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Accelerated Multisecret Sharing Scheme Using Fast Matrix Spectral Factorization.

Selda Çalkavur1, Patrick Solé2, Lasha Ephremidze3

  • 1Department of Mathematics, Kocaeli University, 41380 Kocaeli, Turkey.

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Summary
This summary is machine-generated.

This study introduces an advanced multisecret sharing (MSS) scheme using a fast matrix factorization algorithm. The new method offers enhanced efficiency and security for large-scale applications like cloud storage and IoT networks.

Keywords:
cryptographic securityfast algorithmsfinite fieldslarge-scale distributed systemsmatrix spectral factorizationmultisecret sharingparaunitary matricessecret reconstruction

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Area of Science:

  • Cryptography
  • Information Security
  • Applied Mathematics

Background:

  • Multisecret sharing (MSS) schemes are crucial for secure data distribution.
  • Existing MSS schemes face challenges in efficiency and scalability for large systems.
  • Paraunitary matrices over finite fields are key components in advanced cryptographic constructions.

Purpose of the Study:

  • To propose a novel multisecret sharing (MSS) scheme with improved efficiency and scalability.
  • To integrate an exponential-speedup matrix spectral factorization algorithm into MSS construction.
  • To ensure perfect secrecy, collusion resistance, and efficient reconstruction in the proposed scheme.

Main Methods:

  • Developed a novel MSS scheme by integrating a fast matrix spectral factorization algorithm.
  • Utilized the block-matrix generalization of the Janashia-Lagvilava method.
  • Constructed paraunitary matrices over finite fields for enhanced scheme performance.

Main Results:

  • The proposed MSS scheme demonstrates significantly enhanced efficiency and scalability.
  • The method guarantees perfect secrecy and collusion resistance.
  • Efficient reconstruction of secrets is achieved, enabling practical deployment.

Conclusions:

  • The novel MSS scheme offers a superior alternative to existing methods.
  • The integration of advanced matrix factorization enhances cryptographic performance.
  • The scheme is well-suited for secure cloud storage, IoT, and blockchain applications.