We study the classical problem of privacy amplification, where two parties Alice and Bob share a weak secret X of min-entropy k, and wish to agree on secret key R of length m over a public communication channel completely controlled by a computationally unbounded attacker Eve. Despite being extensively studied in the literature, the problem of designing “optimal ” efficient privacy amplification protocols is still open, because there are several optimization goals. The first of them is (1) minimizing the entropy loss L = k−m (it is known that the optimal value for L = O(λ), where ε = 2−λ is the desired security of the protocol). Other important considerations include (2) minimizing the number of communication rounds, (3) maintaining security even after the secret key is used (this is called post-application robustness), and (4) ensuring that the protocol P does not leak some “useful information ” about the source X (this is called source privacy). Additionally, when dealing with a very long source X, as happens in the so-called Bounded Retrieval Model (BRM), extracting as long a key as possible is no longer the goal. Instead, the goals are (5) to touch as little of X as possible (for efficiency), and (6) to be able to run the protocol many times on the same X, extracting multiple secure keys.
We study the classical problem of privacy amplification, where two parties Alice and Bob share a weak secret X of min-entropy k, and wish to agree on secret key R of length m over a public communication channel completely controlled by a computationally unbounded attacker Eve. Despite being extensively studied in the literature, the problem of designing “optimal ” efficient privacy amplification protocols is still open, because there are several optimization goals. The first of them is (1) minimizing the entropy loss L = k−m (it is known that the optimal value for L = O(λ), where ε = 2−λ is the desired security of the protocol). Other important considerations include (2) minimizing the number of communication rounds, (3) maintaining security even after the secret key is used (this is called post-application robustness), and (4) ensuring that the protocol P does not leak some “useful information ” about the source X (this is called source privacy). Additionally, when dealing with a very long source X, as happens in the so-called Bounded Retrieval Model (BRM), extracting as long a key as possible is no longer the goal. Instead, the goals are (5) to touch as little of X as possible (for efficiency), and (6) to be able to run the protocol many times on the same X, extracting multiple secure keys.
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
We study the problem of privacy amplification with an active adversary in the information theoretic setting. In this setting, two parties Alice and Bob start out with a shared n-bit weak random string W, and try to agree on a secret random key R over a public channel fully controlled by an active and unbounded adversary. Typical assumptions are that these two parties have access to local private uniform random bits. In this paper we seek to minimize the requirements on the local randomness used by the two parties. We make two improvements over previous results. First, we reduce the number of random bits needed for each party to Θ(ℓ+logn), where ℓ is the security parameter, as long as W has min-entropy nΩ(1). Previously, the best known result needs to use Θ((ℓ+logn)logn) bits. Our result is also asymptotically optimal. Second, we generalize the problem to the case where the two parties only have local weak random sources instead of truly uniform random bits. We show that when each party has a local weak random source with min-entropy >n/2, there is an efficient privacy amplification protocol that works nearly as good as if the two parties have access to local uniform random bits. Next, in the case where each party only has a weak random source with arbitrarily linear min-entropy, we give an efficient privacy amplification protocol where we can achieve security parameter up to Ω(logk). Our results give the first protocols that achieve privacy amplification when each party only has access to a local weak random source.
Privacy Amplification, introduced by Bennett et. al in [1] and generalized in [2], is the technique of shrinking a partially secret string to a highly secret one by public discussion. More precisely, in the privacy amplification phase, two legitimate parties, Alice and Bob, who share a partially secret string S about an opponent Eve has partial information to extract, and a shorter but highly-secret string S' by communication through an public channel such that Eve’s information about S' is negligible, i.e., ε= ≥ −S' U uH ( / ) log S2 | '| holds with very high probability for some small ε > 0, where the random variable U summarizes Eve’s complete knowledge about S', and u is the particular value known to Eve [2]. Privacy amplification is an important step in both quantum cryptography and key theoretically secret information agreement [3].
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).
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.).
In this paper, we consider a situation such that legitimate parties, Alice and Bob, share an identical source to generate a secret key, and an eavesdropper, Eve, can access a correlated data that is stored in a storage with bounded size. Then, Alice and Bob want to extract a secret as long as possible. We show a privacy amplification theorem for this problem, i.e., we clarify the rate of key generation for given rate of Eve's storage. The problem can be regarded as a dual randomness generation problem of the Wyner-Ahlswede-Körner type source coding system, and the techniques used in the proof are exchanged, i.e., the so-called Markov lemma is used in the converse part, and the so-called image size characterization is used in the direct part.