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Using Secret Key to Foil an Eavesdropper

Using Secret Key to Foil an Eavesdropper. Paul Cuff Electrical Engineering Princeton University. Main Idea. Secrecy for distributed systems Historic Cryptography Results New Metric for Secrecy. Distributed System. Action. Node B. Message. Information. Node A. Attack. Adversary.

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Using Secret Key to Foil an Eavesdropper

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  1. Using Secret Keyto Foil an Eavesdropper Paul Cuff Electrical Engineering Princeton University

  2. Main Idea • Secrecy for distributed systems • Historic Cryptography Results • New Metric for Secrecy Distributed System Action Node B Message Information Node A Attack Adversary

  3. Cipher • Plaintext: Source of information: • Example: English text: Allerton Conference • Ciphertext: Encrypted sequence: • Example: Non-sense text: cu@sp4isit Key Key Plaintext Ciphertext Plaintext Encipherer Decipherer

  4. Example: Substitution Cipher • Simple Substitution • Example: • Plaintext: …RANDOMLY GENERATE A CODEB… • Ciphertext: …DFLAUIPV WRLRDFNR F SXARQ… • Caesar Cipher

  5. Shannon Model • Schematic • Assumption • Enemy knows everything about the system except the key • Requirement • The decipherer accurately reconstructs the information Key Key Plaintext Ciphertext Plaintext Encipherer Decipherer Adversary For simple substitution: C. Shannon, "Communication Theory of Secrecy Systems," Bell Systems Technical Journal, vol. 28, pp. 656-715, Oct. 1949.

  6. Shannon Analysis • Perfect Secrecy • Adversary learns nothing about the information • Only possible if the key is larger than the information C. Shannon, "Communication Theory of Secrecy Systems," Bell Systems Technical Journal, vol. 28, pp. 656-715, Oct. 1949.

  7. Shannon Analysis • Equivocation vs Redundancy • Equivocation is conditional entropy: • Redundancy is lack of entropy of the source: • Equivocation reduces with redundancy: C. Shannon, "Communication Theory of Secrecy Systems," Bell Systems Technical Journal, vol. 28, pp. 656-715, Oct. 1949.

  8. Computational Secrecy • Some imperfect secrecy is difficult to crack • Public Key Encryption • Trapdoor Functions • Difficulty not proven • Often “cat and mouse” game • Vulnerable to quantum computer attack X 2147483647 1125897758 834 689 524287 W. Diffie and M. Hellman, “New Directions in Cryptography,” IEEE Trans. on Info. Theory, 22(6), pp. 644-654, 1976.

  9. Information Theoretic Secrecy • Achieve secrecy from randomness (key or channel), not from computational limit of adversary. • Physical layer secrecy • Wyner’s Wiretap Channel [Wyner 1975] • Partial Secrecy • Typically measured by “equivocation:” • Other approaches: • Error exponent for guessing eavesdropper [Merhav 2003] • Cost inflicted by adversary [this talk]

  10. Competitive Distributed System Decoder: Encoder: Key Information Action Message Node A Node B Attack Adversary System payoff: . Adversary:

  11. Zero-Sum Game • Value obtained by system: • Objective • Maximize payoff Key Information Message Action Node A Node B Attack Adversary

  12. Payoff-Rate Function Maximum achievable average payoff Markov relationship: Theorem:

  13. Encoding Scheme • Coordination Strategies [Cuff-Permuter-Cover 10] • Empirical coordination for U • Strong coordination for Y K

  14. Lossless Case • Require Y=X • Assume a payoff function • Related to Yamamoto’s work [97] • Very different result Theorem: [Cuff 10] Also required:

  15. Binary-Hamming Case • Binary Source: • Hamming Distortion • Naïve approach • Random hashing or time-sharing • Optimal approach • Reveal excess 0’s or 1’s to condition the hidden bits (black line) (orange line) Source Public message

  16. What the Adversary doesn’t know can hurt him. Knowledge of Adversary: [Yamamoto 97] [Yamamoto 88]:

  17. No Causal Information (Prior Work) [Theorem 3, Yamamoto 97] Theorem: Choose yields

  18. Summary • Framework for Encryption • Average cost inflicted by adversary • Dynamic settings where information is available causally • No use of “equivocation” • Optimal performance uses both “strong” and “empirical” coordination.

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