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Journal of Internet Services and Information Security

Lattice Based Forward-Secure Identity Based Encryption Scheme with Shorter Ciphertext

Kunwar Singh, C. Pandurangan, A. K. Banerjee

Published Jan 1, 2012• 5 citations
OpenAlex

Abstract

In MIST 2012 conference Singh et al [21] presented lattice based forward-secure identity based encryption schemes based on LWE assumption in the random oracle model as well as in the standard model. In this paper we propose lattice based forward-secure identity based encryption scheme with shorter ciphertext in the random oracle model. We have reduced size of the ciphertext C from (m(i+ 2)+ 1)k Zqk to (m+ 1)k Zqk wherekZqk is number of bits required to represent an element of Zq.

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In MIST 2012 conference Singh et al [21] presented lattice based forward-secure identity based encryption schemes based on LWE assumption in the random oracle model as well as in the standard model. In this paper we propose lattice based forward-secure identity based encryption scheme with shorter ciphertext in the random oracle model. We have reduced size of the ciphertext C from (m(i+ 2)+ 1)k Zqk to (m+ 1)k Zqk wherekZqk is number of bits required to represent an element of Zq.
Motivated by an identity-based broadcast encryption scheme from lattice(1) and a forward-secure identity-based encryption scheme(2), we propose a forward-secure identity-based broadcast encryption scheme from lattice by adding the forward-security mechanism on broadcast encryption scheme. Our scheme satisfies the security requirements of both the broadcast encrypt ion scheme and forward-security scheme, that is, it is forward-secure for the secret keys used previously, and we prove that it is semantic secure based on LWE (Learning With Error)assumption(3) in the random oracle model. In addition, our construction is believed to be secure against quantum computer.
Recently,Identity-based Encryption(IBE) scheme based on lattices becomes one of the focuses of cryptographic research.But the IBE scheme based on standard lattice have large key size and high ciphertext expansion rate.So based on ideal lattices,this paper presents an efficient identity-based encryption scheme with small key size and low ciphertext expansion rate.The proposed scheme uses a method that combines the NTRU digital signature and the dual encryption based on ideal lattices.It is provably secure in the random oracle model.Analysis results show that the public key and the private key of key generation center contain one ring element and four ring elements respectively.The decryption key of each user is comprised of two ring elements.The ciphertext contains only two ring elements and the ciphertext expansion rate is a small constant.The encryption and decryption require four and two multiplications in the polynomial ring.Hence,the IBE scheme is more computationally efficient than that of traditional number theory based IBE scheme.
The paradigm of forward security provides a promising approach to deal with the key exposure problem as it can effectively minimize the damage caused by the key exposure. In this paper, we develop a new forward-secure identity-based encryption scheme without random oracles. We formally prove that the proposed scheme is secure against adaptive chosen-ciphertext attacks in the standard model. In the proposed scheme, the running time of the private key extraction and decryption algorithms and the sizes of the user's initial private key and the ciphertext are independent on the total number of time periods, and any other performance parameter has at most log-squared complexity in terms of the total number of time periods. Compared with the previous forward-secure identity-based encryption schemes, the proposed scheme enjoys obvious advantage in the overall performance. To the best of our knowledge, it is the first forward-secure identity-based encryption scheme that achieves direct chosen-ciphertext security in the standard model.
In traditional identity-based encryption schemes, security will be entirely lost once secret keys are exposed. However, with more and more use of mobile and unprotected devices, key exposure seems unavoidable. To deal with this problem, we newly propose a forward-secure identity-based public-key encryption scheme. In this primitive, the exposure of the secret key in one period doesn't affect the security of the ciphertext generated in previous periods. Any parameter in our scheme has at most log-squared complexity in terms of the total number of time periods. We also give the semantic security notions of forward-secure identity-based public-key encryption. The proposed scheme is proven semantically secure in the standard model. As far as we are concerned, it is the first forward-secure identity-based public-key encryption scheme without random oracles.
Blind signature (BS) plays one of key ingredients in electronic cash or electronic voting system. However, the key exposures bring out very serious problems in insecure mobile devices. Forward-secure blind signatures preserve the validity of past signatures and prevent a forger from forging past signatures even if current secret key has been compromised. In this paper, we propose the first forward-secure identity-based shorter blind signature scheme from lattices which can resist quantum attack, and prove that our scheme satisfies the security requirements of blindness, unforgeability, and forward secrecy in the random oracle model. Furthermore, we also extend our construction to a forward-secure identity-based shorter blind signature in the standard model.
Identity-based encryption with equality test (IBE-ET) allows the detection of whether two different ciphertexts encrypt the same plaintext without decryption within the conventional identity-based encryption (IBE) model. This property ensures the confidentiality of communication and reduces the storage overhead of ciphertexts in cryptosystems. However, IBE-ET schemes based on traditional assumptions, such as discrete logarithm and integer factoring, are vulnerable to quantum algorithm attacks, highlighting the importance of designing lattice-based IBE-ET schemes. To address this, researchers have proposed several lattice-based IBE-ET schemes that utilize outdated lattice IBE paradigms and are inefficient in terms of parameter size. In this work, we construct a new lattice-based IBE-ET scheme using the most compact lattice IBE framework known to date. Our new proposal significantly improves the parameters compared to previous constructions. Furthermore, we provide a security reduction in the random oracle model, along with corresponding parameter selection and the comparison between our scheme and known constructions. The results imply that our scheme is efficient.