Multivariate Quadratic Problem

Definition ∞ The Multivariate Quadratic Problem (MQ Problem) is a mathematical problem that involves finding solutions to a system of multivariate quadratic equations over a finite field. It is known to be NP-hard, meaning there is no known efficient algorithm to solve it for sufficiently large parameters. This computational hardness forms the basis for the security of certain post-quantum cryptographic schemes. Its resistance to classical and quantum computing attacks makes it a candidate for future cryptographic standards.
Context ∞ The Multivariate Quadratic Problem is a foundational element in the research and development of post-quantum cryptography, which aims to secure digital communications against future quantum computer attacks. Cryptographers are actively investigating MQ-based signature and encryption schemes as potential replacements for current widely used algorithms. News in this area often discusses the ongoing race to develop and standardize quantum-resistant cryptographic solutions.