Some Remarks on Cocks’ Identity-Based Encryption Scheme

Abstract

The theory of quadratic residues plays an important role in cryptography. In 2001, Cocks developed an identity-based encryption(IBE)scheme based on quadratic residues, resolving Shamir's 17-year-old open problem. However, a notable drawback of Cocks' scheme is the significant expansion of the ciphertext, and some of its limitations have been addressed in subsequent research.Recently, Cotan and Teşeleanu highlighted that previous studies on Cocks' scheme relied on a trial-and-error method based on Jacobi symbols to generate the necessary parameters for the encryption process. They enhanced the encryption speed of Cocks' scheme by eliminating this trialand-error method. Based on security analysis, this study concludes that the security of Cotan-Teşeleanu's proposal cannot be directly derived from the security of the original Cocks' scheme. Furthermore, by adopting the CotanTeşeleanu method and introducing an additional variable as a public element, this study develops a similar enhancement scheme that not only accelerates the encryption speed but also provides security equivalent to the original Cocks' scheme.

Keywords

identity-based encryption(IBE) / quadratic residue / security / Cocks' IBE scheme

References

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Funding

Rising-Star Program of Shanghai 2023 Science and Technology Innovation Action Plan(Yangfan Special Project)

China(23YF1401000)

Fundamental Research Funds for the Central Universities, China(2232022D-25)