Leeza RazaSP23-RMT-014Dr. Tariq Javed ZiaLHR TP 95672026-03-172024-03-17https://repository.cuilahore.edu.pk/handle/123456789/2922Due to the increase in exchange of secret information in todays digital world robust cryptographic systems have been designed to guarantee secure transmission. The world of cryptographic security is transforming continually, however this is considerably at risk due to quantum computers. Cryptosystem based on multivariable equations have been considered resilient against quantum attacks can be a basis of a post-quantum secure communication system. Some important types of this algorithm which are unique in structure and promising in security are oil-vinegar scheme and its types and Rainbow scheme. “Jacques Patarin” introduced Oil-Vinegar scheme” in 1997. This is a digital signature scheme based on solving the multivariate quadratic polynomials over a finite field. This system relies on the structural and balanced oil and vinegar variables which guarantee security, nonlinearity, and efficiency. Depending on the choice of variables, there exist two types of the “oil-vinegar scheme” namely; “Balanced Oil-Vinegar scheme” and Unbalanced Oil-Vinegar scheme (UOV). There is another important digital signature scheme named Rainbow Signature Scheme.enDepartment of MathematicsMathematicsSP23cryptographic systemscryptographic securitymultivariable equationsThesis