Information-Theoretic Cryptography: Partial Secrecy Problem

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Description

This lecture covers the Partial Secrecy Problem in Information-Theoretic Cryptography, focusing on topics such as secret communication, computational security, randomness extraction, and secret key capacity. It discusses the concept of partial secrecy, defining leakage measures between different sources, and explores examples like mutual information and information leakage. The lecture also delves into differential privacy, maximal leakage, and secrecy by design, highlighting motivations, advantages, and disadvantages of each concept.

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Related concepts (45)

Secrecy

Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret. Secrecy is often controversial, depending on the content or nature of the secret, the group or people keeping the secret, and the motivation for secrecy. Secrecy by government entities is often decried as excessive or in promotion of poor operation; excessive revelation of information on individuals can conflict with virtues of privacy and confidentiality.

Interaction information

The interaction information is a generalization of the mutual information for more than two variables. There are many names for interaction information, including amount of information, information correlation, co-information, and simply mutual information. Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables. Unlike the mutual information, the interaction information can be either positive or negative.

Conditional mutual information

In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third. For random variables , , and with support sets , and , we define the conditional mutual information as This may be written in terms of the expectation operator: . Thus is the expected (with respect to ) Kullback–Leibler divergence from the conditional joint distribution to the product of the conditional marginals and .

Shared secret

In cryptography, a shared secret is a piece of data, known only to the parties involved, in a secure communication. This usually refers to the key of a symmetric cryptosystem. The shared secret can be a password, a passphrase, a big number, or an array of randomly chosen bytes. The shared secret is either shared beforehand between the communicating parties, in which case it can also be called a pre-shared key, or it is created at the start of the communication session by using a key-agreement protocol, for instance using public-key cryptography such as Diffie–Hellman or using symmetric-key cryptography such as Kerberos.

Variation of information

In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality. Suppose we have two partitions and of a set into disjoint subsets, namely and .