The Design of Alice
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This article explores the major design characteristics (both pedagogic as well as technical) that helped to shape Alice 2. It identifies several strengths of Alice as well as several weaknesses. An example problem is solved in Alice, covering many of the design characteristics. Finally, the effects and impacts of Alice instruction are presented, and the future directions of Alice development are provided.Keywords:
Strengths and weaknesses
Alice and Bob
Alice may wish to reliably send a message to Bob over a binary symmetric channel (BSC) while ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie observes a “significantly noisier” transmission than Bob does, he should be unable to estimate even whether Alice is transmitting or not. Even when Alice's (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over n channel uses Alice can transmit a message of length O(√n) bits to Bob, deniably from Willie. We also prove information-theoretically order-optimality of our results.
Alice and Bob
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Alice and Bob are connected via a two-way channel, and Alice wants to send a message of L bits to Bob. An adversary flips an arbitrary but finite number of bits, T, on the channel. This adversary knows our algorithm and Alice's message, but does not know any private random bits generated by Alice or Bob, nor the bits sent over the channel, except when these bits can be predicted by knowledge of Alice's message or our algorithm. We want Bob to receive Alice's message and for both players to terminate, with error probability at most δ > 0, where δ is a parameter known to both Alice and Bob. Unfortunately, the value T is unknown in advance to either Alice or Bob, and the value L is unknown in advance to Bob.
Alice and Bob
Value (mathematics)
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We present a scheme for direct and confidential communication between Alice and Bob, where there is no need for establishing a shared secret key first, and where the key used by Alice even will become known publicly. The communication is based on the exchange of single photons and each and every photon transmits one bit of Alice's message without revealing any information to a potential eavesdropper.
Alice and Bob
Secure Communication
Shared secret
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Citations (1)
In this paper, we study the problem of obtaining $1$-of-$2$ string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the $1$-of-$2$ string OT capacity for both $2$-privacy (when Eve can collude with either Alice or Bob) and $1$-privacy (when no such collusion is allowed). We generalize these capacity results to $1$-of-$N$ string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and $1$-of-$2$ string OT is desired between Alice and Bob with $1$-privacy. For this setup, we derive an upper and lower bound on the $1$-of-$2$ string OT capacity which match in one of two possible parameter regimes.
Alice and Bob
Erasure
Oblivious transfer
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Alice and Bob are playing a cooperative game in which Alice must devise a scheme to store n elements in an array from a universe U of size m. Her goal is to store in such a way that for every x∈U Bob can observe the values of two positions (dependent on x) in the array and determine whether x is in the array or not. Alice may share her storage scheme with Bob and they win if such an arrangement is made. The question is how large can the universe U be in terms of n so that Alice and Bob can win? In this paper we give upper and lower bounds on this question for general n and the special case when n=3. We also pose conjectures and further questions for research.
Alice and Bob
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If Alice must communicate with Bob over a channel shared with the adversarial Eve, then Bob must be able to validate the authenticity of the message. In particular we consider the model where Alice and Eve share a discrete memoryless multiple access channel with Bob, thus allowing simultaneous transmissions from Alice and Eve. By traditional random coding arguments, we demonstrate an inner bound on the rate at which Alice may transmit, while still granting Bob the ability to authenticate. Furthermore this is accomplished in spite of Alice and Bob lacking a pre-shared key, as well as allowing Eve prior knowledge of both the codebook Alice and Bob share and the messages Alice transmits.
Alice and Bob
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If Alice must communicate with Bob over a channel shared with the adversarial Eve, then Bob must be able to validate the authenticity of the message. In particular we consider the model where Alice and Eve share a discrete memoryless multiple access channel with Bob, thus allowing simultaneous transmissions from Alice and Eve. By traditional random coding arguments, we demonstrate an inner bound on the rate at which Alice may transmit, while still granting Bob the ability to authenticate. Furthermore this is accomplished in spite of Alice and Bob lacking a pre-shared key, as well as allowing Eve prior knowledge of both the codebook Alice and Bob share and the messages Alice transmits.
Alice and Bob
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If Alice must communicate with Bob over a channel shared with the adversarial Eve, then Bob must be able to validate the authenticity of the message. In particular we consider the model where Alice and Eve share a discrete memoryless multiple access channel with Bob, thus allowing simultaneous transmissions from Alice and Eve. By traditional random coding arguments, we demonstrate an inner bound on the rate at which Alice may transmit, while still granting Bob the ability to authenticate. Furthermore this is accomplished in spite of Alice and Bob lacking a pre-shared key, as well as allowing Eve prior knowledge of both the codebook Alice and Bob share and the messages Alice transmits.
Alice and Bob
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Prediction markets provide a unique and compelling way to sell and aggregate information, yet a good understanding of optimal strategies for agents participating in such markets remains elusive. To model this complex setting, prior work proposes a three stages game called the Alice Bob Alice (A-B-A) game - Alice participates in the market first, then Bob joins, and then Alice has a chance to participate again. While prior work has made progress in classifying the optimal strategy for certain interesting edge cases, it remained an open question to calculate Alice's best strategy in the A-B-A game for a general information structure.
In this paper, we analyze the A-B-A game for a general information structure and (1) show a revelation-principle style result: it is enough for Alice to use her private signal space as her announced signal space, that is, Alice cannot gain more by revealing her information more finely; (2) provide a FPTAS to compute the optimal information revelation strategy with additive error when Alice's information is a signal from a constant-sized set; (3) show that sometimes it is better for Alice to reveal partial information in the first stage even if Alice's information is a single binary bit.
Alice and Bob
Private information retrieval
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Citations (6)
Consider a game where a refereed a referee chooses (x,y) according to a publicly known distribution P_XY, sends x to Alice, and y to Bob. Without communicating with each other, Alice responds with a value "a" and Bob responds with a value "b". Alice and Bob jointly win if a publicly known predicate Q(x,y,a,b) holds. Let such a game be given and assume that the maximum probability that Alice and Bob can win is v<1. Raz (SIAM J. Comput. 27, 1998) shows that if the game is repeated n times in parallel, then the probability that Alice and Bob win all games simultaneously is at most v'^(n/log(s)), where s is the maximal number of possible responses from Alice and Bob in the initial game, and v' is a constant depending only on v. In this work, we simplify Raz's proof in various ways and thus shorten it significantly. Further we study the case where Alice and Bob are not restricted to local computations and can use any strategy which does not imply communication among them.
Alice and Bob
Repetition (rhetorical device)
Value (mathematics)
Constant (computer programming)
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Citations (91)