Executive Summary : | As the use of sophisticated distributed digital technologies becomes ubiquitous, there is a sharper-than-ever focus on the data security of the underlying protocols. Consider, for instance, internet or online gaming where security safeguards that prevent cheating and ensure that the sanctity of game play is maintained among mutually distrustful parties is of paramount importance. The diffused and virtual nature of the medium often precludes ‘audits’ by trusted third parties (or at least involves a non-trivial cost); as such, the server and the player, or two competing players, would prefer access to a functionality that replicates the same audit effect ‘cheaply’ and in a distributed manner. Classic cryptographic primitives like commitment, zero-knowledge proofs (ZKPs), oblivious transfer (OT), etc., hold the key to successfully realizing such secure multi-party computational (SMC) functionalities. It is well known that unconditionally-secure cryptographic functionalities cannot be realized through protocols engaging only in noiseless interactions. However, as Wyner’s classic work on wiretap channels showed, noisy communicating channels prove to be surprising facilitators. Several cryptographic functionalities, endowed with unconditional security, have been realized over the years. The security guarantees of cryptographic protocols built upon noisy channels come with one key caveat: the guarantees hold only if noise ‘behaves’ statistically as ‘expected’, else all bets are off. In other words, for an ‘unreliable’ noisy channel, one cannot naively depend on the guarantees when the statistical behaviour is uncertain. Often in practice a noisy channel may be available under incomplete/limited knowledge of its statistical behaviour. A much more damaging possibility also exists: what if the noise statistics are partially controlled by a dishonest party (when dishonest)? Instead of completely discarding the use of such ‘unreliable’ noisy channels for cryptography, one may ask the question: is it possible to ‘robustify’ existing commitment protocols to work with promised guarantees over such unreliable channels? The principal focus of this work is to understand the fundamental performance limits of different cryptographic functionalities built upon the (repeated) use of an unreliable Gaussian noisy channel. To the best of our knowledge, very little is known regarding the capacities of cryptographic primitives over classic unreliable Gaussian noisy channels. Real-world channels, like the wireless channel for instance, are continuous in nature, and hence, it is of value to understand the "cryptographic-potential" of such channels even when access to them comes with potential unreliability vis-a-vis their statistical behaviour, possibly with partial malicious control. Through the proposal, we seek to address this important question through a principled theoretical approach using ideas from modern cryptography, information theory and coding theory. |