In this paper without tailoring to any presumed condition on communication channel or any restriction on adversary's resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. A key extractor based on a sampler and a Rényi extractor derives secret keys with the required entropy from this source. A general cipher uses this key to ensure the required equivocation for the plaintext and to establish the first layer of secrecy. Using privacy amplification on top of this cipher based on inverse universal2hashing constitutes the second layer of secrecy for highly confidential message transmission with information leakage that is exponentially decreasing. We provide exponent analysis and optimization to minimize information leakage in terms of Eve's distinguishability based on L1norm distance from uniformity. The required key rate is characterized for different source entropies in order to guarantee the secrecy that is demanded in terms of secrecy exponent for the second layer and Eve's error rate for the first layer.
In this paper without tailoring to any presumed condition on communication channel or any restriction on adversary's resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. A key extractor based on a sampler and a Rényi extractor derives secret keys with the required entropy from this source. A general cipher uses this key to ensure the required equivocation for the plaintext and to establish the first layer of secrecy. Using privacy amplification on top of this cipher based on inverse universal2hashing constitutes the second layer of secrecy for highly confidential message transmission with information leakage that is exponentially decreasing. We provide exponent analysis and optimization to minimize information leakage in terms of Eve's distinguishability based on L1norm distance from uniformity. The required key rate is characterized for different source entropies in order to guarantee the secrecy that is demanded in terms of secrecy exponent for the second layer and Eve's error rate for the first layer.
In this paper without tailoring to any physical channel condition or any restriction on adversary's computational resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only advantage for legitimate users over eavesdropper is existence of a key source that is partially known by Eve. A key extractor based on a sampler and a Renyi extractor derives secret keys with the required entropy from this source. Encryption using this key with a general cipher maps Eve's uncertainty about the key to uncertainty about the plaintext that can also be interpreted as degradation in her channel. Using privacy amplification on top of this cipher based on inverse universal2 hashing results in information leakage with decreasing exponent that can be optimized to guarantee a higher level of secrecy.
We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett 's bound based on the Rényi entropy of order 2 because the bound obtained here uses the Rényi entropy of order 1+sfors∈ [0,1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi 's exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.
Motivated by the desirability of universal composability, we analyze in terms of L1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Rényi entropy of order 1+s for s ∈ [0,1], we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wiretap channel model and to secret key generation (distillation) by public discussion.
We study the problem of “privacy amplification”: key agreement between two parties who both know a weak secret w , such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about w , so we assume only that w has some entropy from Eve’s point of view. Thus, the goal of the protocol is to convert this nonuniform secret w into a uniformly distributed string R that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.). Because we make no computational assumptions, the entropy in R can come only from w . Thus, such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. The best previous results have entropy loss of Θ( κ 2 ), where κ is the security parameter, thus requiring the password to be very long even for small values of κ . In this work, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We achieve our improvement through a somewhat surprising application of error-correcting codes for the edit distance. The protocol can be extended to provide also “information reconciliation,” that is, to work even when the two parties have slightly different versions of w (e.g., when biometrics are involved).
In this dissertation we try to achieve secrecy enhancement in communications by resorting to both cryptographic and information theoretic secrecy tools and metrics. Our objective is to unify tools and measures from cryptography community with techniques and metrics from information theory community that are utilized to provide privacy and confidentiality in communication systems. For this purpose we adopt encryption techniques accompanied with privacy amplification tools in order to achieve secrecy goals that are determined based on information theoretic and cryptographic metrics. Every secrecy scheme relies on a certain advantage for legitimate users over adversaries viewed as an asymmetry in the system to deliver the required security for data transmission. In all of the proposed schemes in this dissertation, we resort to either inherently existing asymmetry in the system or proactively created advantage for legitimate users over a passive eavesdropper to further enhance secrecy of the communications. This advantage is manipulated by means of privacy amplification and encryption tools to achieve secrecy goals for the system evaluated based on information theoretic and cryptographic metrics. In our first work discussed in Chapter 2 and the third work explained in Chapter 4, we rely on a proactively established advantage for legitimate users based on eavesdropper’s lack of knowledge about a shared source of data. Unlike these works that assume an errorfree physical channel, in the second work discussed in Chapter 3 correlated erasure wiretap channel model is considered. This work relies on a passive and internally existing advantage for legitimate users that is built upon statistical and partial independence of eavesdropper’s channel errors from the errors in the main channel. We arrive at this secrecy advantage for legitimate users by exploitation of an authenticated but insecure feedback channel. From the perspective of the utilized tools, the first work discussed in Chapter 2 considers a specific scenario where secrecy enhancement of a particular block cipher called Data Encryption standard (DES) operating in cipher feedback mode (CFB) is studied. This secrecy enhancement is achieved by means of deliberate noise injection and wiretap channel encoding as a technique for privacy amplification against a resource constrained eavesdropper. Compared to the first work, the third work considers a more general framework in terms of both metrics and secrecy tools. This work studies secrecy enhancement of a general cipher based on universal hashing as a privacy amplification technique against an unbounded adversary. In this work, we have achieved the
We study the problem of “privacy amplification”: key agreement between two parties who both know a weak secret w, such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about w, so we assume only that w has some entropy from Eve’s point of view. Thus, the goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.). Because we make no computational assumptions, the entropy in R can come only from w. Thus such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. The best previous results have entropy loss of Θ(κ 2), where κ is the security parameter, thus requiring the password to be very long even for small values of κ. In this work, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up