Secret Sharing, Hashes and Commitments | Lesson 4

This lecture covers how to securely share secrets among a group, the mathematical properties of safe primes, the mechanics and vulnerabilities of hash functions, RSA digital signatures, and the basics of polynomial commitments.

As an exercise:

try simulating a small-scale Shamir Secret Sharing scheme. Pick a small prime (e.g., P=11), a secret S=5, and a threshold t=3. Create a random polynomial of degree 2 (t−1), evaluate it for three "users" (x=1,2,3), and then manually use Lagrange interpolation to reconstruct the polynomial and recover the secret S.

References and Links:

• Review how the Birthday Paradox drastically reduces the security of hash functions: math.stackexchange.com/questions/35791/birthday-paradox-expected-number-of-people

• Review the corresponding chapters on RSA and Hash Functions in the course book here: Google Drive Link