Shamir Secret Sharing Presentation
- 1. Securing Emails using Secret Sharing
- 2. Securing Emails using Secret Sharing Have you ever sent your confidential information such as passport and SSN over email?
- 3. Motivation • Most people have done it • Email servers have confidential information about most people
- 4. Shamir Secret Sharing MUA • Secret: Any information that a user wishes to encrypt • Share: The resultant k pieces of information generated from the secret, which will not yield any useful information on the secret until all shares are combined.
- 5. Application • Secure: Perfect information-theoretic security • Extensible: No share is significantly larger than the original secret • Fast: Computational overhead for generating shares and reconstructing secrets is linear based on the number of shares generated and length of the secret.
- 6. System Architecture • Each piece P represents a different email address to which a single share is sent. • Share generation happens on the sending end. • Secret reconstruction happens at the receiving end.
- 7. Why use this? • People should have the option to use completely secure email systems • Connection between user and email provider is typically encrypted and secure, but from then on there is no guarantee. • Using a web browser to interact with email is inherently insecure • Widely used public key encryption schemes are useless if an intruder obtains the private key
- 8. Example Share Generation • S = 1234 • 𝑘 = 3 • 𝑟1 = 166 • 𝑟2 = 9 • 𝑎 = 𝑘 • 𝑎 = 𝑆, 𝑟1, 𝑟2 𝑘 = 3 • 𝑝 = 1631 • 𝑓 𝑥 = 𝑖=0 𝑘 𝑎𝑖 ∗ 𝑥 𝑖 mod p • 𝑆ℎ𝑎𝑟𝑒𝑠 = {𝑓 1 , 𝑓 2 , 𝑓 3 }
- 9. Example Secret Reconstruction x y 1 1494 2 329 3 965 • 𝑓 𝑥 𝑚𝑜𝑑 𝑝 = 𝑗=0 𝑘 𝑦𝑗 ∗ 𝑙𝑗(𝑥) • 𝑙𝑗 𝑥 = 0≤𝑚≤𝑘 𝑚≠𝑗 𝑥−𝑥 𝑚 𝑥 𝑗−𝑥 𝑚 • 𝑓 0 = 𝑆 ∴ 𝑆 = 1234
- 10. Next Steps • Collect data and write a research paper • Convert the program into an Android app