# Questions tagged as ['multivariate-cryptography']

A generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field
Score: 2
Sage code for finding generator matrix of MDS code
1. Let $$L$$ be an $$[n,k]$$ code. A $$k\times n$$ matrix $$G$$ whose rows form a basis for $$L$$ is called a generator matrix for $$L$$.

2. A linear $$[n,k,d]$$ code with largest possible minimum distance is called maximum distance $$d$$ separable or MDS code.

I want to find a generator matrix for MDS code using SageMath or in another way, is there any SageMath code to check a matrix is a generator matrix for the MDS ...

Score: 0
How does the public-key generation work in the multivariate post-quantum digital signature GeMMS?

There are a few steps in the public-key generation of GeMSS that I am trying to understand. The first is the below equations (1).

What does "$$\theta_i$$ forms a basis for $$\mathbb{F}_{2^n}$$ over $$\mathbb{F}_2$$" mean? I know what a basis is in linear algebra, but more details are needed so I can understand.
How do we interpret the map $$\phi$$?

1. $$(\theta_1,\ldots,\theta_n)\in(\mathbb{F}_{2^n})^n$$ form a  ...