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Information Hiding & Digital Watermarking. Tri Van Le. Outlines. Some history State of the art Research goals Possible approaches Research plan. Cryptography in the 80s. Beginning time of open research A lot of schemes proposed Most of them soon broken. Broken Cryptosystems (I).

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outlines
Outlines
  • Some history
  • State of the art
  • Research goals
  • Possible approaches
  • Research plan
cryptography in the 80s
Cryptography in the 80s
  • Beginning time of open research
  • A lot of schemes proposed
  • Most of them soon broken
broken cryptosystems i
Broken Cryptosystems (I)

Merkle

Hellman

1978-1984

Iterated

Knapsack

1978-1984

Lu-Lee

1979-1980

Adiga

Shankar

1985-1988

Nieder-reiter

1986-1988

Merlke

Hellman

Merlke

Hellman

Lu-Lee

Adigar

Shankar

Neiderreiter

Okamoto

1987-1988

Okamoto

1986-1987

Pieprzyk

1985-1988

ChorRivest

1988-1998

GoodmanMcAuly

1984-1988

Chor

Rivest

Okamoto

Okamoto

Pieprzyk

Goodman

McAuly

broken cryptosystems ii
Broken Cryptosystems (II)

Matsumoto

Imai

1983-1984

Cade

1985-1986

Yagisawa

1985-1986

TMKIF

1986-1985

Luccio

Mazzone

1980-1981

Matsumoto

Imai

Cade

Yasigawa

Tsujii, Itoh

Matsumoto

Kurosama

Fujioka

Luccio

Mazzone

Rivest

Adleman

Dertouzos

1978-1987

HighDegree

CG

1988

Rao

Nam

1986-1988

Low

Degree

CG

1982

Kravitz

Reed

1982-1982

Krawczyk

Boyar

Rivest

Adleman

Dertouzos

Rao

Nam

Kravitz

Reed

broken cryptosystems iii
Broken Cryptosystems (III)

Ong

Schnorr

Shamir

1984-1985

Okamoto

Shiraishi

1985-1985

Ong

Schnorr

1983-1984

Ong

Schorr

Shamir

Okamoto

Shiraishi

Ong

Schorr

proven secure cryptosystems i
Proven Secure Cryptosystems (I)
  • Shannon’s work (1949)
    • Mathematical proof of security
    • Information theoretic secrecy
  • Enemy with unlimited power
    • Can compute any desired function
proven secure cryptosystems ii
Proven Secure Cryptosystems (II)
  • Rabin (81), Goldwasser & Micali (82)
    • Mathematical proof of security
    • Computational secrecy
  • Enemy with limited time and space
    • Can run in polynomial time
    • Can use polynomial space
information hiding state of the art
Information Hiding(state of the art)
  • Similar to that of cryptography in 80s
    • Many schemes were proposed
    • Most of them were broken
  • Use heuristic security
    • Subjective measurements
    • Assume very specific enemy
research goals
Research Goals
  • Fundamental way
    • Systematic research
    • Same as Shannon and Goldwasser’s work
  • What have been done
    • Covert channels
    • Anonymous communications
  • What are the properties
fundamental models
Fundamental Models
  • Unconditional hiding
    • Unlimited enemy
  • Statistical hiding
    • Polynomial samples
  • Computational hiding
    • Polynomial time
what have been done
What have been done
  • Covert channels
  • Anonymous communications
  • Information hiding
    • Steganography
    • Digital watermarking
covert channels
Covert Channels
  • Leakage information (e.g. viruses)
    • Disk space
    • CPU load
  • Subliminal channels
    • Digital signatures
    • Encryption schemes
    • Cryptographic malwares
covert computations
Covert Computations
  • Computation inside computations
    • Secret design calculations inside a factoring computation
    • Secret physics simulations inside a cryptographic software or devices
anonymous communications
Anonymous Communications
  • MIX Networks
    • Electronic voting
    • Anonymous communication
  • Onion Routings
    • Limited anonymous communication
  • Blind signatures
    • Digital cash
information hiding
Information Hiding
  • Steganography
    • Invisible inks
    • Small dots
    • Letters
  • Digital watermarking
    • Common lossy compressions
    • Common signal processing operations
information hiding21
Information Hiding
  • Hiding property
    • Output must look like the cover
  • Secrecy
    • No partial information on input message
  • Authenticity
    • Hard to compute valid output
our approaches
Our Approaches
  • Arbitrary key
    • Steganography, watermarking
  • Restricted key
    • Protection of key materials
  • Key = Ciphertext
    • Secret sharing
research plan
Research Plan
  • To understand information hiding
    • Perfect hiding (done)
      • Necessary and sufficient conditions
      • Computational complexity results
      • Constructions of prefect secure schemes
      • Constructions of schemes with non-reliability
    • Computational hiding (under research)
      • Conventional constructions
      • Public key schemes
research plan24
Research Plan
  • Other aspects
    • Replacing privacy by authenticity
  • Extra problem
    • Robustness against modifications
thank you
Thank you
  • Questions?
  • More details?
approaches
Approaches
  • Arbitrary key distribution
    • E: KM  C
    • K: key space
    • M: message space
    • C: cover space
  • Requires
    • E(k,m) is distributed accordingly to Pcover
approaches27
Approaches
  • Restricted key distribution
    • c = E(k,m)
    • k is distributed accordingly to PK
    • c is distributed accordingly to PCover
approaches28
Approaches
  • Key = Ciphertext
    • S: MCC
    • (k1,k2) = S(m)
  • Requires
    • k1 and k2 distributed accordingly to PCover
models
Models
  • Perfect hiding
    • Pc = Pcover
    • Ciphertext distributes exactly as Pcover
  • Statistical Hiding
    • |Pc - Pcover| is a negligible function
  • Negligible function
    • f(n)<n-d for all d>0 and n>Nd.
models30
Models
  • Computational Hiding
    • Pc and Pcover are P-time indistinguishable
    • For all P-time P.T.M. M:
      • Prob(M(Pc)=1) - Prob(M(Pcover)=1)is negligible.
examples
Examples
  • Quadratic residues
    • n = pq
    • S1 = {x2 |x in Zn*}
    • S2 = {x|x in Zn* and J(x)=1}
  • Decision Diffie-Hellman
    • U1 = (g, ga, gb, gab) mod p
    • U2 = (g, ga, gb, gr) mod p