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Asia Joint Conference on Information Security (AsiaJCIS)

Signcryption from NTRU Lattices Without Random Oracles

Ziyuan Liu, Raylin Tso, Yi‐Fan Tseng, Masahiro Mambo

Published Aug 1, 2019• 4 citations
Publisher

Abstract

A signcryption scheme provides both the function of digital signature and encryption scheme at the same time. Additionally, it has lower cost than traditional sign-then-encrypt or encrypt-then-sign approaches. Many useful applications have been found where confidentiality and non-repudiation are both required. On the other hand, with the current development of rapid quantum computing, currently schemes based on traditional numerical assumptions (e.g., decisional Diffie-Hellman assumption) are more likely to be attacked by quantum computers. Therefore, lattice-based signcryption schemes have been extensively studied in recent years. However, most of them are either inefficient or secure-proved under the assumptions of random oracles. Although some of them are proved in the standard model, they are not practical in low-cost devices. Since the security is based on "Learning with Errors" (LWE) or "Short Integer Solution" problems, it will result in extremely large size of keys. In this paper, we propose an efficient NTRU-based signcryption scheme, which is inspired from Pion et al.'s key encapsulation mechanism. We provide rigorous security proofs for the confidentiality and unforgeability under NTRU-based assumptions in the standard model. Compared with other schemes, we conclude that our scheme is more efficient and secure.

DOI
10.1109/asiajcis.2019.00009

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A signcryption scheme provides both the function of digital signature and encryption scheme at the same time. Additionally, it has lower cost than traditional sign-then-encrypt or encrypt-then-sign approaches. Many useful applications have been found where confidentiality and non-repudiation are both required. On the other hand, with the current development of rapid quantum computing, currently schemes based on traditional numerical assumptions (e.g., decisional Diffie-Hellman assumption) are more likely to be attacked by quantum computers. Therefore, lattice-based signcryption schemes have been extensively studied in recent years. However, most of them are either inefficient or secure-proved under the assumptions of random oracles. Although some of them are proved in the standard model, they are not practical in low-cost devices. Since the security is based on "Learning with Errors" (LWE) or "Short Integer Solution" problems, it will result in extremely large size of keys. In this paper, we propose an efficient NTRU-based signcryption scheme, which is inspired from Pion et al.'s key encapsulation mechanism. We provide rigorous security proofs for the confidentiality and unforgeability under NTRU-based assumptions in the standard model. Compared with other schemes, we conclude that our scheme is more efficient and secure.
Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.
Certificateless signcryption can simultaneously provide certificateless signature and encryption. In recent years, many certificateless signcryption schemes have been proposed. However, these schemes are based on traditional mathematical theory and not have the ability of resisting the quantum computing attacks. Up to now, lattice-based certificateless signature or encryption schemes have been proposed; however, these schemes only have one function and cannot fulfill two functions of certificateless signature and encryption at the same time. In consideration of this reason, in this article, a certificateless signcryption scheme from lattice (L-CLSS) is constructed. L-CLSS has three advantages. First, in the random oracle model, it is provably indistinguishable against adaptive ciphertext-chosen attacks under the intractability of the learning with errors (LWE) problem and unforgeable against adaptive message-chosen attacks under the hardness of small integer solution (SIS) problem. Second, comparison with the cryptographic algorithms under the difficulty of large integer decomposition, L-CLSS can resist the quantum computing attacks. Third, L-CLSS has higher computation efficiency and a lower communication cost than the existing schemes.
Signcryption is a cryptographic primitive that can perform digital signature and public encryption simultaneously at a significantly reduced cost. This advantage makes it highly useful in many applications. However, most existing signcryption schemes are seriously challenged by the booming of quantum computations. As an interesting stepping stone in the post-quantum cryptographic community, two lattice-based signcryption schemes were proposed recently. But both of them were merely proved to be secure in the random oracle models. Therefore, the main contribution of this paper is to propose a new lattice-based signcryption scheme that can be proved to be secure in the standard model.
Based on the NTRU trapdoor used in NIST's Falcon, a signcryption scheme following the sign-then-encrypt paradigm is constructed. The existing partitioning technique based on Waters hash over the lattice can not complete the security reduction in the standard model for the signature part due to the "partiality" of the pre-image generated with the NTRU trapdoor. To address this, a variant of Waters hash over small integers is proposed and, the probability of the successful reduction is analyzed. The resulting signcryption achieves existential unforgeability under the adaptive chosen-message attacks. By utilizing the uniqueness of the secret and the noise in an NTRU instance, the tag used in encryption is eliminated. Furthermore, a method to construct tamper-sensitive lattice public key encryption is proposed. This approach implants the ciphertext-sensitive information into the lattice public key encryption and binds it to the encrypted information. The malleability to the public key ciphertext triggers the change of the message-signature pair so that the IND-CCA2 security of the entire ciphertext can be guaranteed by the signature for the message. Thanks to the rational design and the efficiency of the NTRU trapdoor, the computational overhead of the proposed scheme is reduced significantly compared to the existing lattice-based signcryption scheme, reaching orders of magnitude improvement in efficiency. The experiment shows that the proposed scheme is efficient.
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.