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An Identity-Based Signcryption on Lattice without Trapdoor

Brij Bhooshan Gupta, Dongxi Liu, Hongfei Zhu, Xianmin Wang, Yu Zhang

Published Apr 7, 2020• 24 citations
Publisher

Abstract

Identity-based signcryption schemes based on large integer factorization and discrete logarithm problems were considered to be insecure for the quantum computer attack. Thus, choosing a quantum-resist platform and constructing secure schemes based on new hard assumptions are challenges. In this paper, we propose an alternative scheme - an identity-based signcryption on lattice, which does not need to rely on a trapdoor. Meanwhile, our scheme achieves IND-CCA2 and sUF-CMA security, and it is also secure against the current quantum algorithm attacks based on LWE problem for lattice. Furthermore, we demonstrate that the newly proposed scheme has much shorter secret key size, and higher speeds in signcryption and unsigncryption stages, compared with some exiting identity-based signcryption schemes.

DOI
10.3217/jucs-025-03-0282

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Identity-based signcryption schemes based on large integer factorization and discrete logarithm problems were considered to be insecure for the quantum computer attack. Thus, choosing a quantum-resist platform and constructing secure schemes based on new hard assumptions are challenges. In this paper, we propose an alternative scheme - an identity-based signcryption on lattice, which does not need to rely on a trapdoor. Meanwhile, our scheme achieves IND-CCA2 and sUF-CMA security, and it is also secure against the current quantum algorithm attacks based on LWE problem for lattice. Furthermore, we demonstrate that the newly proposed scheme has much shorter secret key size, and higher speeds in signcryption and unsigncryption stages, compared with some exiting identity-based signcryption schemes.
Signcryption is a cryptographic primitive that can provide valid solution for authentication and confidentiality.In this paper, an efficient identity-based signcryption scheme from lattice was proposed.Our scheme based on Macciancio and Piekert's trapdoor generation method and delegate algorithm for lattice.Our main idea is that establish the identity-based system master key via trapdoor generation method for lattice, and extract user's key by trapdoor delegate algorithm.With the aid of random oracle, we prove that the proposed scheme has CCA security under the learning with errors (LWE) assumption and unforgeability against adaptive chosen messages attacks under the small integer solution (SIS) assumption.Comparison with signature-then-encryption approach shows that our scheme is efficient.
The existing lattice-based signcryption schemes are based on trapdoor generation algorithm and preimage sample algorithm. However, both algorithms are complex, require a lot of time to run, and affect the efficiency of latticed-based signcryption schemes deeply. To solve this problem, the first lattice-based signcryption scheme without trapdoor generation algorithm and preimage sample algorithm is proposed, with the help of the technique of lattice signatures without trapdoors and the associated signature compression technique, as well as the encryption method based on the learning with errors assumption. The scheme achieves indistinguishability against adaptive chosen ciphertext attacks under the learning with errors assumption. It also achieves existential unforgeability against adaptive chosen message attacks under the small integer solution assumption. The proposed scheme is not only quantum resistant, but also efficient.
Abstract Signcryption as a cryptographic primitive can carry out signature and encryption simultaneously at a remarkably reduced cost. Identity‐based cryptography is more convenient than public key infrastructure‐based cryptography in certificate management. As a result, identity‐based signcryption has been studied extensively, and many efficient and provably secure constructions have been proposed. However, most of these schemes are based on intractability assumptions from number theory, and these assumptions have been threatened by the booming quantum computation. Therefore, a recent trend in cryptography is to construct cryptosystems that are based on lattice‐based intractability assumptions because of their plausible features of quantum attack resistance. In this paper, several identity‐based signcryption schemes from lattice hardness assumptions are proposed. In the standard model, these schemes are indistinguishable againstinneradaptively chosen ciphertext attacks (IND‐CCA2) and strongly unforgeable againstinnerchosen message attacks. In our construction, it does not matter whether the original encryption scheme used to construct signcryption is deterministic or probabilistic; the resulted signcryption schemes can reach IND‐CCA2 security. To achieve this, we carefully combine three techniques—the identity‐based encryption from lattice due to Agrawal–Boneh–Boyen (EUROCRYPT 2010), the framework of lattice‐based short signature due to Boyen (Public Key Cryptography 2010), and the Canetti–Halevi–Katz (abbr. CHK) technique, with necessary and tailored optimization—for transforming an (ℓ+ 1)‐level indistinguishable under chosen plaintext attack secure hierarchical identity‐based encryption (HIBE) into anℓlevel IND‐CCA2 secure HIBE scheme. In addition, our security proof also contains a more efficient simulation tool that might have separate interest in cryptographic applications. Copyright © 2015 John Wiley & Sons, Ltd.
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.
So far, most ring signature schemes rely on hard number theory problems, such as discrete logarithm, bilinear pairings and so on. Unfortunately, the above underlying number theory problems will be solvable in the post quantum era. Lattice-based cryptography is a hotspot of research recently, due to its implementation simplicity and provable security reductions. When the hash-and-sign signature scheme was constructed based on the hardness of worst-case lattice problems, provably secure lattice-based ring signature schemes were finally constructed. However, the hash-and-sign ring signatures were rather inefficient (with megabytes long signatures). In this paper, we propose an alternative method for constructing lattice-based and identity-based ring signature scheme which does not use the hash-and-sign methodology. In the random oracle model, the proposed signature scheme based on the problem in general lattices is unforgeable and holds anonymity. Compared with the previous instantiations of the hash-and-sign ring signature schemes, the lengths of secret key, public key and signatures in the proposed scheme are much shorter. The signing algorithm is quite simple, with matrix-vector multiplications and rejection samplings.