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Keeping Secrets with Zero Knowledge Proof

Keeping Secrets with Zero Knowledge Proof. Stephanie Lin 6.UAP Concept Talk. You have a Secret!. You. Your Friend. The Secret. The Cave. The Solution. Probability. ¼. ½. ⅛. ½*½. ½*½*½. Real World Use. Authentication on the Internet. I am Stephanie.

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Keeping Secrets with Zero Knowledge Proof

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  1. Keeping SecretswithZero Knowledge Proof Stephanie Lin 6.UAP Concept Talk

  2. You have a Secret! You Your Friend The Secret

  3. The Cave Jean-Jacques, et al. 1998.

  4. The Solution Jean-Jacques, et al. 1998.

  5. Probability ¼ ½ ⅛ ½*½ ½*½*½

  6. Real World Use Authentication on the Internet I am Stephanie. How do I know you are Stephanie? Who Are You? Banker You

  7. Practical Use with Feige -Fiat-Shamir Authentication on the Internet Math Tools: • Hard One Way Problems • Prime Factorization • Modulus Roots

  8. Prime Factorization Example : 15 = 3 * 5 91 = ? * ? 644773 = ? * ? Answer: 91 = 7 * 13 644773 = 797 * 809 Large Prime: 93E8965DAFD9DFECFD00B466B68F90EA68AF5DC9FED915278D1B3A137471E65596C37FED0C7829FF8F8331F81A2700438ECDCC09447DC397C685F397294F722BCC484AEDF28BED25AAAB35D35A65DB1FD62C9D7BA55844FEB1F9401E671340933EE43C54E4DC459400D7AD61248B83A2624835B31FFF2D9595A5B90B276E44F9

  9. Modulus Roots Example : 7 = 42 (mod 9) 7 = ?2 (mod 9) 1 = ?2 (mod 9) • Answer: 7 = 1032 (mod 9) • 1 = 1072 (mod 9)

  10. The Protocol Verifier [given v, n] Prover Primes p, qs.t. n = p*q Find ss.t. gcd(s,n) = 1 v = s2 (mod n) [s = secret] Feige, Fiat, Shamir. 1987.

  11. The Protocol rand intr, x = r2 (mod n) x a = 0 or 1 a y = r*sa (mod n) y y2 = x*va (mod n)

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