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Securing Emails using Secret
Sharing
Securing Emails using Secret Sharing
Have you ever sent your
confidential information
such as passport and
SSN over email?
Motivation
• Most people have done it
• Email servers have confidential information about most people
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.
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.
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.
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
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 }
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
Next Steps
• Collect data and write a research paper
• Convert the program into an Android app

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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