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Group-based cryptography
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<h2 id="examples">Examples</h2> <ul><li>Shpilrain–Zapata public-key protocols</li> <li>Magyarik–Wagner public key protocol</li> <li><a href="/facts/Anshel%25E2%2580%2593Anshel%25E2%2580%2593Goldfeld_key_exchange/cMq0qvzU">Anshel–Anshel–Goldfeld key exchange</a></li> <li>Ko–Lee et al. key exchange protocol</li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Non-commutative_cryptography/T11zAMBm">Non-commutative cryptography</a></li></ul> <ul><li>Myasnikov, A.G.; Shpilrain, V.; Ushakov, A. (2008). <a href="https://books.google.com/books?id=mEa3BAAAQBAJ&pg=PR7"><i>Group-based Cryptography</i></a>. Advanced Courses in Mathematics – CRM Barcelona. Birkhauser. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9783764388270.</li> <li>Myasnikov, A.G.; Shpilrain, V.; Ushakov, A. (2011). <i>Non-commutative cryptography and complexity of group-theoretic problems</i>. Amer. Math. Soc. Surveys and Monographs. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780821853603.</li> <li>Magyarik, M.R.; Wagner, N.R. (1985). <a href="https://doi.org/10.1007/3-540-39568-7_3">"A Public Key Cryptosystem Based on the Word Problem"</a>. <i>Advances in Cryptology—CRYPTO 1984</i>. Lecture Notes in Computer Science. Vol. 196. Springer. pp. 19–36. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F3-540-39568-7_3">10.1007/3-540-39568-7_3</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-39568-3.</li> <li>Anshel, I.; Anshel, M.; Goldfeld, D. (1999). <a href="https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0003/MRL-1999-0006-0003-a003.pdf">"An algebraic method for public-key cryptography"</a> (PDF). <i>Math. Res. Lett</i>. 6 (3): 287–291. <a href="/facts/CiteSeerX_(identifier)/SceDmd3c">CiteSeerX</a> <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.8355">10.1.1.25.8355</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.4310%2FMRL.1999.v6.n3.a3">10.4310/MRL.1999.v6.n3.a3</a>.</li> <li>Ko, K.H.; Lee, S.J.; Cheon, J.H.; Han, J.W.; Kang, J.; Park, C. (2000). <a href="https://link.springer.com/chapter/10.1007/3-540-44598-6_10">"New public-key cryptosystem using braid groups"</a>. <i>Advances in Cryptology—CRYPTO 2000</i>. Lecture Notes in Computer Science. Vol. 1880. Springer. pp. 166–183. <a href="/facts/CiteSeerX_(identifier)/SceDmd3c">CiteSeerX</a> <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.5306">10.1.1.85.5306</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F3-540-44598-6_10">10.1007/3-540-44598-6_10</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-44598-2.</li> <li>Shpilrain, V.; Zapata, G. (2006). "Combinatorial group theory and public key cryptography". <i>Appl. Algebra Eng. Commun. Comput</i>. 17 (3–4): 291–302. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/math/0410068">math/0410068</a>. <a href="/facts/CiteSeerX_(identifier)/SceDmd3c">CiteSeerX</a> <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.888">10.1.1.100.888</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2Fs00200-006-0006-9">10.1007/s00200-006-0006-9</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:2251819">2251819</a>.</li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Paul, Kamakhya; Goswami, Pinkimani; Singh, Madan Mohan. (2022). <a href="https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_52_v2_2022/52_2_p26-218-223.pdf">"ALGEBRAIC BRAID GROUP PUBLIC KEY CRYPTOGRAPHY"</a>, <i><a href="http://www.vijnanaparishadofindia.org/jnanabha">Jnanabha</a></i>, Vol. 52(2) (2022), 218-223. ISSN 0304-9892 (Print) ISSN 2455-7463 (Online)</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20170717103854/http://kodu.ut.ee/~lipmaa/crypto/link/public/braid/">Cryptography and Braid Groups page</a> (archived version 7/17/2017)</li></ul>