Public-Key Identification Schemes Based on Multivariate Cubic Polynomials

Sakumoto, Koichi

doi:10.1007/978-3-642-30057-8_11

Cited by 14 publications

(16 citation statements)

References 25 publications

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“…Cryptosystems based on multivariate polynomial systems are attractive for the post-quantum world since they are efficient and easy to construct. In [9,11,12], zero-knowledge identification schemes based on multivariate quadratic or cubic polynomial systems were proposed. The comparison of identification schemes includes memory requirements, communication length, impersonation probability, and computation time for efficiency.…”

Section: Motivationmentioning

confidence: 99%

“…In [11], Sakumoto mentioned whether or not a public key identification scheme based on multivariate polynomials of degree more than two is efficient and presented new 3 -and 5 -pass identification schemes based on multivariate cubic polynomials. Sakumoto stated that the 3 -pass identification scheme was not productive but the 5 -pass identification scheme was highly efficient.…”

Section: Introductionmentioning

confidence: 99%

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A novel 3-pass identification scheme and signature scheme based on multivariate quadratic polynomials

Akleylek¹,

Soysaldi²

2019

Turk J Math

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Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure 3-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability compared to the work of Sakumoto et al. We also propose a new signature scheme constructed from the proposed identification scheme. In addition, we compare the signature scheme with the previous schemes in view of signature and key sizes. We improve the signature size compared to that given in previous work by Chen et al.

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Section: Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel 3-pass identification scheme and signature scheme based on multivariate quadratic polynomials

Akleylek¹,

Soysaldi²

2019

Turk J Math

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“…There are lattice-based systems which reduce to hard lattice problems, but these are much less ecient than NTRU. Analogously, there are multivariate PKCs that are provably secure in the sense that a break of such a PKC would imply an advance in the solution to an MQ-related computational problem [22,32,33], which happen to be much less ecient. Hence we take the approach that only careful study of cryptanalytic techniques can determine the security of a cryptosystem.…”

Section: Conventional Wisdom About Hfe Securitymentioning

confidence: 99%

Degree of Regularity for HFEv and HFEv-

Ding

Yang

2013

Lecture Notes in Computer Science

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Abstract. In this paper, we rst prove an explicit formula which bounds the degree of regularity of the family of HFEv (HFE with vinegar) and HFEv-(HFE with vinegar and minus) multivariate public key cryptosystems over a nite eld of size q. The degree of regularity of the polynomial system derived from an HFEv-system is less than or equal to (q − 1)(r + v + a − 1) 2 + 2 if q is even and r + a is odd,where the parameters v, D, q, and a are parameters of the cryptosystem denoting respectively the number of vinegar variables, the degree of the HFE polynomial, the base eld size, and the number of removed equations, and r is the rank paramter which in the general case is determined by D and q as r = log q (D − 1) + 1. In particular, setting a = 0 gives us the case of HFEv where the degree of regularity is bound by (q − 1)(r + v − 1) 2 + 2 if q is even and r is odd,This formula provides the rst solid theoretical estimate of the complexity of algebraic cryptanalysis of the HFEv-signature scheme, and as a corollary bounds on the complexity of a direct attack against the QUARTZ digital signature scheme. Based on some experimental evidence, we evaluate the complexity of solving QUARTZ directly using F4/F5 or similar Gröbner methods to be around 2 92 .

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“…In the literature, identification schemes based on multivariate quadratic polynomials as well as cubic ones have received interest since they are efficient for different platforms [19,20,21]. In [19], 3 and 5-pass zero-knowledge identification schemes based on multivariate quadratic false(MQfalse) polynomials over a finite field were proposed.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Polar Form of Any Degree of Multivariate Polynomials with Applications in IoT

Akleylek

Soysaldi

Boubiche

et al. 2019

Sensors

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Identification schemes based on multivariate polynomials have been receiving attraction in different areas due to the quantum secure property. Identification is one of the most important elements for the IoT to achieve communication between objects, gather and share information with each other. Thus, identification schemes which are post-quantum secure are significant for Internet-of-Things (IoT) devices. Various polar forms of multivariate quadratic and cubic polynomial systems have been proposed for these identification schemes. There is a need to define polar form for multivariate dth degree polynomials, where d ≥ 4 . In this paper, we propose a solution to this need by defining constructions for multivariate polynomials of degree d ≥ 4 . We give a generic framework to construct the identification scheme for IoT and RFID applications. In addition, we compare identification schemes and curve-based cryptoGPS which is currently used in RFID applications.

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Public-Key Identification Schemes Based on Multivariate Cubic Polynomials

Cited by 14 publications

References 25 publications

A novel 3-pass identification scheme and signature scheme based on multivariate quadratic polynomials

A novel 3-pass identification scheme and signature scheme based on multivariate quadratic polynomials

Degree of Regularity for HFEv and HFEv-

A Novel Method for Polar Form of Any Degree of Multivariate Polynomials with Applications in IoT

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