We give tightly matching upper and lower bounds on the
maximum rate of any secure stegosystem. We introduce the concept of steganographic key exchange and public-key steganography, and show that provably secure protocols for these objectives exist under a variety of standard number-theoretic assumptions. We consider several notions of active attacks against steganography, show how to achieve each under standard assumptions, and consider the relationships between these notions. Finally, we extend the concept of steganograpy as covert communication to include the more general concept of covert computation.
Steganographic \protocols" have a long and intriguing history that goes back to antiquity. There are stories of secret messages written in invisible ink or hidden in love letters (the rst character of each sentence can be used to spell a secret, for instance). More recently, steganography was used by prisoners, spies and soldiers during World War II because mail was carefully inspected by both the Allied and Axis governments at the time . Postal censors crossed out anything that looked like sensitive information (e.g. long strings of digits), and they prosecuted individuals whose mail seemed suspicious. In many cases, censors even randomly deleted innocent-looking sentences or entire paragraphs in order to prevent secret messages from being delivered. More recently there has been a great deal of interest in digital steganography, that is, in hiding secret messages in communications between computers. The recent interest in digital steganography is fueled by the increased amount of communication which is mediated by computers and by the numerous potential commercial applications: hidden information could potentially be used to detect or limit the unauthorized propagation of the innocent-looking \carrier" data.
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