Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Secure one-way interactive communication.

Abhinav Aggarwal, Varsha Dani, Thomas P. Hayes, Jared Saia

Published May 15, 2016• 5 citations
OpenAlex

Abstract

Alice and Bob are connected via a two-way binary channel. This paper describes an algorithm to enable Alice to send a message to Bob when 1) an oblivious adversary flips an unknown number of bits, $T$, on the channel; and 2) the message length $L$, and a desired error probability, $\epsilon$ are public knowledge. With probability at least $1-\epsilon$, our algorithm ensures that Bob receives the correct message, and that Alice and Bob terminate after sending a total of $L + O \left( T + \min \left(T+1,\frac{L}{\log L} \right) \log \left( \frac{L}{\epsilon} \right) \right)$ bits. When $\epsilon = \Omega\left( \frac{1}{poly(L)} \right)$ and $T$ is large, the number of bits sent is $L + O\left( T \right)$, which is asymptotically optimal, assuming a conjecture by Haeupler.

Related papers

Sending a Message with Unknown Noise

Abhinav Aggarwal, Varsha Dani, Thomas P. Hayes +1 more

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.

arXiv:1605.04486•International Conference on Distributed Computing and Networking (ICDCN)•Jan 4, 2018•5 citations

Covert Communication over Adversarially Jammed Channels

Qiaosheng Eric Zhang, Mayank Bakshi, Sidharth Jaggi

Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observation. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, reliable covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(log n)) even when Bob has a better channel than James. We present inner and outer bounds on the information-theoretically optimal throughputs as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. Further, these bounds match for a wide range of parameters of interest.

IEEE Information Theory Workshop (ITW)•Nov 1, 2018•17 citations

Perfectly Secure Message Transmission in Two Rounds

Gabriele Spini, Gilles Zémor

In the model that has become known as "Perfectly Secure Message Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely. In this paper, we focus on protocols that work in two transmission rounds for n= 2t+1. We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size O(n^2 log n) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of O(n log n) bits. Additionally, we show how our protocol can be adapted to a Network Coding context.

arXiv:1608.01909•Aug 5, 2016•1 citation

Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate

Nicolas Resch, Chen Yuan

In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob. In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).

Leibniz international proceedings in informatics•Jan 1, 2023•1 citation

Efficient Protocols for Perfectly Secure Message Transmission With Applications to Secure Network Coding

Gabriele Spini, Gilles Zémor

In the model that has become known as “Perfectly Secure Message Transmission” (PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve gains no information about the message while Bob is able to recover it completely. We focus on PSMT protocols that work in two transmission rounds for n = 2t + 1. We break from previous work by following a conceptually simpler blueprint. This has two consequences: first, we obtain improved efficiency, namely, we reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n3log n) to O(n2log n). Our solution also reaches optimal transmission rate for a secret of size O(n log n), thus answering the hitherto open question of attaining a threshold below O(n2log n) bits. Second, our construction can be adapted to more general scenarios relevant to Network Coding, where the adversary is given more power.

IEEE Transactions on Information Theory•May 13, 2020•4 citations

Public key encryption and encryption emulation attacks.

Denis Osin, Vladimir Shpilrain

Abstract. The main purpose of this paper is to show that public key encryption can be secure against the “encryption emulation ” attack (on the sender’s encryption) by computationally unbounded adversary, with one reservation: a legitimate receiver decrypts correctly with probability that can be made arbitrarily close to 1, but not equal to 1. 1. Summary of our claims We thought it would make sense to summarize, for the reader’s convenience, our two main claims in a separate section, before proceeding to a narrative introduction. In Section 3, we describe a public-key encryption protocol that allows Bob (the sender) to send secret information to Alice (the receiver), encrypted one bit at a time, so that: (1) Assuming that Eve (the adversary): (a) is computationally unbounded, (b) knows everything about Bob’s encryption algorithm and hardware, (c) does not know Alice’s algorithm for creating public key, then: she cannot decrypt any single bit correctly with probability> 3 4

•Jan 1, 2008•0 citations
Alice and Bob are connected via a two-way binary channel. This paper describes an algorithm to enable Alice to send a message to Bob when 1) an oblivious adversary flips an unknown number of bits, TTT, on the channel; and 2) the message length LLL, and a desired error probability, ϵ\epsilonϵ are public knowledge. With probability at least 1−ϵ1-\epsilon1−ϵ, our algorithm ensures that Bob receives the correct message, and that Alice and Bob terminate after sending a total of L+O(T+min⁡(T+1,Llog⁡L)log⁡(Lϵ))L + O \left( T + \min \left(T+1,\frac{L}{\log L} \right) \log \left( \frac{L}{\epsilon} \right) \right)L+O(T+min(T+1,logLL​)log(ϵL​)) bits. When ϵ=Ω(1poly(L))\epsilon = \Omega\left( \frac{1}{poly(L)} \right)ϵ=Ω(poly(L)1​) and TTT is large, the number of bits sent is L+O(T)L + O\left( T \right)L+O(T), which is asymptotically optimal, assuming a conjecture by Haeupler.
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.
Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observation. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, reliable covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Ω(log n)) even when Bob has a better channel than James. We present inner and outer bounds on the information-theoretically optimal throughputs as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. Further, these bounds match for a wide range of parameters of interest.
In the model that has become known as "Perfectly Secure Message Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely. In this paper, we focus on protocols that work in two transmission rounds for n= 2t+1. We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size O(n^2 log n) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of O(n log n) bits. Additionally, we show how our protocol can be adapted to a Network Coding context.
In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob. In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).
In the model that has become known as “Perfectly Secure Message Transmission” (PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve gains no information about the message while Bob is able to recover it completely. We focus on PSMT protocols that work in two transmission rounds for n = 2t + 1. We break from previous work by following a conceptually simpler blueprint. This has two consequences: first, we obtain improved efficiency, namely, we reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n3log n) to O(n2log n). Our solution also reaches optimal transmission rate for a secret of size O(n log n), thus answering the hitherto open question of attaining a threshold below O(n2log n) bits. Second, our construction can be adapted to more general scenarios relevant to Network Coding, where the adversary is given more power.
Abstract. The main purpose of this paper is to show that public key encryption can be secure against the “encryption emulation ” attack (on the sender’s encryption) by computationally unbounded adversary, with one reservation: a legitimate receiver decrypts correctly with probability that can be made arbitrarily close to 1, but not equal to 1. 1. Summary of our claims We thought it would make sense to summarize, for the reader’s convenience, our two main claims in a separate section, before proceeding to a narrative introduction. In Section 3, we describe a public-key encryption protocol that allows Bob (the sender) to send secret information to Alice (the receiver), encrypted one bit at a time, so that: (1) Assuming that Eve (the adversary): (a) is computationally unbounded, (b) knows everything about Bob’s encryption algorithm and hardware, (c) does not know Alice’s algorithm for creating public key, then: she cannot decrypt any single bit correctly with probability> 3 4