Design and analysis of a quasigroup-based DNA encryption schemeTools Tiong, Yih Lian (2026) Design and analysis of a quasigroup-based DNA encryption scheme. MPhil thesis, University of Nottingham.
AbstractDNA cryptography is an interdisciplinary field of cryptography inspired from DNA computing which uses DNA molecules’ role as information carrier for cryptographic purposes. In this thesis, we present an improvement on the existing algorithm with the implementation of quasigroup in the process of encryption and decryption of DNA cryptography. As opposed to traditional cryptography, which is based on numerical values, the proposed scheme makes use of DNA bases as elements of a quasigroup and unlike conventional approaches that rely solely on standard DNA bases (A, T, C, G), the proposed method introduces a DNA base U as an additional element, which appears only in the process of encryption. The encryption process involves 2 phases, namely Phase I, in which the DNA form of the plaintext undergoes transformation through a randomly generated leader and a quasigroup of order 5, and Phase II, in which the process repeats itself but the quasigroup is replaced by one of its random parastrophes. The utilisation of quasigroup operations for the proposed cryptographic scheme provides a mathematical foundation for data transformation. Notably, since the total number of quasigroups of order n increases exponentially with n, this makes them advantageous for constructing cryptosystems with extensive key space, thus ensuring enhanced security without increasing computational complexity. In summary, this thesis proposes a novel, two-phase cryptographic scheme that successfully integrates quasigroup operations with DNA encoding. The introduction of the Uracil base and the use of parastrophes were shown to produce ciphertext with near-ideal entropy, providing enhanced security against statistical attacks while maintaining linear-time efficiency suitable for larger plaintexts.
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