Consider the field F := (Z/5Z)[x]/(f) and set g := x+(f) F^x

Assume that the letters A-Z are labeled by the elements g⁰, g¹, . . . , g²⁵ F^x

(a) Is this reasonable? In other words, are the elements g⁰, g¹, . . . , g²⁵ without repetition?

(b) Using the group F, the element g F^x and the El Gamal cryptosystem, send the message NOW to a person whose published key is a = 3. Use the number k = 2 for the "clue" g^k