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Making An Empty Promise With A Quantum Computer

H. F. Chau, Hoi-Kwong Lo

Published Jan 1, 1997• 21 citations
OpenAlex

Abstract

Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bob's trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes.

Related papers

Making an Empty Promise with a Quantum Computer

H.F. Chau, Hoi-Kwong Lo

Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bob's trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes. PACS numbers: 03.65.Bz, 89.70.+c, 89.80.+h

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In the history of cryptography, quantum cryptography is a new and important chapter. It is a recent technique that can be used to ensure the confidentiality of information transmitted between two parties, usually called Alice and Bob, by exploiting the counterintuitive behavior of elementary particles such as photons. The physics of elementary particles is governed by the laws of quantum mechanics, which were discovered in the early twentieth century by talented physicists. Quantum mechanics fundamentally change the way we must see our world. At atomic scales, elementary particles do not have a precise location or speed, as we would intuitively expect. An observer who would want to get information on the particle's location would destroy information on its speed – and vice versa – as captured by the famous Heisenberg uncertainty principle . This is not a limitation due to the observer's technology but rather a fundamental limitation that no one can ever overcome. The uncertainty principle has long been considered as an inconvenient limitation, until recently, when positive applications were found. In the meantime, the mid-twentieth century was marked by the creation of a new discipline called information theory . Information theory is aimed at defining the concept of information and mathematically describing tasks such as communication, coding and encryption. Pioneered by famous scientists like Turing and von Neumann and formally laid down by Shannon, it answers two fundamental questions: what is the fundamental limit of data compression, and what is the highest possible transmission rate over a communication channel?

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Defeating classical bit commitments with a quantum computer

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Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bob's trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes.
Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bob's trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes. PACS numbers: 03.65.Bz, 89.70.+c, 89.80.+h
a cryptographic key, enabling Alice to scramble her messages in a way only Bob, knowing the same key, could unscramble. Privacy thus appeared to be generally unavailable to users lacking the means and foresight by which diplomats and spies share secret keys with their intended correspondents. Classical cryptography offered no purely mathematical solution to this "key distribution problem ". Meanwhile the only solution to the discreet communications problem appeared to be for Alice and Bob to confide their secrets in a trusted intermediary, who might later choose to blackmail them. All this was changed by PKC. The idea of PKC is for each user (eg Alice) to randomly choose a pair of mutually inverse transformations---a scrambling transformation and an unscrambling transformation---and to publish the directions for performing the former but not the latter. Anyone, including Bob, can then use Alice's public scrambling algorithm to prepare a message that only she can unscramble. Si
Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or perhaps even the function she is trying to compute. We describe a simple, efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. We also discuss techniques for Alice to detect whether Bob is honestly helping her or if he is introducing errors.
In the history of cryptography, quantum cryptography is a new and important chapter. It is a recent technique that can be used to ensure the confidentiality of information transmitted between two parties, usually called Alice and Bob, by exploiting the counterintuitive behavior of elementary particles such as photons. The physics of elementary particles is governed by the laws of quantum mechanics, which were discovered in the early twentieth century by talented physicists. Quantum mechanics fundamentally change the way we must see our world. At atomic scales, elementary particles do not have a precise location or speed, as we would intuitively expect. An observer who would want to get information on the particle's location would destroy information on its speed – and vice versa – as captured by the famous Heisenberg uncertainty principle . This is not a limitation due to the observer's technology but rather a fundamental limitation that no one can ever overcome. The uncertainty principle has long been considered as an inconvenient limitation, until recently, when positive applications were found. In the meantime, the mid-twentieth century was marked by the creation of a new discipline called information theory . Information theory is aimed at defining the concept of information and mathematically describing tasks such as communication, coding and encryption. Pioneered by famous scientists like Turing and von Neumann and formally laid down by Shannon, it answers two fundamental questions: what is the fundamental limit of data compression, and what is the highest possible transmission rate over a communication channel?
It has been recently shown by Mayers that no bit commitment scheme is secure if the participants have unlimited computational power and technology. However it was noticed that a secure protocol could be obtained by forcing the cheater to perform a measurement. Similar situations had been encountered previously in the design of Quantum Oblivious Transfer. The question is whether a classical bit commitment could be used for this specific purpose. We demonstrate that, surprisingly, classical unconditionally concealing bit commitments do not help.
Information Security is a buzz word today. Due to the emergence and recent developments of quantum computers, there is a possible threat on all present cryptographic methods. Researchers claim that once a powerful quantum computer comes into reality, the existing cryptosystems such as RSA, AES etc will be in trouble. So we must start developing post quantum or quantum secure cryptographic methods because changing the existing cryptosystems by quantum secure methods will be a very slow and rigorous task. So keeping this agenda in mind, in this paper, we discuss quantum computing, existing cryptosystems and possible post quantum methods in brief so that the readers of this paper can develop a clear idea about it for their future work.