Lower Bounds for Private Broadcast Encryption

Yan Zhu, Ruyun Yu, E Chen +1 more

Jianhong Zhang, Yuwei Xu, Zhipeng Chen

Identity-based Broadcast Encryption (IBBE) has the inherent key escrow problem that Private Key Generator (PKG) can fully determine the user's private key, which is an obstacle of the application of IBBE. The existing approaches to solving key escrow problem need the user to submit identity to multiple PKGs or interactions between PKG and the user in the private key extraction phase. For Point-to-Multipoint Identity-based Broadcast Encryption (P2MIBBE) that the computing capabilities of receiver are limited, these approaches are impracticable. We propose a new approach what we call Augmented Broadcaster Identity-based Broadcast Encryption (AB- IBBE). It requires neither multiple PKGs nor calculation of receiver in the private key extraction phase. We construct a universal scheme to realize AB-IBBE, such that any IND-ID-CPA secure IBBE scheme can be extended to an IND-ID-CPA secure AB-IBBE scheme.

Shangping Wang, 胡予濮, 孙瑾

Schuknecht, Christine

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.

Carlo Blundo, Antonella Cresti

Anne Broadbent, Carlos E. González-Guillén, Christine Schuknecht

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.