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IET Information Security

Quantum‐resistant anonymous identity‐based encryption with trable identities

Ziyuan Liu, Yi‐Fan Tseng, Raylin Tso, Masahiro Mambo, Yu‐Chi Chen

Published Nov 23, 2021• 6 citations
Publisher

Abstract

Abstract Identity‐based encryption (IBE), introduced by Shamir, eliminates the need for public‐key infrastructure. The sender can simply encrypt a message by using the recipient's identity (such as email or IP address) without needing to look up the public key. In particular, when ciphertexts of an IBE do not reveal recipient's identity, this scheme is known as an anonymous IBE scheme. Recently, Blazy et al. (ARES '19) analysed the trade‐off between public safety and unconditional privacy in anonymous IBE and introduced a new notion that incorporates traceability into anonymous IBE, called anonymous IBE with traceable identities (AIBET). However, their construction is based on the discrete logarithm assumption, which is insecure in the quantum era. In this paper, we first formalize the consistency of tracing key of the AIBET scheme to ensure that a ciphertext cannot be traced with the use of wrong tracing keys. Subsequently, we present a generic formulation concept that can be used to transform structure‐specific lattice‐based anonymous IBE schemes into an AIBET. Finally, we apply this concept to Katsumata and Yamada's compact anonymous IBE scheme (Asiacrypt '16) to obtain the first quantum‐resistant AIBET scheme that is adaptively secure under the ring learning with errors assumption without random oracle.

DOI
10.1049/ise2.12049

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To prevent eavesdropping and tampering, network security protocols take advantage of asymmetric ciphers to establish session-specific shared keys with which further communication is encrypted using symmetric ciphers. Commonly used asymmetric algorithms include public key encryption, key exchange, and identity-based encryption (IBE). However, network security protocols based on classic identity-based encryption schemes do not have perfect forward secrecy. To solve this problem, we construct the first quantum IBE (QIBE) scheme based on the learning with errors (LWE) problem, which is also the first cryptographic scheme that applies the LWE problem to quantum encryption. We prove that our scheme is fully secure under the random oracle model and highlight the following advantages: (1) Network security protocols with our QIBE scheme provide perfect forward secrecy. The ciphertext is transmitted in the form of a quantum state unknown to the adversary and cannot be copied and stored. Thus, in network security protocols based on QIBE construction, the adversary does not have any previous quantum ciphertext to decrypt for obtaining the previous session key, even if the private identity key is threatened. (2) Classic key generation centre (KGC) systems can still be used in the QIBE scheme to generate and distribute private identity keys, reducing the cost when implementing this scheme. The classic KGC systems can be used because the master public and secret keys of our scheme are both in the form of classic bits. Finally, we present quantum circuits to implement this QIBE scheme and analyse its required quantum resources for given numbers of qubits, Hadamard gates, phase gates, T gates, and CNOT (controlled-NOT) gates. One of our main findings is that the quantum resources required by our scheme increase linearly with the number of plaintext bits to be encrypted.

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Abstract Identity‐based encryption (IBE), introduced by Shamir, eliminates the need for public‐key infrastructure. The sender can simply encrypt a message by using the recipient's identity (such as email or IP address) without needing to look up the public key. In particular, when ciphertexts of an IBE do not reveal recipient's identity, this scheme is known as an anonymous IBE scheme. Recently, Blazy et al. (ARES '19) analysed the trade‐off between public safety and unconditional privacy in anonymous IBE and introduced a new notion that incorporates traceability into anonymous IBE, called anonymous IBE with traceable identities (AIBET). However, their construction is based on the discrete logarithm assumption, which is insecure in the quantum era. In this paper, we first formalize the consistency of tracing key of the AIBET scheme to ensure that a ciphertext cannot be traced with the use of wrong tracing keys. Subsequently, we present a generic formulation concept that can be used to transform structure‐specific lattice‐based anonymous IBE schemes into an AIBET. Finally, we apply this concept to Katsumata and Yamada's compact anonymous IBE scheme (Asiacrypt '16) to obtain the first quantum‐resistant AIBET scheme that is adaptively secure under the ring learning with errors assumption without random oracle.
Anonymous Identity Based Encryption (AIBET) scheme allows a tracer to use the tracing key to reveal the recipient's identity from the ciphertext while keeping other data anonymous. This special feature makes AIBET a promising solution to distributed IoT data security. In this paper, we construct an efficient quantum-safe Hierarchical Identity-Based cryptosystem with Traceable Identities (AHIBET) with fully anonymous ciphertexts. We prove the security of the AHIBET scheme under the Learning with Errors (LWE) problem in the standard model.
An anonymous identity based encryption (anonymous IBE) scheme requires that an adversary can not determine the identity of the recipient from a ciphertext encrypted by the corresponding public key. The anonymity was formalized in previous works [1], [13], and this can be considered under chosen plaintext attack and adaptive chosen ciphertext attack, yielding two notions of security, ID-II-CPA and ID-II-CCA, where II denotes “indistinguishability of identities.” However, how to obtain an ID-II-CCA secure anonymous IBE in the random oracle model is still a challenging problem. We firstly propose a new notion of plaintext awareness in the two identities setting, called PATI. Secondly, we prove that the IBE scheme is ID-II-CCA secure if it is PATI secure. Finally, we propose the first generic conversion for anonymous IBE from ID-II-CPA to ID-II-CCA in the random oracle model.
Identity-based encryption is an important cryptographic system that is employed to ensure confidentiality of a message in communication. This article presents a provably secure identity based encryption based on post quantum security assumption. The security of the proposed encryption is based on the hard problem, namely Learning with Errors on integer lattices. This construction is anonymous and produces pseudo random ciphers. Both public-key size and ciphertext-size have been reduced in the proposed encryption as compared to those for other relevant schemes without compromising the security. Next, we incorporate the constructed identity based encryption (IBE) for Internet of Things (IoT) applications, where the IoT smart devices send securely the sensing data to their nearby gateway nodes(s) with the help of IBE and the gateway node(s) secure aggregate the data from the smart devices by decrypting the messages using the proposed IBE decryption. Later, the gateway nodes will securely send the aggregated data to the cloud server(s) and the Big data analytics is performed on the authenticated data using the Artificial Intelligence (AI)/Machine Learning (ML) algorithms for accurate and better predictions.
Revocable identity-based encryption (RIBE) is an extension of IBE that satisfies a key revocation mechanism to manage a number of users dynamically and efficiently. To resist quantum attacks, two adaptively secure lattice-based RIBE schemes are known in the (quantum) random oracle model ((Q)ROM). Wang et al.’s scheme that is secure in the ROM has large secret keys depending on the depth of a binary tree and its security reduction is not tight. Ma and Lin’s scheme that is secure in the QROM has large ciphertexts depending on the length of identities and is not anonymous. In this paper, we propose an adaptively secure lattice-based RIBE scheme that is secure in the QROM. Our scheme has compact parameters, where the ciphertext-size is smaller than Wang et al.’s scheme and the secret key size is the same as Ma and Lin’s scheme. Moreover, our scheme is anonymous and its security reduction is completely tight. We design the proposed scheme by modifying Ma–Lin’s scheme instantiated by the Gentry–Peikert–Vaikuntanathan (GPV) IBE. We can obtain the advantages of our scheme by making use of Katsumata et al.’s proof technique of the GPV IBE in the QROM.
Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users' public keys by using users' identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user's identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into l' segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when l' is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.
To prevent eavesdropping and tampering, network security protocols take advantage of asymmetric ciphers to establish session-specific shared keys with which further communication is encrypted using symmetric ciphers. Commonly used asymmetric algorithms include public key encryption, key exchange, and identity-based encryption (IBE). However, network security protocols based on classic identity-based encryption schemes do not have perfect forward secrecy. To solve this problem, we construct the first quantum IBE (QIBE) scheme based on the learning with errors (LWE) problem, which is also the first cryptographic scheme that applies the LWE problem to quantum encryption. We prove that our scheme is fully secure under the random oracle model and highlight the following advantages: (1) Network security protocols with our QIBE scheme provide perfect forward secrecy. The ciphertext is transmitted in the form of a quantum state unknown to the adversary and cannot be copied and stored. Thus, in network security protocols based on QIBE construction, the adversary does not have any previous quantum ciphertext to decrypt for obtaining the previous session key, even if the private identity key is threatened. (2) Classic key generation centre (KGC) systems can still be used in the QIBE scheme to generate and distribute private identity keys, reducing the cost when implementing this scheme. The classic KGC systems can be used because the master public and secret keys of our scheme are both in the form of classic bits. Finally, we present quantum circuits to implement this QIBE scheme and analyse its required quantum resources for given numbers of qubits, Hadamard gates, phase gates, T gates, and CNOT (controlled-NOT) gates. One of our main findings is that the quantum resources required by our scheme increase linearly with the number of plaintext bits to be encrypted.