University of Massachusetts - Boston Dr. Xiaohui Liang
Special Topics in Applied Cryptography CS 480/697 – Spring 2020

Project 5: Practice on Zero-knowledge Proof
Due date: May 13
Preparation
1. Check lecture notes a13 Zero-knowledge Proof
Submission
1. Upload your document to Piazza, using file name as your lastname+hw5.
Practice Questions (9 points)
1. Prove the following Perdersen scheme is a zero-knowledge protocol
System parameter: g, h are elements of Zp* with order q
Public commitment c = gxhr (mod p)
Private knowledge x,r

One-round protocol
• Commit: P: picks random y, s in [1..q], sends d = gyhs mod p
• Challenge: V: sends random challenge e in [1..q]
• Response: P: sends u=y+ex, v=s+er (mod q)
• Verification: V: accepts if guhv = dce (mod p)
Hints: separately prove completeness, soundness, and zero-knowledge