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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 鄭振牟(Chen-Mou Cheng) | |
| dc.contributor.author | Kuan-Wei Chen | en |
| dc.contributor.author | 陳冠瑋 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:36:03Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.copyright | 2012-08-01 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-26 | |
| dc.identifier.citation | [1] ISSAC ’02: Proceedings of the 2002 international symposium on Symbolic and algebraic computation, New York, NY, USA, 2002. ACM. 505020.
[2] Luk Bettale, Jean-Charles Faugere, and Ludovic Perret. Cryptanalysis of multi- variate and odd-characteristic hfe variants. In Catalano et al. [5], pages 441–458. [3] Dan Boneh, editor. Advances in Cryptology - CRYPTO 2003, 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, 2003, Proceedings, volume 2729 of Lecture Notes in Computer Science. Springer, 2003. [4] Wieb Bosma, John Cannon, and Catherine Playoust. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4):235–265, 1997. Computational algebra and number theory (London, 1993). [5] Dario Catalano, Nelly Fazio, Rosario Gennaro, and Antonio Nicolosi, editors. Public Key Cryptography - PKC 2011 - 14th International Conference on Prac- tice and Theory in Public Key Cryptography, Taormina, Italy, March 6-9, 2011. Proceedings, volume 6571 of Lecture Notes in Computer Science. Springer, 2011. [6] Jean Charles Faugere. A new efficient algorithm for computing grobner bases without reduction to zero (f5). In Proceedings of the 2002 international sym- posium on Symbolic and algebraic computation, ISSAC ’02, pages 75–83, New York, NY, USA, 2002. ACM. [7] Jean-Charles Faugere and Antoine Joux. Algebraic cryptanalysis of hidden field equation (hfe) cryptosystems using grobner bases. In Boneh [3], pages 44–60. [8] Harriet J. Fell and Whitfield Diffie. Analysis of a public key approach based on polynomial substitution. In Advances in Cryptology, CRYPTO ’85, pages 340–349, London, UK, UK, 1986. Springer-Verlag. [9] Shuhong Gao, Yinhua Guan, and Frank Volny. A new incremental algorithm for computing groebner bases. In Koepf [16], pages 13–19. [10] Michael R. Garey and David S. Johnson. Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA, 1990. [11] Guang Gong and Kishan Chand Gupta, editors. Progress in Cryptology - IN- DOCRYPT 2010 - 11th International Conference on Cryptology in India, Hy- derabad, India, December 12-15, 2010. Proceedings, volume 6498 of Lecture Notes in Computer Science. Springer, 2010. [12] Hideki Imai and Tsutomu Matsumoto. Algebraic methods for constructing asymmetric cryptosystems. In Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes, AAECC-3, pages 108– 119, London, UK, UK, 1986. Springer-Verlag. [13] Aviad Kipnis, Jacques Patarin, and Louis Goubin. Unbalanced oil and vinegar signature schemes. In IN ADVANCES IN CRYPTOLOGY - EUROCRYPT 1999, pages 206–222. Springer, 1999. [14] Aviad Kipnis and Adi Shamir. Cryptanalysis of the oil and vinegar signature scheme. In Proceedings of CRYPTO’98, Springer, LNCS n o 1462, pages 257– 266. Springer Verlag, 1998. [15] Aviad Kipnis and Adi Shamir. Cryptanalysis of the hfe public key cryptosystem by relinearization. In Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology, CRYPTO ’99, pages 19–30, London, UK, UK, 1999. Springer-Verlag. [16] Wolfram Koepf, editor. Symbolic and Algebraic Computation, International Symposium, ISSAC 2010, Munich, Germany, July 25-28, 2010, Proceedings. ACM, 2010. [17] Jacques Patarin. Hidden fields equations (hfe) and isomorphisms of polyno- mials (ip): Two new families of asymmetric algorithms. In Proceedings of the 15th annual international conference on Theory and application of cryp- tographic techniques, EUROCRYPT’96, pages 33–48, Berlin, Heidelberg, 1996. Springer-Verlag. [18] Albrecht Petzoldt, Stanislav Bulygin, and Johannes Buchmann. Cyclicrainbow - a multivariate signature scheme with a partially cyclic public key. In Gong and Gupta [11], pages 33–48. [19] Albrecht Petzoldt, Stanislav Bulygin, and Johannes Buchmann. Linear recur- ring sequences for the uov key generation. In Catalano et al. [5], pages 335–350. [20] Albrecht Petzoldt, Enrico Thomae, Stanislav Bulygin, and Christopher Wolf. Small public keys and fast verification for multivariate quadratic public key systems. In Proceedings of the 13th international conference on Cryptographic hardware and embedded systems, CHES’11, pages 475–490, Berlin, Heidelberg, 2011. Springer-Verlag. [21] Peter W. Shor. Polynomial-time algorithms for prime factorization and dis- crete logarithms on a quantum computer. SIAM J. Comput., 26(5):1484–1509, October 1997. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65314 | - |
| dc.description.abstract | Shortening the public key of the Multivariate Public-Key Cryptographic(MPKC) schemes [20] is the most active issue in recent MPKC research. In this article we extend the results of PTBW11 [20] which is applied only to single field schemes, we show a method shortening the public key of embedded field transformation schemes like Hidden Field Equations(HFE) [17]. We also explain how the structure of central map restricts the short form of public key. This restriction only depends on the structure of central map so all MPKC schemes are affected. The affine map S can also participate in shortening the public key although the capacity and efficiency is not as well as central map because the resulting equations for solving S are not on-to in the big field. Unlike S, the affine map T gives a better result in the key shortening process. As a proof of concept, we propose a short public-key version of HFE- signature scheme and quantify the reduction in public key size in the end. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:36:03Z (GMT). No. of bitstreams: 1 ntu-101-R99921051-1.pdf: 1460451 bytes, checksum: 8bdbcbd334d9467b5c321aa3ec17fd09 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 1 Introduction 1
1.1 Motivation................................. 1 1.2 Ourcontribution ............................. 2 1.3 Organization ............................... 2 2 Preliminaries 3 2.1 MQproblem ............................... 3 2.2 MPKC................................... 4 2.3 ShortpublickeyinUOVscheme .................... 5 2.3.1 OilandVinegarsignaturescheme................ 5 2.3.2 Short-keyUOV .......................... 6 2.4 HFE.................................... 7 3 Generate short public key 9 3.1 EmbeddedFieldtransformationinSandT . . . . . . . . . . . . . . 9 3.1.1 ThefieldtransformationmatrixMn............... 9 3.1.2 MnmodifiedS .......................... 10 3.2 Shortkeygeneratingprocess....................... 11 3.3 AffinemapS ............................... 12 3.4 AffinemapT ............................... 13 4 Restriction of short public key 15 4.1 Therestrictionoftheshortpublickey ................. 15 4.2 Atoyexample............................... 18 4.3 Fullkeygeneratingprocess........................ 19 5 About security 22 5.1 Securityofshort-UOV .......................... 22 5.2 Securityofshort-HFE .......................... 25 5.3 AttackingHFE .............................. 25 6 An example : Shorten the public key of HFE- 27 6.1 HFE-.................................... 27 6.2 ShortkeyHFE-.............................. 28 7 Conclusion 33 | |
| dc.language.iso | en | |
| dc.subject | 後量子密碼學 | zh_TW |
| dc.subject | 多變量公開金鑰密碼系統 | zh_TW |
| dc.subject | 隱藏體方程組密碼系統 | zh_TW |
| dc.subject | 非平衡油醋密碼系統 | zh_TW |
| dc.subject | 多變量二次方程組問題 | zh_TW |
| dc.subject | HFE | en |
| dc.subject | Post-Quantum | en |
| dc.subject | Multivariate | en |
| dc.subject | MPKC | en |
| dc.subject | MQ Problem | en |
| dc.subject | UOV | en |
| dc.title | 縮短嵌入體變換多變量公開金鑰密碼系統的金鑰長度 | zh_TW |
| dc.title | Reducing the Key Size of MPKC with Embedded Field Transformation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳君明,楊柏因 | |
| dc.subject.keyword | 後量子密碼學,多變量公開金鑰密碼系統,多變量二次方程組問題,非平衡油醋密碼系統,隱藏體方程組密碼系統, | zh_TW |
| dc.subject.keyword | Post-Quantum,Multivariate,MPKC,MQ Problem,UOV,HFE, | en |
| dc.relation.page | 36 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-26 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電機工程學研究所 | zh_TW |
| 顯示於系所單位： | 電機工程學系 | |
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