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Advances in Mathematics of Communications

Quantum-safe identity-based broadcast encryption with provable security from multivariate cryptography

Ramprasad Sarkar, Mriganka Mandal, Sourav Mukhopadhyay

Published Apr 16, 2022• 4 citations
Publisher

Abstract

Identity-Based Broadcast Encryption ($\textsf{IBBE}$) is a novel concept that can efficiently and securely transmit confidential content to a group of authorized users without the traditional Public-Key Infrastructure ($\textsf{PKI}$). After carefully exploring these areas, we have observed that none of the existing works have adopted the quantum-attack resistant cryptographic machinery Multivariate Public-Key Cryptography ($\textsf{MPKC}$) with provable security. We are the first to design a quantum-safe $\textsf{IBBE}$ that solely relies on the $\textsf{MPKC}$ framework. Our proposed protocol has achieved $ \mathcal{O}(n) $-size communication bandwidth and $ {n^3}\cdot\mathcal{O}\big(\max\big\{N, {\delta}^4\big\}\big) $-size overhead storage without any security breach. Here, $ n $ is the number of variables for each multivariate polynomial, $ N $ represents the total number of system users, and $ \delta $ denotes a positive fixed-length. More positively, our design has achieved the adaptive INDistinguishable Chosen-Ciphertext Attack ($\textsf{IND-CCA}$) security in the Random Oracle Model ($\textsf{ROM}$) under the hardness of standard Multivariate Quadratic ($\textsf{MQ}$) problem. We emphasize that our system can also be immune against collusion attacks where several users come together to create an illicit decryption box.

DOI
10.3934/amc.2022026

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Identity-Based Broadcast Encryption (IBBE\textsf{IBBE}IBBE) is a novel concept that can efficiently and securely transmit confidential content to a group of authorized users without the traditional Public-Key Infrastructure (PKI\textsf{PKI}PKI). After carefully exploring these areas, we have observed that none of the existing works have adopted the quantum-attack resistant cryptographic machinery Multivariate Public-Key Cryptography (MPKC\textsf{MPKC}MPKC) with provable security. We are the first to design a quantum-safe IBBE\textsf{IBBE}IBBE that solely relies on the MPKC\textsf{MPKC}MPKC framework. Our proposed protocol has achieved O(n)\mathcal{O}(n)O(n)-size communication bandwidth and n3⋅O(max⁡{N,δ4}){n^3}\cdot\mathcal{O}\big(\max\big\{N, {\delta}^4\big\}\big)n3⋅O(max{N,δ4})-size overhead storage without any security breach. Here, nnn is the number of variables for each multivariate polynomial, NNN represents the total number of system users, and δ\deltaδ denotes a positive fixed-length. More positively, our design has achieved the adaptive INDistinguishable Chosen-Ciphertext Attack (IND-CCA\textsf{IND-CCA}IND-CCA) security in the Random Oracle Model (ROM\textsf{ROM}ROM) under the hardness of standard Multivariate Quadratic (MQ\textsf{MQ}MQ) problem. We emphasize that our system can also be immune against collusion attacks where several users come together to create an illicit decryption box.
When Kevin Ashton proposed the catchword 'Internet of Things' in 1999, little did he know that technology will become an indispensable part of human lives in just two decades. In short, the Internet of Things (IoT), is a catch-all terminology used to describe devices connected to the internet. These devices can share and receive data as well as provide instructions over a network. By design itself, the IoT system requires multicasting data and information to a set of designated devices, securely. Taking everything into account, Broadcast Encryption (BE) seems to be the natural choice to address the problem. BE allows an originator to broadcast ciphertexts to a big group of receivers in a well-organized and competent way, while ensuring that only designated people can decrypt the data. In this work, we put forward the first Identity-Based Broadcast Encryption scheme based on multivariate polynomials that achieves post-quantum security. Multivariate public key cryptosystems (MPKC), touted as one of the most promising post-quantum cryptography candidates, forms the foundation on which our scheme relies upon, which allows it to be very cost-effective and faster when implemented. In addition, it also provides resistance to collusion attack, and as a consequence our scheme can be utilized to form an efficient and robust IoT system.
The existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC), which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC) based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.
In this paper, we present an adaptively secure identity-based broadcast encryption system featuring constant sized ciphertext in the standard model. The size of the public key and the private keys of our system are both linear in the maximum number of receivers. In addition, our system is fully collusion-resistant and has stateless receivers. Compared with the state-of-the-art, our scheme is well optimized for the broadcast encryption. The computational complexity of decryption of our scheme depends only on the number of receivers, not the maximum number of receivers of the system. Technically, we employ dual system encryption technique and our proposal offers adaptive security under the general subgroup decisional assumption. Our scheme demonstrates that the adaptive security of the schemes utilizing a composite order group can be proven under the general subgroup decisional assumption, while many existing systems working in a composite order group are secure under multiple subgroup decision assumptions. We note that this finding is of an independent interest, which may be useful in other scenarios.
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.
The potential of the swift development of quantum computing is an extreme danger to the traditional cryptographic programs, and they are the foundation of the modern communication infrastructure. RSA and ECC are classical public-key algorithms that can be successfully quantum-attacked, in particular, Shor's algorithm can easily factor large integers and calculate discrete logarithms (Bernstein et al., 2017). The Post-Quantum Cryptography (PQC) has become the key to secure the next-generation communication networks against these threats, which relies on lattice problem-based algorithms, hash-based based algorithms, multivariate polynomials-based algorithms, and code-based cryptography. The paper examines the concepts, design, and implementation issues of PQC within current network infrastructure focusing on the secure transmission of data, authentication, and key management in the upcoming 5G and 6G networks. The approach will include the survey of existing algorithms of PQC, model the integration of protocol in the communication systems and test computational efficiency, security strength, and scalability. It has been found that PQC is suitable to protect network communications against quantum attackers, and achieves reasonable performance, though trade-offs can be seen in terms of computation overhead, key size, and latency. The research offers understanding to the researcher, network engineers and policy makers in order to adopt quantum resistant cryptography protocols to secure the confidentiality, integrity and authenticity of information in the future communication networks.