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arXiv:2506.05711

A symmetric LWE-based Multi-Recipient Cryptosystem

Saikat Gope, Srinivasan Krishnaswamy, Chayan Bhawal

Published Jun 6, 2025• 0 citations
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Abstract

This article describes a post-quantum multirecipient symmetric cryptosystem whose security is based on the hardness of the LWE problem. In this scheme a single sender encrypts multiple messages for multiple recipients generating a single ciphertext which is broadcast to the recipients. Each recipient decrypts the ciphertext with her secret key to recover the message intended for her. In this process, the recipient cannot efficiently extract any information about the other messages. This scheme is intended for messages like images and sound that can tolerate a small amount of noise. This article introduces the scheme and establishes its security based on the LWE problem. Further, an example is given to demonstrate the application of this scheme for encrypting multiple images.

DOI
10.48550/arxiv.2506.05711

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This article describes a post-quantum multirecipient symmetric cryptosystem whose security is based on the hardness of the LWE problem. In this scheme a single sender encrypts multiple messages for multiple recipients generating a single ciphertext which is broadcast to the recipients. Each recipient decrypts the ciphertext with her secret key to recover the message intended for her. In this process, the recipient cannot efficiently extract any information about the other messages. This scheme is intended for messages like images and sound that can tolerate a small amount of noise. This article introduces the scheme and establishes its security based on the LWE problem. Further, an example is given to demonstrate the application of this scheme for encrypting multiple images.
A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a corresponding set of independently chosen receiver public keys. The resulting ''multi-recipient ciphertext'' can be then be reduced (by any 3rd party) to a shorter, receiver specific, ''invidual ciphertext.'' Finally, to recover the i-th message in the batch from their indvidual ciphertext the i-th receiver only needs their own decryption key. A special case of mmPKE is multi-recipient PKE (mPKE) where all receivers are sent the same message. By treating (m)mPKE and their KEM counterparts as a stand-alone primitives we allow for more efficient constructions than trivially composing individual PKE/KEM instances. This is especially valuable in the post-quantum setting, where PKE/KEM ciphertexts and public keys tend to be far larger than their classic counterparts.
Signcryption is a public-key cryptographic primitive which combines the functions of public-key encryption and digital signature into a single logical step at low computational and communication costs. While multi-receiver signcryption is suited for a situation where a sender wants to send a signcrypted message to multiple receivers in a confidential and authenticated way. Due to this attractive property, recently, multi-receiver signcryption plays an important role in some practical applications such as virtual conference as well as authenticated mail transferring. In this paper, we present an efficient multi-receiver identity-based signcryption (MIBSC) scheme from lattice assumption which is believed to resist quantum computer attacks. The proposed scheme is provably secure in the random oracle model, which has the indistinguishability against chosen ciphertext attacks under the hardness of learning with errors (LWE), and existentially unforgeability against chosen message attacks under the small integer solution assumption (SIS). Moreover, we also compare our MIBSC scheme with existing schemes from performance efficiency and security, the result shows that our proposed scheme is more efficient and more secure. In particular, our scheme can be properly applied in the post-quantum communication environments.
Signcryption is a public-key cryptographic primitive which combines the functions of public-key encryption and digital signature into a single logical step at low computational and communication costs. While multi-receiver signcryption is suited for a situation where a sender wants to send a signcrypted message to multiple receivers in a confidential and authenticated way. Due to this attractive property, recently, multi-receiver signcryption plays an important role in some practical applications such as virtual conference as well as authenticated mail transferring. In this paper, we present an efficient multi-receiver identity-based signcryption (MIBSC) scheme from lattice assumption which is believed to resist quantum computer attacks. The proposed scheme is provably secure in the random oracle model, which has the indistinguishability against chosen ciphertext attacks under the hardness of learning with errors (LWE), and existentially unforgeability against chosen message attacks under the small integer solution assumption (SIS). Moreover, we also compare our MIBSC scheme with existing schemes from performance efficiency and security, the result shows that our proposed scheme is more efficient and more secure. In particular, our scheme can be properly applied in the post-quantum communication environments.
This article deals with designing an efficient post-quantum lattice based encryption scheme that relies on the multi-authority Ciphertext-Policy Attribute-Based Encryption (CP-ABE). The security of the proposed scheme is based on the hardness of the ring learning with errors (RLWE) problem. The construction of the proposed scheme is done using the Shamir's threshold secret sharing along with the Lagrange interpolation during the key generation and decryption processes in order to achieve the segmentation and restoration of private keys. A comparative study with the existing state of art schemes has been performed to show the feasibility and efficiency of the proposed scheme. Furthermore, experiments on the proposed scheme have been conducted to illustrate the computational time required during the key generation, encryption and decryption processes.
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.
Quantum-secure cryptography is a dynamic field due to its crucial role in various domains. This field aligns with the ongoing efforts in data security. Post-quantum encryption (PQE) aims to counter the threats posed by future quantum computers, highlighting the need for further improvement. Based on the learning with error (LWE) system, this paper introduces a novel asymmetric encryption technique that encrypts entire messages of n bits rather than just 1 bit. This technique offers several advantages including an additive homomorphic cryptosystem. The robustness of the proposed lightweight public key encryption method, which is based on a new version of LWE, ensures that private keys remain secure and that original data cannot be recovered by an attacker from the ciphertext. By improving encryption and decryption execution time—which achieve speeds of 0.0427 ms and 0.0320 ms, respectively—and decreasing ciphertext size to 708 bits for 128-bit security, the obtained results are very promising.