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A message recovery attack on multivariate polynomial trapdoor function.

Rashid Ali1, Muhammad Mubashar Hussain2, Shamsa Kanwal3

  • 1Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan.

Peerj. Computer Science
|September 14, 2023
PubMed
Summary
This summary is machine-generated.

This study demonstrates a Gröbner basis attack on a multivariate polynomial cryptosystem. The attack successfully recovers plaintext from ciphertext, compromising the system's security.

Keywords:
Algebraic cryptanalysisGröbner basisMultivariate polynomial systemPublic key cryptosystem

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Area of Science:

  • Cryptography
  • Computer Science
  • Number Theory

Background:

  • Cybersecurity relies on secure information exchange via public channels, ensuring data confidentiality and integrity.
  • Multivariate polynomial trapdoor functions are proposed for cryptographic systems, with security claims based on system complexity.

Purpose of the Study:

  • To analyze the security of a cryptosystem based on multivariate polynomial trapdoor functions over rational numbers.
  • To demonstrate the vulnerability of the proposed cryptosystem to specific mathematical attacks.

Main Methods:

  • The study involves mounting an attack on a cryptosystem utilizing multivariate polynomial trapdoor functions.
  • A Gröbner basis attack is employed to analyze the system's security vulnerabilities.

Main Results:

  • The proposed trapdoor function is shown to be vulnerable to a Gröbner basis attack.
  • Specific polynomials from the Gröbner basis enable plaintext recovery from ciphertext without the secret key.

Conclusions:

  • The cryptosystem's security, based on the complexity of solving polynomial systems, is undermined by the Gröbner basis attack.
  • The findings highlight potential weaknesses in cryptosystems relying on multivariate polynomial trapdoor functions.