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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. - PowerPoint PPT Presentation
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Keeping Secretswith
Zero Knowledge Proof
Stephanie Lin6.UAP Concept Talk
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You have a Secret!
Your Friend You The Secret
Jean-Jacques, et al. 1998. 3
The Cave
Jean-Jacques, et al. 1998. 4
The Solution
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Probability
½ ⅛
½*½*½½*½
¼
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Real World UseAuthentication on the Internet
Banker You
Who Are You?
I amStephanie.
How do I know you are
Stephanie?
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Practical Use with Feige -Fiat-Shamir
Authentication on the Internet
Math Tools:• Hard One Way Problems• Prime Factorization• Modulus Roots
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Prime Factorization
Answer: 91 = 7 * 13 644773 = 797 * 809
Large Prime:93E8965DAFD9DFECFD00B466B68F90EA68AF5DC9FED915278D1B3A137471E65596C37FED0C7829FF8F8331F81A2700438ECDCC09447DC397C685F397294F722BCC484AEDF28BED25AAAB35D35A65DB1FD62C9D7BA55844FEB1F9401E671340933EE43C54E4DC459400D7AD61248B83A2624835B31FFF2D9595A5B90B276E44F9
Example : 15 = 3 * 5 91 = ? * ? 644773 = ? * ?
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Modulus Roots
Example : 7 = 42 (mod 9) 7 = ?2 (mod 9) 1 = ?2 (mod 9)
Answer: 7 = 1032 (mod 9) 1 = 1072 (mod 9)
Feige, Fiat, Shamir. 1987. 10
The ProtocolProver
Primes p, q s.t. n = p*qFind s s.t. gcd(s,n) = 1v = s2 (mod n)[s = secret]
Verifier
[given v, n]
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The Protocol
y = r*sa (mod n)
rand int r, x = r2 (mod n)
a = 0 or 1
y2 = x*va (mod n)
x
a
y
