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Register a new userRandomness Efficient Steganography
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Added by
Narasimha Shashidhar
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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Steganographic protocols enable one to embed covert messages into inconspicuous data over a public communication channel in such a way that no one, aside from the sender and the intended receiver, can even detect the presence of the secret message. In this paper, we provide a new provably-secure, private-key steganographic encryption protocol secure in the framework of Hopper et al. We first present a one-time stegosystem that allows two parties to transmit messages of length at most that of the shared key with information-theoretic security guarantees. The employment of a pseudorandom generator (PRG) permits secure transmission of longer messages in the same way that such a generator allows the use of one-time pad encryption for messages longer than the key in symmetric encryption. The advantage of our construction, compared to all previous work is randomness efficiency: in the information theoretic setting our protocol embeds a message of length n bits using a shared secret key of length (1+o(1))n bits while achieving security 2^{-n/log^{O(1)}n}; simply put this gives a rate of key over message that is 1 as n tends to infinity (the previous best result achieved a constant rate greater than 1 regardless of the security offered). In this sense, our protocol is the first truly randomness efficient steganographic system. Furthermore, in our protocol, we can permit a portion of the shared secret key to be public while retaining precisely n private key bits. In this setting, by separating the public and the private randomness of the shared key, we achieve security of 2^{-n}. Our result comes as an effect of the application of randomness extractors to stegosystem design. To the best of our knowledge this is the first time extractors have been applied in steganography.
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We provide a new provably-secure steganographic encryption protocol that is proven secure in the complexity-theoretic framework of Hopper et al. The fundamental building block of our steganographic encryption protocol is a one-time stegosystem that allows two parties to transmit messages of length shorter than the shared key with information-theoretic security guarantees. The employment of a pseudorandom generator (PRG) permits secure transmission of longer messages in the same way that such a generator allows the use of one-time pad encryption for messages longer than the key in symmetric encryption. The advantage of our construction, compared to that of Hopper et al., is that it avoids the use of a pseudorandom function family and instead relies (directly) on a pseudorandom generator in a way that provides linear improvement in the number of applications of the underlying one-way permutation per transmitted bit. This advantageous trade-off is achieved by substituting the pseudorandom function family employed in the previous construction with an appropriate combinatorial construction that has been used extensively in derandomization, namely almost t-wise independent function families.
Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only if it has a random preimage. This result (for computable distributions and mappings, and Martin-Lof randomness) was known for a long time (folklore); in this paper we prove its natural generalization for layerwise computable mappings, and discuss the related quantitative results.
The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans) however often involve large amounts of shared correlations among the communicating players, but rarely allow for perfect sharing of randomness. Can the communication complexity benefit from shared correlations as well as it does from shared randomness? This question was considered mainly in the context of simultaneous communication by Bavarian et al. (ICALP 2014). In this work we study this problem in the standard interactive setting and give some general results. In particular, we show that every problem with communication complexity of $k$ bits with perfectly shared randomness has a protocol using imperfectly shared randomness with complexity $exp(k)$ bits. We also show that this is best possible by exhibiting a promise problem with complexity $k$ bits with perfectly shared randomness which requires $exp(k)$ bits when the randomness is imperfectly shared. Along the way we also highlight some other basic problems such as compression, and agreement distillation, where shared randomness plays a central role and analyze the complexity of these problems in the imperfectly shared randomness model. The technical highlight of this work is the lower bound that goes into the result showing the tightness of our general connection. This result builds on the intuition that communication with imperfectly shared randomness needs to be less sensitive to its random inputs than communication with perfectly shared randomness. The formal proof invokes results about the small-set expansion of the noisy hypercube and an invariance principle to convert this intuition to a proof, thus giving a new application domain for these fundamental results.
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.
Two parties wish to carry out certain distributed computational tasks, and they are given access to a source of correlated random bits. It allows the parties to act in a correlated manner, which can be quite useful. But what happens if the shared randomness is not perfect? In this work, we initiate the study of the power of different sources of shared randomness in communication complexity. This is done in the setting of simultaneous message passing (SMP) model of communication complexity, which is one of the most suitable models for studying the resource of shared randomness. Toward characterising the power of various sources of shared randomness, we introduce a measure for the quality of a source - we call it collision complexity. Our results show that the collision complexity tightly characterises the power of a (shared) randomness resource in the SMP model. Of independent interest is our demonstration that even the weakest sources of shared randomness can in some cases increase the power of SMP substantially: the equality function can be solved very efficiently with virtually any nontrivial shared randomness.
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