Cryptography and Theory prove

Hello, I hope all of you are doing ok. I have a project that I need to fix and proved elegantly. The proof and fix related to Hash Function and Lattice Encryption too. Moreover, I want you to help me to fix and formate the problem statement and structure. I don't need implementation or code, I want a professional in cryptography and theory. So, you don't waste my time or your time. I prefer if the freelancer is at the Ph.D. level and has years of experience. Thank you.