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Due to the weakness of public key cryptosystems encounter of quantumcomputers, the need to provide a solution was emerged. The McEliececryptosystem and its security equivalent, the Niederreiter cryptosystem, whichare based on Goppa codes, are one of the solutions, but they are not practicaldue to their long key length. Several prior attempts to decrease the length ofthe public key in code-based cryptosystems involved substituting the Goppa codefamily with other code families. However, these efforts ultimately proved to beinsecure. In 2016, the National Institute of Standards and Technology (NIST)called for proposals from around the world to standardize post-quantumcryptography (PQC) schemes to solve this issue. After receiving of variousproposals in this field, the Classic McEliece cryptosystem, as well as theHamming Quasi-Cyclic (HQC) and Bit Flipping Key Encapsulation (BIKE), chosen ascode-based encryption category cryptosystems that successfully progressed tothe final stage. This article proposes a method for developing a code-basedpublic key cryptography scheme that is both simple and implementable. Theproposed scheme has a much shorter public key length compared to the NISTfinalist cryptosystems. The key length for the primary parameters of theMcEliece cryptosystem (n=1024, k=524, t=50) ranges from 18 to 500 bits. Thesecurity of this system is at least as strong as the security of theNiederreiter cryptosystem. The proposed structure is based on the Niederreitercryptosystem which exhibits a set of highly advantageous properties that makeit a suitable candidate for implementation in all extant systems.

A tiny public key scheme based on Niederreiter Cryptosystem