Cryptography Based on Correlated Data: Foundations and Practice
Correlated data can be very useful in cryptography. For instance, if a uniformly random key is available to Alice and Bob, it can be used as an one time pad to transmit a message with perfect security. With more elaborate forms of correlated data, the parties can achieve even more complex cryptographic tasks, such as secure multiparty computation. This thesis explores (from both a theoretical and a practical point of view) the topic of cryptography based on correlated data. The first part considers physical assumptions that can be used to obtain simple forms of correlated data suitable for cryptographic purposes. We aim at constructing two important cryptographic primitives, namely commitments and oblivious transfer, and investigate the question of their existence as well as the theoretical limits of how efficiently the underlying resources can be used to construct them. For example, the existence of noisy channels between the parties allows unconditionally secure realizations of both primitives. As it turns out that noisy channels are valuable resources for cryptography, it becomes important to understand the optimal way in which these noisy channels can be used for implementing cryptographic tasks. Therefore, commitment and oblivious transfer capacities have been studied in the literature, which capture respectively the optimal way in which commitment and oblivious transfer can be realized using noisy channels. These capacities are cryptographic equivalents of Shannon's definition of channel capacity for the task of transmitting messages reliably over noisy channels. In the thesis we will further investigate the commitment and oblivious transfer capacity of some important channels. Another example is the so called bounded storage model, in which it is assumed that the parties have limited storage capacity (an assumption orthogonal to the restrictions on computational power that are normally made in cryptography based on complexity theory) In this model there is a public random source available to the parties during an initial transmission phase, but since the parties only have bounded storage they can only store parts of this random source and therefore they end up with correlated data that can be used subsequently to implement cryptographic primitives. It is known that both commitment and oblivious transfer can be implemented in the bounded storage model without errors. We present the first secure protocols for commitment and oblivious transfer in the more realistic bounded storage model with errors, in which the public random sources available to the parties are not exactly the same, but instead are only required to have a small