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Journal of Quantum Information Science

On Security of Quantum Cryptography by Probabilistic Analysis

Jianzhong Zhao

Published Jan 1, 2022• 0 citations
Publisher

Abstract

The existing quantum cryptography is a classical cryptography in nature and basically insecure because of its classical (conventional) bits, classical encryption algorithm and classical (public) channel. A novel topic about successful communication between the legitimate users, Alice and Bob, is discussed with probability of solution uniqueness of Bob’s decryption equation. We find, by probabilistic analysis, that success of communication between Alice and Bob is probabilistic with a probability bigger than 1/2. It is also novel to define insecurity of the quantum cryptography by probability of solution uniqueness of the search equation of Eve, the eavesdropper. The probability of Eve’s success to find the plain-text of Alice (and Bob) is greater than 1/2, and so the quantum cryptography is seriously insecure.

DOI
10.4236/jqis.2022.124008

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The existing quantum cryptography is a classical cryptography in nature and basically insecure because of its classical (conventional) bits, classical encryption algorithm and classical (public) channel. A novel topic about successful communication between the legitimate users, Alice and Bob, is discussed with probability of solution uniqueness of Bob’s decryption equation. We find, by probabilistic analysis, that success of communication between Alice and Bob is probabilistic with a probability bigger than 1/2. It is also novel to define insecurity of the quantum cryptography by probability of solution uniqueness of the search equation of Eve, the eavesdropper. The probability of Eve’s success to find the plain-text of Alice (and Bob) is greater than 1/2, and so the quantum cryptography is seriously insecure.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
We define a keyless communication as a message sent from one party (Alice) to another (Bob), such that the message is totally secure. This means that if a third party (Eve) is trying to eavesdrop, she will receive only random bits. She cannot understand the content of the message, even if she is able to intercept it in such away that Alice and Bob do not know it has been intercepted. For such a totally secure message, Alice and Bob do not need to set up any key beforehand, as it can add no further security. Starting with a system that we felt sure met such criteria, we were shocked to find out that it could be broken in at least two ways, by a semi-classical method and by a quantum method, such that Eve could read a message and Alice and Bob would not know it. Alice and Bob can counter such eavesdropping, but only by sending out test messages. This will enable them to ascertain that Eve is on the line, but then she can still occasionally pick up snippets of their conversation. In that case, in order to be totally secure, it is better to establish an unbreakable key beforehand. We postulate and give plausibility arguments that in general it is impossible to establish keyless communication between two parties.
Quantum cryptography aims at solving the everlasting problem of unconditional security in private communication. Every time we send personal information over a telecom channel a sophisticate algorithm protect our privacy making our data unintelligible to unauthorized receivers. These protocols resulted from the long history of cryptography. The security of modern cryptographic systems is guaranteed by complexity: the computational power that would be needed for gaining info on the code key largely exceed available one. Security of actual crypto systems is not “by principle” but “practical”. On the contrary, quantum technology promises to make possible to realize provably secure protocols. Quantum cryptology exploits paradigmatic aspects of quantum mechanics, like superposition principle and uncertainty relations. In this contribution, after a brief historical introduction, we aim at giving a survey on the physical principles underlying the quantum approach to cryptography. Then, we analyze a possible continuous variable protocol.
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4) m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
Quantum cryptography exploits the quantum mechanical properties of communication lines to enhance the security of the so-called key distribution. In this work, we explain the role played by quantum mechanics in cryptographic tasks and also investigate how secure is quantum cryptography. More importantly, we show by a simple security proof that for any state sent by the sender, the eavesdropper can only guess the output state with a probability that will allow her not to learn more than half of the classical Shannon information shared between the legitimate parties. This implies that with high probability, the shared key is secure.
In classical three-node communication scenario, two legitimate users (Alice and Bob) communicate over a fading channel and a third one (Eve) observes their transmission as an eavesdropper. Alice can transmit the signal with artificial noise to ensure security communication. The artificial noise degrades the performance of Eve, and it can be cancelled by Bob because of pre-knowing. In this paper, a new concept - equivalent security SNR is denned for clarity and simplicity. And we make analysis for the existence probability of positive security capacity and the security outage probability. Then we derive the optimal factor of power allocation for artificial noise and give the theoretical results when the eavesdropper's channel quality is very high. Theory analysis and simulation results show that by using artificial noise, the security capacity is increased greatly and the security of the physical layer communication is promised.