I am reading a paper by Shacham and Waters on Compact Proofs of Retrievability. In this paper on page number 3 under section 1.1 in the very first line the author states that an encoded file is broken into n number of blocks $m_1,m_2...m_n \in Z_p$ for some large prime p.
I am not able to understand that in terms of programmimg what does it exactly mean to have a chunk of file data in a group/field. On the same page they mention an equation:
$σ_i = f_k(i) + αm_i \in Z_p$
What is the value of this $m_i$ in this equation. Is it the number of bytes/bits in each block? What value of $m_i$ would I take if I have to calculate this $σ_i$ in the equation ? The calculated value of sigma lies in the group of prime order $Z_p$.
I am not sure if I have posted the question in the right forum but I could not get any comments in stack overflow hence I have posted it to a forum I find closely related to. Any help will be valuable.
Thanks and Regards