In a one-way secret key agreement (OW-SKA) protocol in source model, Alice and Bob have private samples of two correlated variables X and Y that are partially leaked to Eve through the variable Z, and use a single message from Alice to Bob to obtain a shared secret key. We propose an efficient secure OW-SKA when the sent message over the public channel can be tampered with by an active adversary. Our construction uses a specially designed hash function that is used for reconciliation, as well as detection of tampering. In detection of tampering the function is a Message Authentication Code (MAC) that maintains its security when the key is partially leaked. We prove the secrecy of the established key and robustness of the protocol, and discuss our results.
In a one-way secret key agreement (OW-SKA) protocol in source model, Alice and Bob have private samples of two correlated variables X and Y that are partially leaked to Eve through the variable Z, and use a single message from Alice to Bob to obtain a shared secret key. We propose an efficient secure OW-SKA when the sent message over the public channel can be tampered with by an active adversary. Our construction uses a specially designed hash function that is used for reconciliation, as well as detection of tampering. In detection of tampering the function is a Message Authentication Code (MAC) that maintains its security when the key is partially leaked. We prove the secrecy of the established key and robustness of the protocol, and discuss our results.
Information-theoretic secret key agreement (SKA) protocols are a fundamental cryptographic primitive that are used to establish a shared secret key between two or more parties. In a two-party SKA in source model, Alice and Bob have samples of two correlated variables that are partially leaked to Eve, and their goal is to establish a shared secret key by communicating over a reliable public channel. Eve must have no information about the established key. In this paper, we study the problem of one-way secret key agreement where the key is established by Alice sending a public message to Bob. We propose a one-way SKA (OW-SKA) protocol, prove that it achieves the one-way secret key capacity, and use it to derive a finite blocklength bound on the achievable secret key length. We compare our results with existing OW-SKAs and show the protocol achieves a longer key, and has a combination of desirable properties.
Secret key agreement (SKA) is a basic cryptographic primitive that establishes a shared secret key between parties. In the two-party source model of SKA, Alice and Bob want to share a secret key. They each have private samples of two correlated variables that are partially leaked to Eve. In a one-way SKA protocol, Alice sends a single message to Bob over a public channel, allowing the two parties to calculate a shared secret key that will be essentially unknown to Eve. The length of the key is a function of the number of samplesn. In this paper, we prove a tight second-order asymptotic approximation of the key length of one-way SKA protocols, and propose an approach to construct a computationally efficient one-way SKA protocol with near-optimum finite key length. We compare our results with related work, and discuss future research directions.
Information-theoretic secret key agreement (SKA) protocols are a fundamental cryptographic primitive that are used to establish a shared secret key between two or more parties. In a two-party SKA in source model, Alice and Bob have samples of two correlated variables, that are partially leaked to Eve, and their goal is to establish a shared secret key by communicating over a reliable public channel. Eve must have no information about the established key. In this paper, we study the problem of one-message secret key agreement where the key is established by Alice sending a single message to Bob. We propose a one-message SKA (OM-SKA) protocol, prove that it achieves the one-way secret key capacity, and derive finite blocklength approximations of the achievable secret key length. We compare our results with existing OM-SKAs and show the protocol has a unique combination of desirable properties.
This is the third part of a three-part paper on se- cret-key agreement secure against active adversaries. Here, we con- sider the special case where the legitimate partners already share a mutual string which might, however, be partially known to the adversary. The problem of generating a key in this case has been well studied in the passive-adversary model—for instance, in the context of quantum key agreement—under the name of privacy amplification. We consider the same problem with respect to an ac- tive adversary and propose two protocols, one based on universal hashing and one based on extractors, allowing for privacy ampli- fication secure against an adversary whose knowledge about the initial partially string is limited to one third of the length of this string. Our results are based on novel techniques for au- thentication secure even against adversaries knowing a substantial amount of the secret key. information about . From Eve's point of view, the length of can in this case be roughly equal to the Renyi entropy of . In this paper, we investigate the same problem under the as- sumption that the communication between Alice and Bob is not authenticated. Note that, in contrast to the model where many independent repetitions of the involved random variables are given (15), the same piece of information must be used here both for authentication and as the input for privacy amplifica- tion. Two problems that arise in this context are authentication with an only partially key, and the fact that this authenti- cation leaks information about , hence potentially also about , to the adversary. We show that for our purpose, a new, inter- active, authentication method is better than one-way authentica- tion by strongly universal hashing, and that so-called extractors, requiring fewer random bits (i.e., shorter messages to be com- municated), are a better technique for privacy amplification than
Key agreement (KA) is a fundamental cryptographic primitive. Assuming that Alice and Bob do not have any prior shared correlation, it has been proved that key agreement with security against a computationally unbounded adversary is impossible if communication is either over a fully public channel, or the channel is fully controlled by the adversary. In this paper we consider a setting where communication is over a partially corrupted channel, and there is no prior shared correlation. We formalize security and reliability of key agreement protocols in this setting, derive bounds on the rate of secret key agreement, and give constructions that achieve the respective bounds. Our results show that secret key agreement, and hence secret message transmission, is possible, as long as a small fraction of the transmitted symbols in each round remain untouched by the adversary. Our results can be extended to key agreement between nodes in a network, when the two nodes are connected by a set of disjoint paths, and in each round a subset of paths is eavesdropped and another subset (possibly with overlap) is tampered with. We relate our results to previous works, and discuss future directions.
We study the question of basing symmetric key cryptography on weak secrets. In this setting, Alice and Bob share an n-bit secret W, which might not be uniformly random, but the adversary has at least k bits of uncertainty about it (formalized using conditional min-entropy). Since standard symmetric-key primitives require uniformly random secret keys, we would like to construct an authenticated key agreement protocol in which Alice and Bob use W to agree on a nearly uniform key R, by communicating over a public channel controlled by an active adversary Eve. We study this question in the information theoretic setting where the attacker is computationally unbounded. We show that single-round (i.e. one message) protocols do not work when k ≤ n/2, and require poor parameters even when n/2<k<<n.