In Private Broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among the parties, and to send each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum (i.e. in Quantum Private Broadcasting (QPB)). In this work, we give three solutions to t-recipient QPB and compare them in terms of encryption key length. We examine independent encryption with the quantum one-time pad, unitary t-designs, and a new concept we define as symmetric unitary t-designs. Of these three, symmetric t-designs are the best choice when t is large, and these symmetric designs may be of independent interest beyond QPB.
In private broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among all parties, and to send to each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum [i.e., in quantum private broadcasting (QPB)]. In this work, we give three solutions to
t-recipient quantum private broadcasting (
t-QPB) and compare them in terms of key lengths. The first method is the independent encryption with the quantum one-time pad, which requires a key linear in the number of recipients,
t. We show that the key length can be decreased to be logarithmic in
t by using unitary
t-designs. Our main contribution is to show that this can be improved to a key length that is logarithmic in the dimension of the symmetric subspace, using a concept that we define of symmetric unitary
t-designs, which may be of independent interest.
A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.
Quantum cryptography-the application of quantum information processing and quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs. In this work we propose a non-OTP quantum encryption design utilizing a quantum state creation process to encrypt messages. As essentially a non-OTP quantum block cipher the method stands out against existing methods with the following features: 1. complex key-ciphertext relation (i.e. confusion) and complex plaintext-ciphertext relation (i.e. diffusion); 2. mode of operation design for practical encryption on multiple blocks. These features provide key reusability and protection against eavesdropping and standard cryptanalytic attacks.
Transmitting message in secret is getting more and more important nowadays. In the classical world, the message we sent run the risk of being intercepted by an attacker. As a result, we have to encrypt the message, or send it using a private channel. However, if we transmit messages via such methods, there are still some ways to decipher the information. For example, a powerful computer can be used to decrypt the message or try to steal the message from the private channel. In quantum cryptography, entanglement can be used as a secure channel to transmit information with absolute secrecy. From this perspective, quantum entanglement pairs are equivalent to a quantum private key. However, like the classical key distribution problem, the entanglement has to be shared before it can be used. In this paper, we propose a protocol that can be used to distribute such entanglement pairs securely, so they can be subsequently used to transmit messages with perfect security. The security of this protocol is based on the laws of nature, instead of unproven mathematical hard problems.
The 2-receiver broadcast channel with primary and third-party receivers is studied. The messages are classified into public, private and confidential. The messages in the public class are messages intended for both receivers. The private messages are intended for the primary receiver with no secrecy requirements imposed upon them. And the confidential messages are aimed exclusively to the primary receiver such that they must not be accessible to the other receiver. The encoder performs the necessary encryption by virtue of local randomness whose rate is assumed to be limited. We find an achievability region on the trade-off between the rates of the three messages and the source of randomness in the one-shot regime of a quantum broadcast channel.
Quantum private broadcasting (\textsf{QPB}) asks whether a quantum message can be encrypted once, broadcast to several recipients, and decrypted locally while the joint ciphertext reveals no plaintext information. Broadbent, González-Guillén, and Schuknecht showed that the full tensor-power space
Hd⊗t is generally unsuitable for \textsf{QPB}, identified
Symt(Hd) as a natural plaintext space, introduced symmetric unitary
t-designs, and asked which other subspaces support private broadcast. Using Schur-Weyl duality, we classify all subspaces
S⊆Hd⊗t on which the collective Haar twirl
T(t) is a replacement channel. Precisely, every Schur-Weyl block weight must be independent of the encoded state, and in each active block
Vλ⊗Wλ, the reduced state on the multiplicity space
Wλ must be fixed. This yields explicit two-block and general multiblock constructions and realizes the classification as the Schur-Weyl form of the Knill-Laflamme conditions for a complementary channel of
T(t). We also introduce a canonical reduction under deletion of a recipient and characterize privacy heredity, design heredity, and \textsf{QPB}-heredity for exact restricted designs. The symmetric tower is fully \textsf{QPB}-hereditary, whereas the antisymmetric tower is fully privacy-hereditary and is design-hereditary from level
s to
s−1 exactly when
s≤(d+1)/2. For canonical carriers in arbitrary Schur-Weyl blocks, hereditary reduction is governed by multiplicity-free branching along the Young graph and inclusion of the associated Peter-Weyl coefficient spaces.