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<p>Elliptic Curve Cryptography (ECC) is among the most widely used asymmetric key cryptography for its efficient security with smaller key sizes. Dawahdeh et al. Journal of King Saud University - Computer and Information 590 Sciences 30(3):349–355. (2018) recently suggested an image encryption system based on the Hill cipher and ECC. In their method, the Hill cipher algorithm’s security is enhanced by utilizing the security of the ECC, which is based on the discrete logarithm problem of the elliptic curve. Additionally, the ECC is used to generate a self-invertible matrix key for the Hill cipher. However, the elliptic curve’s order used by the authors is not large enough to resist the obvious attacks on Discrete Logs. This paper points out the weakness of the encryption method in Dawahdeh et al. Journal of King Saud University - Computer and Information 590 Sciences 30(3):349–355. (2018), where it can be cryptanalysed by using the ciphertext-only attack. Simulation of the Dawahdeh <i>et al.</i> method is successfully carried out with different images using different secret keys generating different cipher images. All the cipher images are successfully cryptanalysed by generating the self-invertible matrix key using the Naive attack or the Baby Step - Giant Step attack on the public keys of the communicating parties. The original images are successfully retrieved from the encrypted images. A robustness improvement of Dawahdeh <i>et al.</i> is proposed to withstand the cryptanalysis possible in the original Dawahdeh <i>et al.</i> method. Statistical and security analyses are conducted on the improved method to comprehend the security of the improved method.</p>

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Cryptanalysis and improvement of an image cryptosystem based on Hill cipher combined with elliptic curve cryptography

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Dolendro Singh Laiphrakpam,
  • Rohit Sharma,
  • Ripon Patgiri,
  • Motilal Singh Khoirom

摘要

Elliptic Curve Cryptography (ECC) is among the most widely used asymmetric key cryptography for its efficient security with smaller key sizes. Dawahdeh et al. Journal of King Saud University - Computer and Information 590 Sciences 30(3):349–355. (2018) recently suggested an image encryption system based on the Hill cipher and ECC. In their method, the Hill cipher algorithm’s security is enhanced by utilizing the security of the ECC, which is based on the discrete logarithm problem of the elliptic curve. Additionally, the ECC is used to generate a self-invertible matrix key for the Hill cipher. However, the elliptic curve’s order used by the authors is not large enough to resist the obvious attacks on Discrete Logs. This paper points out the weakness of the encryption method in Dawahdeh et al. Journal of King Saud University - Computer and Information 590 Sciences 30(3):349–355. (2018), where it can be cryptanalysed by using the ciphertext-only attack. Simulation of the Dawahdeh et al. method is successfully carried out with different images using different secret keys generating different cipher images. All the cipher images are successfully cryptanalysed by generating the self-invertible matrix key using the Naive attack or the Baby Step - Giant Step attack on the public keys of the communicating parties. The original images are successfully retrieved from the encrypted images. A robustness improvement of Dawahdeh et al. is proposed to withstand the cryptanalysis possible in the original Dawahdeh et al. method. Statistical and security analyses are conducted on the improved method to comprehend the security of the improved method.