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

arXiv:1204.5884

Unicity Distance of Quantum Encryption Protocols

Chong Xiang, Yang Li

Published Apr 26, 2012• 0 citations
arXivHTMLPDF

Abstract

Shannon presented the concept `unicity distance' for describing the security of secret key encryption protocols against various ciphertext-only attacks. We develop this important concept of cryptanalysis into the quantum context, and find that there exist quantum encryption protocols reusing a short key have infinite unicity distance.

DOI
10.48550/arxiv.1204.5884

Related papers

Quantum unicity distance

Chong Xiang, Li Yang

We attempt to develop Shannon's concept of the unicity distance into the quantum context. Based on the definition of information-theoretic security for quantum cryptography, we present a quantum probabilistic encryption algorithm with bounded information-theoretic security, and then work out its quantum unicity distances. The result shows that quantum unicity distance is much bigger than the unicity distance of classical cryptography.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 10, 2012•1 citation

Shannon unicity distance, ε -secrecy criterion and Holevo information in quantum cryptography

Igor M. Arbekov, S. N. Molotkov

Abstract In this paper, we consider the relationship between C Shannon’s unicity distance, which is determined by the number of symbols of the encrypted message required to uniquely find the encryption key of the cryptosystem in information-theoretical sense, ε -secrecy criterion in quantum cryptography and Holevo information. A lower bound for the unicity distance for ε -secret keys in quantum cryptography is obtained. The relationship between unicity distance, ε -secrecy criterion in quantum cryptography and Holevo information is demonstrated.

Laser Physics Letters•Dec 21, 2020•0 citations

Design of Quantum Stream Cipher: Part-I -Lifting the Shannon Impossibility Theorem-

Osamu Hirota

This paper is dedicated to the late Professor H.P. Yuen in commemoration to our 50-year friendship. He invented the concept of quantum stream cipher. It is designed based on a completely different concept from conventional ciphers. The purpose of this cipher is to provide information-theoretic security of long data and secret key with short key length. It is based on hiding the ciphertext of mathematical cipher with quantum noise, achieving unprecedented information-theoretic security in any cipher. The protocol corresponds to randomizing the ciphertext by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. In this paper, we introduce some progress on the specific method to develop from the standard type to generalized quantum stream cipher (Quantum Enigma Cipher). There are two methods for generalization. One is the additional randomization method by the product cipher form and the other is the M-th order extended quantum coding method. Here we discuss the former. The results proved that it has sufficient information-theoretic security against known plaintext attack on key in comparison with quantum data locking. The latter method will be reported in Part II.

arXiv:2503.14872•Mar 19, 2025•0 citations

Quantum probabilistic encryption protocol based on conjugate coding

Li Yang, Chong Xiang, Bao Li

We present a quantum probabilistic encryption algorithm of private-key encryption scheme based on conjugate coding of qubit-string. Usually, probabilistic encryption algorithm is adopted in public-key encryption protocols. Here we consider its function of increasing the unicity distance of both classical and quantum private-key encryption scheme. The security of quantum probabilistic private-key encryption against two kinds of attacks is analyzed. Based on no-signalling postulate we show that the scheme can resist the attack to the key. The protocol's security against plaintext attack is also investigated under the concept of information-theoretic indistinguishability of encryption. Finally, we give a conjecture related with the Breidbart's attack.

arXiv:1204.6664•Apr 30, 2012•0 citations

On the Key-Uncertainty of Quantum Ciphers and the Computational Security of One-way Quantum Transmission

Ivan Damgaard, Thomas B. Pedersen, Louis Salvail

We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to obtain perfect secrecy with key length smaller then $n$. We study the question of whether there might still be fundamental differences between the case where quantum as opposed to classical communication is used. In this direction, we show that there exist ciphers with perfect security producing quantum ciphertext where, even if an adversary knows the plaintext and applies an optimal measurement on the ciphertext, his Shannon uncertainty about the key used is almost maximal. This is in contrast to the classical case where the adversary always learns $n$ bits of information on the key in a known plaintext attack. We also show that there is a limit to how different the classical and quantum cases can be: the most probable key, given matching plain- and ciphertexts, has the same probability in both the quantum and the classical cases. We suggest an application of our results in the case where only a short secret key is available and the message is much longer.

arXiv:quant-ph/0407066•Jul 8, 2004•1 citation

Quantum stream cipher and Quantum block cipher -The Era of 100 Gbit/sec real-time encryption-

Osamu Hirota

This paper is the part-II of the previous paper and introduces the world of Yuen's concept. In the theory of cryptology, the Shannon impossibility theorem states that the upper bound of the security of a plaintext against a ciphertext-only attack is the entropy of the secret key. At the same time, it gives the upper bound of the unicity distance against a known plaintext attack. Hence the development of a new symmetric key cipher requires finding a way to undo or lift this theorem. Such challenges have been attempted with quantum stream cipher and quantum data locking as block cipher. Both ciphers are designed by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. Thus, the origin of security of both ciphers come from the principle of keyed communication in quantum noise (KCQ) proposed by Yuen. In this paper, we explain and compare the principles and features of both cipher and assist to improve the quantum data locking scheme. Then we will introduce experimental research on quantum stream cipher towards commercialization, which has performance superior to conventional cipher.

arXiv:2504.17240•Apr 24, 2025•0 citations
Shannon presented the concept `unicity distance' for describing the security of secret key encryption protocols against various ciphertext-only attacks. We develop this important concept of cryptanalysis into the quantum context, and find that there exist quantum encryption protocols reusing a short key have infinite unicity distance.
Abstract In this paper, we consider the relationship between C Shannon’s unicity distance, which is determined by the number of symbols of the encrypted message required to uniquely find the encryption key of the cryptosystem in information-theoretical sense, ε -secrecy criterion in quantum cryptography and Holevo information. A lower bound for the unicity distance for ε -secret keys in quantum cryptography is obtained. The relationship between unicity distance, ε -secrecy criterion in quantum cryptography and Holevo information is demonstrated.
This paper is dedicated to the late Professor H.P. Yuen in commemoration to our 50-year friendship. He invented the concept of quantum stream cipher. It is designed based on a completely different concept from conventional ciphers. The purpose of this cipher is to provide information-theoretic security of long data and secret key with short key length. It is based on hiding the ciphertext of mathematical cipher with quantum noise, achieving unprecedented information-theoretic security in any cipher. The protocol corresponds to randomizing the ciphertext by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. In this paper, we introduce some progress on the specific method to develop from the standard type to generalized quantum stream cipher (Quantum Enigma Cipher). There are two methods for generalization. One is the additional randomization method by the product cipher form and the other is the M-th order extended quantum coding method. Here we discuss the former. The results proved that it has sufficient information-theoretic security against known plaintext attack on key in comparison with quantum data locking. The latter method will be reported in Part II.
We present a quantum probabilistic encryption algorithm of private-key encryption scheme based on conjugate coding of qubit-string. Usually, probabilistic encryption algorithm is adopted in public-key encryption protocols. Here we consider its function of increasing the unicity distance of both classical and quantum private-key encryption scheme. The security of quantum probabilistic private-key encryption against two kinds of attacks is analyzed. Based on no-signalling postulate we show that the scheme can resist the attack to the key. The protocol's security against plaintext attack is also investigated under the concept of information-theoretic indistinguishability of encryption. Finally, we give a conjecture related with the Breidbart's attack.
We consider the scenario where Alice wants to send a secret (classical) nnn-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to obtain perfect secrecy with key length smaller then nnn. We study the question of whether there might still be fundamental differences between the case where quantum as opposed to classical communication is used. In this direction, we show that there exist ciphers with perfect security producing quantum ciphertext where, even if an adversary knows the plaintext and applies an optimal measurement on the ciphertext, his Shannon uncertainty about the key used is almost maximal. This is in contrast to the classical case where the adversary always learns nnn bits of information on the key in a known plaintext attack. We also show that there is a limit to how different the classical and quantum cases can be: the most probable key, given matching plain- and ciphertexts, has the same probability in both the quantum and the classical cases. We suggest an application of our results in the case where only a short secret key is available and the message is much longer.
This paper is the part-II of the previous paper and introduces the world of Yuen's concept. In the theory of cryptology, the Shannon impossibility theorem states that the upper bound of the security of a plaintext against a ciphertext-only attack is the entropy of the secret key. At the same time, it gives the upper bound of the unicity distance against a known plaintext attack. Hence the development of a new symmetric key cipher requires finding a way to undo or lift this theorem. Such challenges have been attempted with quantum stream cipher and quantum data locking as block cipher. Both ciphers are designed by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. Thus, the origin of security of both ciphers come from the principle of keyed communication in quantum noise (KCQ) proposed by Yuen. In this paper, we explain and compare the principles and features of both cipher and assist to improve the quantum data locking scheme. Then we will introduce experimental research on quantum stream cipher towards commercialization, which has performance superior to conventional cipher.