Commitment is a key primitive which resides at the heart of several cryptographic protocols. Noisy channels can help realize information-theoretically secure commitment schemes, however, their imprecise statistical characterization can severely impair such schemes, especially their security guarantees. Keeping our focus on channel unreliability in this work, we study commitment over unreliable continuous alphabet channels called the Gaussian unfair noisy channels or Gaussian UNCs. We present the first results on the optimal throughput or commitment capacity of Gaussian UNCs. It is known that classical Gaussian channels have infinite commitment capacity, even under finite transmit power constraints. For unreliable Gaussian UNCs, we prove the surprising result that their commitment capacity may be finite, and in some cases, zero. When commitment is possible, we present achievable rate lower bounds by constructing positive - throughput protocols under given input power constraint, and (two-sided) channel elasticity at committer Alice and receiver Bob. Our achievability results establish an interesting fact - Gaussian UNCs with zero elasticity have infinite commitment capacity - which brings a completely new perspective to why classic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have infinite capacity. Finally, we precisely characterize the positive commitment capacity threshold for a Gaussian UNC in terms of the channel elasticity, when the transmit power tends to infinity.
Commitment is a key primitive which resides at the heart of several cryptographic protocols. Noisy channels can help realize information-theoretically secure commitment schemes, however, their imprecise statistical characterization can severely impair such schemes, especially their security guarantees. Keeping our focus on channel unreliability in this work, we study commitment over unreliable continuous alphabet channels called the Gaussian unfair noisy channels or Gaussian UNCs. We present the first results on the optimal throughput or commitment capacity of Gaussian UNCs. It is known that classical Gaussian channels have infinite commitment capacity, even under finite transmit power constraints. For unreliable Gaussian UNCs, we prove the surprising result that their commitment capacity may be finite, and in some cases, zero. When commitment is possible, we present achievable rate lower bounds by constructing positive - throughput protocols under given input power constraint, and (two-sided) channel elasticity at committer Alice and receiver Bob. Our achievability results establish an interesting fact - Gaussian UNCs with zero elasticity have infinite commitment capacity - which brings a completely new perspective to why classic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have infinite capacity. Finally, we precisely characterize the positive commitment capacity threshold for a Gaussian UNC in terms of the channel elasticity, when the transmit power tends to infinity.
Commitment is a key primitive which resides at the heart of several cryptographic protocols. Noisy channels can help realize information-theoretically secure commitment schemes; however, their imprecise statistical characterization can severely impair such schemes, especially their security guarantees. Keeping our focus on channel ‘unreliability’ in this work, we study commitment over unreliable continuous alphabet channels called the Gaussian unfair noisy channels or Gaussian UNCs.We present the first results on the optimal throughput or commitment capacity of Gaussian UNCs. It is known that ‘classical’ Gaussian channels have infinite commitment capacity, even under finite transmit power constraints. For ‘unreliable’ Gaussian UNCs, we prove the surprising result that their commitment capacity may be finite, and in some cases, zero. When commitment is possible, we present achievable rate lower bounds by constructing positive-throughput protocols under given input power constraint, and (two-sided) channel elasticity at committer Alice and receiver Bob. Our achievability results establish an interesting fact – Gaussian UNCs with zero elasticity have infinite commitment capacity. This result brings a completely new perspective as to why classic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have infinite capacity. Finally, we precisely characterize the positive commitment capacity threshold for a Gaussian UNC in terms of the channel elasticity, when the transmit power tends to infinity.
We study information-theoretically secure commitment over a class of unreliable noisy channels i.e., a Gaussian Unfair Noisy Channel (UNC). We provide an impossibility result for the positive rate commitment under the unconstrained input power i.e., P → ∞. In addition, we provide a commitment scheme based on a spherical error correcting code, hash function and randomness extractor, that achieves a positive (finite) rate for any finite power constraint P > 0. Moreover, together with an information-theoretic converse, we completely characterize the commitment capacity over Gaussian UNC when P → ∞.
In this work, we study commitment over a class of channels called reverse elastic channels (RECs). In the commitment problem, two mutually distrustful parties, say Alice and Bob, seek to commit on a bit string available to Alice. The parties interact via a commitment protocol comprising two phases, viz., commit phase followed by reveal phase. Alice commits to a string, and transmits it to Bob securely in a manner Bob cannot learn it until Alice chooses to reveal it; at the time of reveal, however, Bob can successfully detect if Alice cheats. It is well known that noisy channels are a promising resource to realize information-theoretically secure commitment; however, oftentimes, channel behaviour may be poorly characterized thereby limiting the commitment throughput and/or degrading the security guarantees. Particularly problematic is a scenario where dishonest parties can actively alter the channel characteristics. RECs are an interesting class of such unreliable channels, where essentially only a dishonest committer Alice can meaningfully alter the channel; RECs have attracted active recent interest. Our principal contribution is the REC commitment capacity characterization for all parameters; this proves a recent related conjecture. Apart from presenting an achievable scheme, a key result in our work is a tight converse which analyses a specific cheating strategy by Alice. The significance of RECs stems from the fact that along with elastic channels (ECs), where only a dishonest receiver Bob can alter the channel, these two channel models represent special cases of the more widely studied unfair noisy channels (UNCs). Interestingly, for a given set of parameters, our result shows that the REC commitment capacity is no larger than that for the ECs. Furthermore, similar to the ECs, RECs offer non-trivial commitment throughput for all meaningful parameters; this is in stark contrast to UNCs where the throughput may possibly be zero.
Commitment is an important cryptographic primitive. It is well known that noisy channels are a promising resource to realize commitment in aninformation-theoreticallysecure manner. However, oftentimes, channel behaviour may be poorly characterized thereby limiting the commitment throughput and/or degrading the security guarantees; a particularly problematic situation arises when a dishonest party, unbeknown to the honest one, maliciously alters the channel characteristics. Reverse elastic channels (RECs) are an interesting class of suchunreliablechannels where only a dishonestcommitter, say Alice, can maliciously alter the channel. RECs have attracted recent interest in the study of several cryptographic primitives. Our principal contribution is the REC commitment capacity characterization; this proves a recent related conjecture. A key result is our tight converse which analyses a specific cheating strategy by Alice. Along with elastic channels (ECs), where only a dishonestreceiverBob can alter the channel, RECs are also closely related to the classic unfair noisy channels (UNCs). In stark contrast to UNCs, both RECs and ECs always exhibit positive commitment throughput for all non-trivial channel parameters. Interestingly, our results show that channels with exclusiveone-sided elasticityfor dishonest parties, exhibit a fundamentalasymmetrywhere, a committer with one-sided elasticity has a significantly more debilitating effect on the commitment throughput than a similarly capable receiver.
We study commitments over unreliable compound noisy channels, where parties may know the compound channel state but lack control over that state. Commitment is one of the common building blocks for many cryptographic protocols which realize multi-party computational functionalities in a secure manner. A noisy channel, among others, is widely acknowledged as a promising resource for realizing information-theoretically secure cryptographic primitives, including commitment. However, unreliable noisy channels with poorly or imprecisely characterized statistical behaviour can severely degrade commitment guarantees. Our focus is unreliability on account of a compound channel state, albeit under public awareness of that state.Building on prior work, we seek to characterize the optimal commitment throughput or commitment capacity of compound binary symmetric channels when parties may be state-aware. State-awareness implies a passive and publicly known capability of precise channel knowledge (whether said party is honest or dishonest); however, state-awareness precludes any active and private channel state control as in, for instance, the classic unfair noisy channels (UNCs). We present new results on the commitment capacity under all possible configurations where individual parties may (or may not) be state-aware. An important takeaway of our work is the following: even a fairly weak capability of state-awareness (albeit when asymmetric and only at the committer-side) can degrade the commitment throughput to the same extent as under strongly capable parties that can privately control the compound state.
Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy channels have to be considered in the scenario where a cheating party has some degree of control over the channel characteristics. Damgård et al. (EUROCRYPT 1999) proposed a more realistic model where such level of control is permitted to an adversary, the so called unfair noisy channels, and proved that they can be used to obtain commitment and oblivious transfer protocols. Given that noisy channels are a precious resource for cryptographic purposes, one important question is determining the optimal rate in which they can be used. The commitment capacity has already been determined for the cases of discrete memoryless channels and Gaussian channels. In this work we address the problem of determining the commitment capacity of unfair noisy channels. We compute a single-letter characterization of the commitment capacity of unfair noisy channels. In the case where an adversary has no control over the channel (the fair case) our capacity reduces to the well-known capacity of a discrete memoryless binary symmetric channel.