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Provably Secure Steganography

Provably Secure Steganography. Nick Hopper With Luis von Ahn John Langford. Ward. Alice. Bob. Steganography: The Prisoner’s Problem. Can’t they use Encryption?. ?. Encrypts “JL BRK 2300H” to get “NM DTQ 0599K”. Ward. “NM DTQ 0599K”. Alice. Bob. Can’t they use Encryption?. ?.

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Provably Secure Steganography

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  1. Provably Secure Steganography Nick Hopper With Luis von Ahn John Langford NSF Aladdin Site Review

  2. Ward Alice Bob Steganography:The Prisoner’s Problem NSF Aladdin Site Review

  3. Can’t they use Encryption? ? Encrypts “JL BRK 2300H” to get “NM DTQ 0599K” Ward “NM DTQ 0599K” Alice Bob NSF Aladdin Site Review

  4. Can’t they use Encryption? ? Ward Alice Bob • Cryptography only hides the content of a message • Steganography hides the existence of a message NSF Aladdin Site Review

  5. Secure Stegosystem NSF Aladdin Site Review

  6. Secure Stegosystem A Channel , C, is a distribution on a set D of documents NSF Aladdin Site Review

  7. Secure Stegosystem A Channel , C, is a distribution on a set D of documents A Stegosystem S = (SE,SD) is a pair of algorithms: NSF Aladdin Site Review

  8. Input: Key K Message m Output: sin D* Secure Stegosystem A Channel , C, is a distribution on a set D of documents A Stegosystem S = (SE,SD) is a pair of algorithms: SE NSF Aladdin Site Review

  9. Input: KeyK s in D* Output: Message m Input: Key K Message m Output: sin D* Secure Stegosystem A Channel , C, is a distribution on a set D of documents A Stegosystem S = (SE,SD) is a pair of algorithms: SE SD NSF Aladdin Site Review

  10. Input: KeyK s in D* Output: Message m Input: Key K Message m Output: sin D* Secure Stegosystem A Channel , C, is a distribution on a set D of documents A Stegosystem S = (SE,SD) is a pair of algorithms: SE SD With high probability, SD(K,SE(K,m)) = m NSF Aladdin Site Review

  11. Input: KeyK s in D* Output: Message m Input: Key K Message m Output: sin D* Secure Stegosystem A Channel , C, is a distribution on a set D of documents A Stegosystem S = (SE,SD) is a pair of algorithms: SE SD With high probability, SD(K,SE(K,m)) = m S is secure if output distribution of SE(K,m) for any m is computationally indistinguishable from C NSF Aladdin Site Review

  12. SE FK FK SD Construction C NSF Aladdin Site Review

  13. SE FK FK SD Construction C Shared Pseudorandom Function NSF Aladdin Site Review

  14. m 0 SE SD Construction C FK FK FK 1 0 0 1 1 NSF Aladdin Site Review

  15. SE SD Construction C FK FK FK majority=0 0 0 1 NSF Aladdin Site Review

  16. Results • Secure steganography exists if and only if one-way functions exist • “Robust Steganography” is possible if one-way functions exist • There is a CAPTCHA such that, either the CAPTCHA is secure, or robust steganography for images is possible. • Public-Key steganography is possible, under widely believed cryptographic assumptions • Essentially tight upper and lower bounds on the maximum rate of a stegosystem NSF Aladdin Site Review

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