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Journal articles on the topic 'Multivariate cryptosystem'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Singh, Rajesh P., Bhaba K. Sarma, and Anupam Saikia. "A Public Key Cryptosystem Using a Group of Permutation Polynomials." Tatra Mountains Mathematical Publications 77, no. 1 (2020): 139–62. http://dx.doi.org/10.2478/tmmp-2020-0013.

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Abstract In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field F q m. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2 k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m 3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m 2+3m – 4 left cyclic shifts, 5m 2 +3m + 4 xor operations and 7 permutations on bits for decryption.

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2

Li, Weijian, Xian Huang, Huimin Zhao, Guoliang Xie, and Fuxiang Lu. "Fuzzy Matching Template Attacks on Multivariate Cryptography: A Case Study." Discrete Dynamics in Nature and Society 2020 (June 20, 2020): 1–11. http://dx.doi.org/10.1155/2020/9475782.

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Multivariate cryptography is one of the most promising candidates for post-quantum cryptography. Applying machine learning techniques in this paper, we experimentally investigate the side-channel security of the multivariate cryptosystems, which seriously threatens the hardware implementations of cryptographic systems. Generally, registers are required to store values of monomials and polynomials during the encryption of multivariate cryptosystems. Based on maximum-likelihood and fuzzy matching techniques, we propose a template-based least-square technique to efficiently exploit the side-channel leakage of registers. Using QUAD for a case study, which is a typical multivariate cryptosystem with provable security, we perform our attack against both serial and parallel QUAD implementations on field programmable gate array (FPGA). Experimental results show that our attacks on both serial and parallel implementations require only about 30 and 150 power traces, respectively, to successfully reveal the secret key with a success rate close to 100%. Finally, efficient and low-cost strategies are proposed to resist side-channel attacks.

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3

NIE, Xu-Yun, Zhao-Hu XU, Yong-Jian LIAO, and Ting ZHONG. "Cryptanalysis of Extended Multivariate Public Key Cryptosystem." Chinese Journal of Computers 36, no. 6 (2014): 1177–82. http://dx.doi.org/10.3724/sp.j.1016.2013.01177.

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4

Yuan, Feng, Hai Wen Ou, and Sheng Wei Xu. "A New Public Key Cryptographic Scheme." Applied Mechanics and Materials 303-306 (February 2013): 1944–47. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1944.

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The multivariate public key cryptosystem is a new and fast public key cryptosystem. This paper presents a multivariate public key cryptographic scheme over a finite field with odd prime characteristic. The idea of embedding and layering is manifested in its construction. The security of the scheme is analyzed in detail. The result indicates that the proposed scheme can resist all known attacks effectively.

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5

Selvakumar, K., and S. Naveen Kumar. "Multivariate Quadratic Quasigroup Polynomial based Cryptosystem in Vanet." International Journal of Engineering & Technology 7, no. 4.10 (2018): 832. http://dx.doi.org/10.14419/ijet.v7i4.10.26767.

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Vehicular Ad-hoc Network (VANET) is a developing transmission system to abet in the everyday organization of vehicular traffic and safety of vehicles (nodes). Unsigned verification is one of the key necessities in VANET gives the confidentiality of the root of the message. Current security conventions in VANET’s gives unsigned verification depends on the two-tier architecture, comprises of two VANET components, particularly nodes and Roadside Units (RsU’s) functioning as the key developing server (KDS). This protocol depends densely on RsU’s to give unsigned identification to the nodes. In this paper, we propose the K-means Cluster Head algorithm which is utilized for guide assortment, for both personal-best (’pbest’) and global-best (’gbest’), are observed a tremendously successful and complete well evaluate to the before existing methods. Here, we also propose an asymmetric encryption algorithm, with emphasis on Multivariate Quadratic Quasigroups (MVQQ) algorithm, in a circumstance of VANET. We set forward prime pseudonyms reasonably make a long time cycle that are worn to interact with semi-confided in experts and alternate pseudonyms with a minor lifetime which are utilized to talk with different nodes.

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6

Smith-Tone, Daniel, and Cristina Tone. "A multivariate cryptosystem inspired by random linear codes." Finite Fields and Their Applications 69 (January 2021): 101778. http://dx.doi.org/10.1016/j.ffa.2020.101778.

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7

Huixian, Li, Gao Jin, Wang Lingyun, and Pang Liaojun2. "MPKC-based Threshold Proxy Signcryption Scheme." International Arab Journal of Information Technology 17, no. 2 (2019): 196–206. http://dx.doi.org/10.34028/iajit/17/2/7.

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The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.

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8

Singh, Rajesh P., Anupam Saikia, and Sarma B. K. "Little Dragon Two: An efficient Multivariate Public Key Cryptosystem." International journal of Network Security & Its Applications 2, no. 2 (2010): 1–10. http://dx.doi.org/10.5121/ijnsa.2010.2201.

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9

Sun, Xiaoyan, Maosheng Zhang, Shaowu Mao, Zhengwei Ren, and Huanguo Zhang. "Software watermarking scheme based on multivariate public key cryptosystem." Wuhan University Journal of Natural Sciences 21, no. 3 (2016): 257–61. http://dx.doi.org/10.1007/s11859-016-1168-3.

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10

Sun, Yan Jun, Chang Ming Liu, Hai Yu Li, and Zhe Yuan. "One-Way Function Construction Based on the MQ Problem and Logic Function." Applied Mechanics and Materials 220-223 (November 2012): 2360–63. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2360.

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Multivariate quadratic based public-key cryptography called MQ problem which based on calculation of a secure cryptography of multivariate equations and MQ cryptography security is based on the difficulty of the solution of multivariate equations. But computer and mathematician scientists put a lot of effort and a long time to research MQ cryptography and they have proved that MQ cryptography is NP complete problem. Therefore, before the P problem Equal to the NP problem we do not figure out selected multivariate equations by random in polynomial time. So we can use this feature to construct the relative safety method of the public key encryption. A new type of public-key cryptosystem has been brought up in this paper that one-way shell core function which has such advantages as more security and flexibility, and provides a more inclusive public-key cryptosystem.

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11

Ghadbane, Nacer. "On Public-key Cryptosystem Based on the Problem of Solving a Non-Linear System of Polynomial Equations." WSEAS TRANSACTIONS ON COMPUTER RESEARCH 8 (June 25, 2020): 106–10. http://dx.doi.org/10.37394/232018.2020.8.13.

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The basic idea behind multivariate cryptography is to choose a system of polynomials which can be easily inverted (central map). After that one chooses two affine invertible maps to hide the structure of the central map. Fellows and Koblitz outlined a conceptual key cryptosystem based on the hardness of POSSO. Let Fp s be a finite field of p s elements, where p is a prime number, and s ∈ N, s ≥ 1. In this paper, we used the act of GLn (Fp s ) on the set F n p s and the transformations group, to present the public key cryptosystems based on the problem of solving a non-linear system of polynomial equations

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12

Wang, Ling Ling. "A New Multivariate-Based Ring Signature Scheme." Applied Mechanics and Materials 347-350 (August 2013): 2688–92. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.2688.

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Most of the existing ring signature schemes are based on traditional cryptography, such as RSA and discrete logarithm. Unfortunately these schemes would be broken if quantum computers emerge. The MQ-problem based Public-Key Cryptosystem (MPKC) is an important alternative to traditional PKCs for its potential to resist future attacks of quantum computers. In this paper, we proposed a new ring signature scheme based on MPKC, which has the properties of consistent, unforgery, signer-anonymity.

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13

Yuan, Feng, Hai Wen Ou, and Sheng Wei Xu. "Security Analysis of Square Minus Scheme." Applied Mechanics and Materials 321-324 (June 2013): 2669–73. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2669.

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The multivariate public key cryptosystem is a new and fast public key cryptosystem. This paper investigates the security of Square minus scheme, and presents a method to attack the scheme. The attack utilizes the affine parts of the private keys and the weakness caused by the structures of the private keys to find a large number of linear equations. The attack can recover the private keys efficiently when the parameters are small enough.

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14

Tao, Chengdong, Hong Xiang, Albrecht Petzoldt, and Jintai Ding. "Simple Matrix – A Multivariate Public Key Cryptosystem (MPKC) for Encryption." Finite Fields and Their Applications 35 (September 2015): 352–68. http://dx.doi.org/10.1016/j.ffa.2015.06.001.

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15

Singaravelu, Pradheepkumar, and Shekhar Verma. "Performance analysis of multivariate cryptosystem schemes for wireless sensor network." Computers & Electrical Engineering 39, no. 6 (2013): 1880–93. http://dx.doi.org/10.1016/j.compeleceng.2012.07.010.

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16

Wang, Ling Ling. "A Verifiable Ring Signature Scheme Based on Multivariate Public-Key Cryptosystem." Applied Mechanics and Materials 380-384 (August 2013): 1899–902. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.1899.

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Most existing verifiable ring signature schemes are based on traditional PKCs, which cannot resist future attacks of quantum computers. Fortunately, the MQ-problem based Multivariate Public-Key Cryptosystem (MPKC) is an important alternative to traditional PKCs for its potential to resist future attacks of quantum computers. In this paper, we proposed a construction of verifiable ring signature based on MPKC, which has the properties of consistent, unforgery, signer-anonymity and verifiability.

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17

WANG, Yacheng, Yasuhiko IKEMATSU, Dung Hoang DUONG, and Tsuyoshi TAKAGI. "The Secure Parameters and Efficient Decryption Algorithm for Multivariate Public Key Cryptosystem EFC." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A, no. 9 (2019): 1028–36. http://dx.doi.org/10.1587/transfun.e102.a.1028.

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18

Wang, Xin, and Bo Yang. "An improved signature model of multivariate polynomial public key cryptosystem against key recovery attack." Mathematical Biosciences and Engineering 16, no. 6 (2019): 7734–50. http://dx.doi.org/10.3934/mbe.2019388.

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19

TSUJII, Shigeo, Kohtaro TADAKI, Ryo FUJITA, and Masahito GOTAISHI. "Proposal of the Multivariate Public Key Cryptosystem Relying on the Difficulty of Factoring a Product of Two Large Prime Numbers." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E99.A, no. 1 (2016): 66–72. http://dx.doi.org/10.1587/transfun.e99.a.66.

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20

Ustimenko, V. A. "On new multivariate cryptosystems based on hidden Eulerian equations." Reports of the National Academy of Sciences of Ukraine, no. 5 (May 23, 2017): 17–24. http://dx.doi.org/10.15407/dopovidi2017.05.017.

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21

Luo, Yuling, Shunsheng Zhang, Junxiu Liu, and Lvchen Cao. "Cryptanalysis of a Chaotic Block Cryptographic System Against Template Attacks." International Journal of Bifurcation and Chaos 30, no. 15 (2020): 2050223. http://dx.doi.org/10.1142/s0218127420502235.

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The security of chaotic cryptographic system can be theoretically evaluated by using conventional statistical tests and numerical simulations, such as the character frequency test, entropy test, avalanche test and SP 800-22 tests. However, when the cryptographic algorithm operates on a cryptosystem, the leakage information such as power dissipation, electromagnetic emission and time-consuming can be used by attackers to analyze the secret keys, namely the Side Channel Analysis (SCA) attack. In this paper, a cryptanalysis method is proposed for evaluating the security of a chaotic block cryptographic system from a hardware perspective by utilizing the Template Attacks (TAs). Firstly, a chaotic block cryptographic system is described briefly and implemented based on an Atmel XMEGA microcontroller. Then the TA using a multivariate Gaussian model is introduced. In order to reduce computational complexity and improve the efficiency of TA, the Hamming weight is used in this work to model power consumption traces. The proposed TA method has the following advantages including (a) using the sum of difference to select points of interest of traces, (b) using a data processing method to minimize the influences on power information modeling from the redundant sampling points, and (c) all the traces are aligned precisely before establishing the templates. Experimental results show that the TA can be used to attack the chaotic cryptographic systems and is more efficient, i.e. [Formula: see text]32% less attack traces than correlation power analysis, when the templates are properly built.

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22

Liu, Mingjie, Lidong Han, and Xiaoyun Wang. "On the equivalent keys in multivariate cryptosystems." Tsinghua Science and Technology 16, no. 3 (2011): 225–32. http://dx.doi.org/10.1016/s1007-0214(11)70033-5.

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23

Gao, Shuhong, and Raymond Heindl. "Multivariate public key cryptosystems from diophantine equations." Designs, Codes and Cryptography 67, no. 1 (2011): 1–18. http://dx.doi.org/10.1007/s10623-011-9582-1.

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24

Kumar, Manish. "Quantum Computing and Post Quantum Cryptography." International Journal of Innovative Research in Physics 2, no. 4 (2021): 37–51. http://dx.doi.org/10.15864/ijiip.2405.

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The present knowledge we had in quantum computer and the most possible architecture of a quantum computer might be able to break RSA 2048 in future. In classical computer two bits represents any one of four bit information whereas in quantum due to superposition it can be represent all four states. For ‘n’ qubits system is analogous to 2n classical bits. Quantum teleportation, quantum entanglement and other makes it possible to break present cryptosystem. Shor’s Algorithm is used for integer factorization which is polynomial time for quantum computer. This can be threat for RSA security. In this paper matlab implementation of Shor’s algorithm is presented. Used classical way for getting period of function because classical computers not engage quantum phenomena. As numbers of iterations grow, probability of getting exact factor of ‘n’ acutely increased. This paper also discusses popular methods for making qubits like Silicon based Qubits in which electron is put inside nano material which is used as a transistor. In Superconducting circuit method insulator is used as a sandwich in between two metal layers. Used by Google, IBM, Intel, Microsoft. In Flux qubits method very small size loop of superconducting metal is used. This paper also discusses Quantum Proof Algorithm like Lattice-based cryptography used concept of good and bad base. In Learning with errors method if we have more equation then variable, it is over defined system. In Code based cryptography some matrixes allow for efficient error correction (good matrix) but most matrix’s does not (bad matrix) concept is used. In Hash based signatures scheme have long signatures or keys, but they are secure. Also discuss Multivariate Quantum proof algorithm. The abstract should contain maximum of 300 words. No abbreviation should be mentioned in the abstract. Give a brief summary of your research work.

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25

HASHIMOTO, Yasufumi, Tsuyoshi TAKAGI, and Kouichi SAKURAI. "General Fault Attacks on Multivariate Public Key Cryptosystems." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E96.A, no. 1 (2013): 196–205. http://dx.doi.org/10.1587/transfun.e96.a.196.

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26

Singaravelu, Pradheepkumar, Shekhar Verma, and Charles A. Shoniregun. "Feasibility of position-based multivariate cryptosystems for WSN." International Journal of Internet Technology and Secured Transactions 4, no. 2/3 (2012): 237. http://dx.doi.org/10.1504/ijitst.2012.047967.

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27

Ustimenko, Vasyl. "Explicit constructions of extremal graphs and new multivariate cryptosystems." Studia Scientiarum Mathematicarum Hungarica 52, no. 2 (2015): 185–204. http://dx.doi.org/10.1556/012.2015.52.2.1312.

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New multivariate cryptosystems are introduced. Sequences f(n) of bijective polynomial transformations of bijective multivariate transformations of affine spaces Kn, n = 2, 3, ... , where K is a finite commutative ring with special properties, are used for the constructions of cryptosystems. On axiomatic level, the concept of a family of multivariate maps with invertible decomposition is proposed. Such decomposition is used as private key in a public key infrastructure. Requirements of polynomiality of degree and density allow to estimate the complexity of encryption procedure for a public user. The concepts of stable family and family of increasing order are motivated by studies of discrete logarithm problem in Cremona group. Statement on the existence of families of multivariate maps of polynomial degree and polynomial density with the invertible decomposition is formulated. We observe known explicit constructions of special families of multivariate maps. They correspond to explicit constructions of families of nonlinear algebraic graphs of increasing girth which appeared in Extremal Graph Theory. The families are generated by pseudorandom walks on graphs. This fact ensures the existence of invertible decomposition; a certain girth property guarantees the increase of order for the family of multivariate maps, good expansion properties of families of graphs lead to good mixing properties of graph based private key algorithms. We describe the general schemes of cryptographic applications of such families (public key infrastructure, symbolic Diffie—Hellman protocol, functional versions of El Gamal algorithm).

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28

Chen, Jiahui, Jie Ling, Jianting Ning, and Jintai Ding. "Identity-Based Signature Schemes for Multivariate Public Key Cryptosystems." Computer Journal 62, no. 8 (2019): 1132–47. http://dx.doi.org/10.1093/comjnl/bxz013.

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Abstract In this paper, we proposed an idea to construct a general multivariate public key cryptographic (MPKC) scheme based on a user’s identity. In our construction, each user is distributed a unique identity by the key distribution center (KDC) and we use this key to generate user’s private keys. Thereafter, we use these private keys to produce the corresponding public key. This method can make key generating process easier so that the public key will reduce from dozens of Kilobyte to several bits. We then use our general scheme to construct practical identity-based signature schemes named ID-UOV and ID-Rainbow based on two well-known and promising MPKC signature schemes, respectively. Finally, we present the security analysis and give experiments for all of our proposed schemes and the baseline schemes. Comparison shows that our schemes are both efficient and practical.

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29

Wang, HouZhen, HuanGuo Zhang, ZhangYi Wang, and Ming Tang. "Extended multivariate public key cryptosystems with secure encryption function." Science China Information Sciences 54, no. 6 (2011): 1161–71. http://dx.doi.org/10.1007/s11432-011-4262-3.

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30

Wang, Shangping, Rui Ma, Yaling Zhang, and Xiaofeng Wang. "Ring signature scheme based on multivariate public key cryptosystems." Computers & Mathematics with Applications 62, no. 10 (2011): 3973–79. http://dx.doi.org/10.1016/j.camwa.2011.09.052.

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31

Kandiy, S. O., and G. A. Maleeva. "Analysis of the complexity of attacks on multivariate cryptographic transformations using algebraic field structure." Radiotekhnika, no. 204 (April 9, 2021): 59–65. http://dx.doi.org/10.30837/rt.2021.1.204.06.

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In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization. One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme. The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.

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32

DING, JINTAI, TIMOTHY J. HODGES, VICTORIA KRUGLOV, DIETER SCHMIDT, and STEFAN TOHǍNEANU. "GROWTH OF THE IDEAL GENERATED BY A QUADRATIC MULTIVARIATE FUNCTION OVER GF(3)." Journal of Algebra and Its Applications 12, no. 05 (2013): 1250219. http://dx.doi.org/10.1142/s0219498812502192.

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Let K be the field GF(3). We calculate the growth of the ideal Aλ where A is the algebra of functions from Kn → Kn and λ is a quadratic function. Specifically we calculate dim Akλ where Ak is the space of polynomials of degree less than or equal to k. This question arises in the analysis of the complexity of Gröbner basis attacks on multivariate quadratic cryptosystems such as the Hidden Field Equation systems. We also prove analogous results over the associated graded ring [Formula: see text] and state conjectures for the case of a general finite field of odd order.

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33

Ustimenko, Vasyl. "On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications." Tatra Mountains Mathematical Publications 70, no. 1 (2017): 107–17. http://dx.doi.org/10.1515/tmmp-2017-0021.

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Abstract Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.

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34

HASHIMOTO, Yasufumi. "Key Recovery Attacks on Multivariate Public Key Cryptosystems Derived from Quadratic Forms over an Extension Field." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A, no. 1 (2017): 18–25. http://dx.doi.org/10.1587/transfun.e100.a.18.

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35

TSUJII, S., K. TADAKI, and R. FUJITA. "Proposal for Piece in Hand Matrix: General Concept for Enhancing Security of Multivariate Public Key Cryptosystems." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 5 (2007): 992–99. http://dx.doi.org/10.1093/ietfec/e90-a.5.992.

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36

Ustimenko, Vasyl, and Oleksandr Pustovit. "On effective computations in subsemigroups of affine Cremona semigroup and implentations of new postquantum multivariate cryptosystems." Physico-mathematical modelling and informational technologies, no. 32 (July 6, 2021): 27–31. http://dx.doi.org/10.15407/fmmit2021.32.050.

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Multivariate cryptography (MC) together with Latice Based, Hash based, Code based and Superelliptic curves based Cryptographies form list of the main directions of Post Quantum Cryptography.Investigations in the framework of tender of National Institute of Standardisation Technology (the USA) indicates that the potential of classical MC working with nonlinear maps of bounded degree and without the usage of compositions of nonlinear transformation is very restricted. Only special case of Rainbow like Unbalanced Oil and Vinegar digital signatures is remaining for further consideration. The remaining public keys for encryption procedure are not of multivariate. nature. The paper presents large semigroups and groups of transformations of finite affine space of dimension n with the multiple composition property. In these semigroups the composition of n transformations is computable in polynomial time. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of these protocols rests on the complexity of the word decomposition problem, Finally presented algebraic protocols expanded to cryptosystems of El Gamal type which is not a public key system.

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37

DING, JINTAI, and TIMOTHY HODGES. "CRYPTANALYSIS OF AN IMPLEMENTATION SCHEME OF THE TAMED TRANSFORMATION METHOD CRYPTOSYSTEM." Journal of Algebra and Its Applications 03, no. 03 (2004): 273–82. http://dx.doi.org/10.1142/s0219498804000861.

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A Tamed Transformation Method (TTM) cryptosystem was proposed by T. T. Moh in 1999. We describe how the first implementation scheme of the TTM system can be defeated. The computational complexity of our attack is 233 computations on the finite field with 28 elements. The cipher of the TTM systems are degree 2 polynomial maps derived from composition of invertible maps of either total degree 2 or linear maps which can be easily calculated and can be easily inverted. To ensure the system to be of degree two, the key construction of the implementation schemes of the TTM systems is a multivariable polynomial Q8(x1,…,xn) and a set of linearly independent quadratic polynomials qi(x1,…,xm), i=1,…,n such that Q8(q1,…,qn) is again a degree 2 polynomials of x1,…,xm. In this paper, we study the first implementation scheme of the TTM systems [6]. We discovered that in this implementation scheme the specific polynomial Q8 can be decomposed further into a factorization in terms of composition. By taking powers of the equality satisfied by the new composition factors, we can actually derive a set of equations, that can produce linear equations satisfied by the plaintext. These linear equations lead us to find a way to defeat this implementation scheme.

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38

Yesina, M. V., S. O. Kandiy, E. V. Ostryanska, and I. D. Gorbenko. "Generation of general system parameters for Rainbow electronic signature scheme for 384 and 512 security bits." Radiotekhnika, no. 204 (April 9, 2021): 16–23. http://dx.doi.org/10.30837/rt.2021.1.204.02.

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Today, there is rapid progress in the creation of quantum computers to solve various computational problems and for different purposes. At the same time, special efforts are made to create such a quantum computer that can solve the problems of cryptanalysis of existing cryptosystems: asymmetric ciphers, key encapsulation protocols, electronic signatures, etc. Prevention of such threats can be achieved by developing cryptographic systems that will be protected against both quantum and classical attacks, and be able to interact with existing protocols and communication networks. There is also a significant need for protection against attacks by side channels. Currently, significant efforts of cryptologists are focused on the NIST PQC open competition. The main idea of the NIST PQC competition is to define mathematical methods based on which standards for asymmetric cryptotransformations, primarily electronic signatures, as well as asymmetric ciphers and key encapsulation protocols can be developed. Three electronic signature schemes – Crystals-Dilithium, Falcon and Rainbow become the finalists of the third stage of the NIST PQC competition according to the results of the second stage. The first two are based on the mathematics of algebraic lattices, and Rainbow is based on multivariate transformations. Currently, a comprehensive analysis of the finalists is an important task for the entire global crypto community. The vast majority of schemes that have become finalists or alternative algorithms are based on problems in the theory of algebraic lattices. Special attention was also paid to the Rainbow electronic signature scheme based on multivariate transformations. The purpose of this work consists in a preliminary analysis of existing attacks on promising electronic signature Rainbow, definition of requirements to the system-wide parameters to ensure cryptographic stability of at least 512 bits against classical and 256 bits against quantum cryptanalysis, as well as development and practical implementation of Rainbow algorithms for generating system-wide parameters for 512 bits against classical and 256 bits against quantum cryptanalysis.

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Singh, Rajesh P., A. Saikia, and B. K. Sarma. "Poly-Dragon: an efficient multivariate public key cryptosystem." Journal of Mathematical Cryptology 4, no. 4 (2011). http://dx.doi.org/10.1515/jmc.2011.002.

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Harayama, Tomohiro, and Donald K. Friesen. "Weil sum for birthday attack in multivariate quadratic cryptosystem." Mathematical Cryptology 1, no. 1 (2007). http://dx.doi.org/10.1515/jmc.2007.006.

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Dai, Songsong. "Quantum Cryptanalysis on a Multivariate Cryptosystem Based on Clipped Hopfield Neural Network." IEEE Transactions on Neural Networks and Learning Systems, 2021, 1–5. http://dx.doi.org/10.1109/tnnls.2021.3059434.

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Huang, Ning. "Analysis of a Multivariate Public Key Cryptosystem and Its Application in Software Copy Protection." Journal of Software 9, no. 8 (2014). http://dx.doi.org/10.4304/jsw.9.8.2010-2017.

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Alam, Bilal, Ferruh Özbudak, and Oğuz Yayla. "Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems." Journal of Mathematical Cryptology 9, no. 1 (2015). http://dx.doi.org/10.1515/jmc-2013-0019.

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AbstractT. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽

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Ustimenko, Vasyl. "On Multivariate Cryptosystems Based on Computable Maps with Invertible Decomposition." Annales UMCS, Informatica 14, no. 1 (2014). http://dx.doi.org/10.2478/umcsinfo-2014-0001.

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Romańczuk, Urszula, and Vasyl Ustimenko. "On the family of cubical multivariate cryptosystems based on the algebraic graph over finite commutative rings of characteristic 2." Annales UMCS, Informatica 12, no. 3 (2012). http://dx.doi.org/10.2478/v10065-012-0029-8.

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