Graded q-Differential Algebra Approach to q-Connection

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

Download Full-text

Monocular Lie algebra approach for 3D motion estimation

Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. ◽

10.1109/icpr.2004.1334095 ◽

2004 ◽

Author(s):

J. Ortegon-Aguilar ◽

E. Bayro-Corrochano

Keyword(s):

Motion Estimation ◽

Lie Algebra ◽

3D Motion ◽

Algebra Approach ◽

3D Motion Estimation

Download Full-text

Two-State Quantum Systems Revisited: A Clifford Algebra Approach

Advances in Applied Clifford Algebras ◽

10.1007/s00006-020-01116-1 ◽

2021 ◽

Vol 31 (2) ◽

Author(s):

Pedro Amao ◽

Hernan Castillo

Keyword(s):

Clifford Algebra ◽

Quantum Systems ◽

Algebra Approach

Download Full-text

Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

Journal of Mathematical Cryptology ◽

10.1515/jmc-2019-0054 ◽

2020 ◽

Vol 15 (1) ◽

pp. 266-279

Author(s):

Atul Pandey ◽

Indivar Gupta ◽

Dhiraj Kumar Singh

Keyword(s):

Discrete Logarithm ◽

Public Key Cryptography ◽

Public Key ◽

Quantum Computers ◽

Group Rings ◽

Diffie Hellman ◽

Algebra Approach ◽

Elgamal Cryptosystem ◽

Diffie Hellman Key Exchange ◽

Equivalent Keys

AbstractElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

Download Full-text