eab8565eba0067d169990da4bb683afd0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36492-7_24"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On Security of XTR Public Key Cryptosystems Against Side Channel Attacks [chapter]

Dong-Guk Han, Jongin Lim, Kouichi Sakurai
<span title="">2004</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;
The XTR public key system was introduced at Crypto 2000.  ...  This paper shows that XTR-SE is immune against simple power analysis (SPA) under assumption that the order of the computation of XTR-SE is carefully considered.  ...  Introduction In Crypto 2000 Lenstra and Verheul proposed XTR public key system [LV00a] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-27800-9_39">doi:10.1007/978-3-540-27800-9_39</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rlo3tn56drdvraz7hejgw57q7a">fatcat:rlo3tn56drdvraz7hejgw57q7a</a> </span>
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Percutaneous Edge-to-Edge Mitral Valve Repair Using the New MitraClip XTR System

Rezo Jorbenadze, Juergen Schreieck, Carola Barthel, Peter Seizer, Christian Schlensak, Meinrad Gawaz, Johannes Patzelt, Harald F. Langer
<span title="">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6zzub4svrffdtc4lxvpbcjwxkm" style="color: black;">JACC: Cardiovascular Interventions</a> </i> &nbsp;
Our interdisciplinary heart team recommended interventional mitral valve repair because of the profoundly reduced left ventricular function (left ventricular ejection fraction 25%) and severe comorbidities  ...  The percutaneous edge-to-edge mitral valve repair (PMVR) procedure was performed using a new-generation MitraClip, the XTR system (Abbott Vascular, Santa Clara, California).  ...  Currently the MitraClip NT system is in use.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcin.2018.04.005">doi:10.1016/j.jcin.2018.04.005</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/29860072">pmid:29860072</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dxpdofvxxvh37i6k4p65qtz52a">fatcat:dxpdofvxxvh37i6k4p65qtz52a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200318175805/http://interventions.onlinejacc.org/content/jint/early/2018/05/24/j.jcin.2018.04.005.full.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/a3/f5/a3f56d01ffbec16a9bc4263fb5f94a535d169179.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcin.2018.04.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Torus-Based Cryptography [chapter]

Karl Rubin, Alice Silverberg
<span title="">2003</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;
We introduce cryptography based on algebraic tori, give a new public key system called CEILIDH, and compare it to other discrete log based systems including LUC and XTR.  ...  Like those systems, we obtain small key sizes. While LUC and XTR are essentially restricted to exponentiation, we are able to perform multiplication as well.  ...  Similarly for LUC, the trace map induces a birational embedding T 2 /S 2 → A 1 , the variety T 2 /S 2 is not a group, and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-45146-4_21">doi:10.1007/978-3-540-45146-4_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ng35a3y7nf7hga6pbqdmyralm">fatcat:2ng35a3y7nf7hga6pbqdmyralm</a> </span>
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Collision Attack on XTR and a Countermeasure with a Fixed Pattern [chapter]

Dong-Guk Han, Tsuyoshi Takagi, Tae Hyun Kim, Ho Won Kim, Kyo Il Chung
<span title="">2005</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;
Public-key cryptosystem (PKC) is one of inevitable key technologies in order to accomplish fruitful security applications in ubiquitous computing systems.  ...  The analysis complexity of the proposed one is about 2 40 where the key size is 160-bit, which is 55% improvement from the previously best known analysis of Page-Stam.  ...  After a brief description of XTR public key systems in Section 2, and an introduction into side channel attacks on XTR in Section 3, we will propose a new analysis technique, called as XTR collision attack  ... 
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Speeding Up XTR [chapter]

Martijn Stam, Arjen K. Lenstra
<span title="">2001</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 describes several speedups and simplifications for XTR. The most important results are new XTR double and single exponentiation methods where the latter requires a cheap precomputation.  ...  Both methods are on average more than 60% faster than the old methods, thus more than doubling the speed of the already fast XTR signature applications.  ...  The authors thank Peter Montgomery from Microsoft Research whose remarks [16] stimulated this research.  ... 
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