Is DEHP a kind of Multivariate hard problem?

[smslca]

Please correct me if I am wrong. To my understanding , given a '$m$' multivariate set of equations in '$n$' variables in a integer field '$F$' is hard to solve, even in case of $MQ(multiquadratic)$ usually with field having characteristic as '$2$'. Where in case of $DEHP(Diophatine Equation Hard Problem)$ , it is a multivariate congruence with odd modulo field.
I would like to know that , is DEHP a case of multivariate hard problem with some large odd characteristic and a single equation.

 

[jvicens]

Thank you for your post. You are correct in your understanding that solving a multivariate set of equations in a finite field is generally a difficult problem, particularly when the field has a characteristic of 2. The specific problem you mentioned, DEHP (Diophantine Equation Hard Problem), is indeed a multivariate congruence problem with an odd modulo field.

To answer your question, DEHP can be considered a case of a multivariate hard problem with a large odd characteristic and a single equation. This is because solving a single equation in a finite field with a large odd characteristic is already a challenging task, and when multiple variables are involved, the difficulty increases significantly.

I hope this clarifies your understanding. Let me know if you have any further questions.