ℓ-Invertible Cycles for $\mathcal{M}$ultivariate $\mathcal{Q}$uadratic (${\mathcal{MQ}}$) Public Key Cryptography.

We propose a new basic trapdoor $\mathcal{\ell}$IC (ℓ-Invertible Cycles) of the mixed field type for $\mathcal{M}$ultivariate $\mathcal{Q}$uadratic public key cryptosystems. This is the first new basic trapdoor since the invention of Unbalanced Oil and Vinegar in 1997. $\mathcal{\ell}$IC can be considered an extended form of the well-known Matsumoto-Imai Scheme A (also MIA or C ∗ ), and share some features of stagewise triangular systems. However ${\mathcal{\ell}}$IC has very distinctive properties of its own. In practice, ${\mathcal{\ell}}$IC is much faster than MIA, and can even match the speed of single-field ${\mathcal{MQ}}$ schemes. [ABSTRACT FROM AUTHOR]