What is it about?
Weak mathematical structures not to be chosen in multi- variate publuc key cryptosystem construction/ design.
Featured Image
Why is it important?
With certain assumptions towards birthday attack paradox, Haryama and Friesen prposed Linearised Binomial Attack (LBA). LBA involves obtaining collision among the signature evaluations through multivariate cryptosystem public key polynomial map and hash values of messages in reduced image space of Im(L). This was equivalent to finding solutions of bivariate equation. When number of solutions of that equation was more than certain bound, LBA exhibits reduced time complexity than normal birthday attack. We identify these classes of involved univariate polynomials termed as Weak Dembowski-Ostrom polynomials.
Perspectives
Harayama and Friesen proposed linearised binomial attack for multivariate quadr- atic cryptosystems and introduced weak Dembowski Ostrom(DO) polynomials in this framework over the finite field F2. They conjecture about the existence of infinite class of weak DO polynomials and presented the open problem of enumer- ating their classes. We extend linearised binomial attack to multivariate quadratic cryptosystems over Fp for any prime p and redefine the weak DO polynomials for general case. We identify an infinite class of weak Dembowski Ostrom polynomials for these systems by considering highly degenerate quadratic forms over algebraic function fields and Artin-Schreir type curves to achieve our results.
Dr. Bilal Alam
Orta Dogu Teknik Universitesi
Read the Original
This page is a summary of: Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems, Journal of Mathematical Cryptology, January 2015, De Gruyter,
DOI: 10.1515/jmc-2013-0019.
You can read the full text:
Contributors
The following have contributed to this page
