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Non-interactive and Non-malleable Commitment Scheme Based on Lattice

Xia Feng

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

NTRU is a well-known public-key cryptosystem based on the difficulty of lattice reduction problems,and is mainly applied in public-key encryption and digital signature.This paper constructed a non-interactive and non-malleable commitment scheme,which relies the security on the intractable CVP on lattice,and the binding property of committer is satisfied.The validity of commitment is verified by hash function's collision resistance.Perturbing the plaintext with randomized mapping,plaintext will be in random distribution,and this scheme satisfies the hiding property of verifier and is non-malleable with respect to decommitment.This scheme has high efficiency as well as NTRU,and can resist channel eavesdropping attack,message replay attack and copying commitment attack.

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NTRU is a well-known public-key cryptosystem based on the difficulty of lattice reduction problems,and is mainly applied in public-key encryption and digital signature.This paper constructed a non-interactive and non-malleable commitment scheme,which relies the security on the intractable CVP on lattice,and the binding property of committer is satisfied.The validity of commitment is verified by hash function's collision resistance.Perturbing the plaintext with randomized mapping,plaintext will be in random distribution,and this scheme satisfies the hiding property of verifier and is non-malleable with respect to decommitment.This scheme has high efficiency as well as NTRU,and can resist channel eavesdropping attack,message replay attack and copying commitment attack.
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.
Abstract Shared key protocol is an important research issue in distributed networks security. The most existing shared key protocols are based on the discrete logarithm or large number decomposition problem. Those protocols’ cost is related to the network scale, and has the problem of high computation cost and message overhead. To solve the question, this paper proposes a shared key agreement protocol based on the lattice key mechanism (sNTRU). All network members share the key material via public channel, after execution those members has a shared encryption key and a number of different decryption keys satisfying the key independence. Compared with the traditional shared key agreement protocol based on DLP or RSA problem, this scheme only needs one round of interaction, and it is more efficient in calculation cost. In security aspect, its security proof can be reduced to the shortest vector difficulty problem, and it can resist the chosen plaintext attack, forwards security and backwards security are guaranteed.
In this paper we report a more secure and efficient encryption algorithm based on the NTRU cryptographic scheme.NTRU is lattice based scheme resistant to quantum computing, hence it falls under the class of post quantum cryptosystems.It is based on shortest vector problem (svp) [9].The main characteristics of the system are low memory and low computational requirements but it provides high level of security.We present modifications in the NTRU scheme for making it more secure and efficient particul arly for applications in wireless and constrained devices.In the original scheme, repetitions in the plaintext message lead to repetitions in the cipher text, which is a source of weakness in the system.To overcome this problem each byte of the input has been digested with different operations that produce different encrypted text even for repeated content of the Plain text message.The second modification is enhancing the public key scheme that makes this system more robust.These two modifications in the NTRU scheme makes it secure even for use in the Quantum Computing environment.
The identity-based encryption (IBE) scheme takes the user's identity as the public key, which avoids the disadvantages of digital certificate management. Lattice-based IBE scheme has the advantages of resistant to quantum attack, high efficiency and simple structure, and has become a research hotspot in the field of post-quantum information security. In this paper, an IBE scheme is designed based on NTRU lattice, and the hybrid sampling algorithm proposed by Ducas and Prest is used in the private key extraction algorithm of the scheme, which improves the implementation efficiency of the key generation algorithm while ensuring the security of the private key. The encryption and decryption algorithm of the IBE scheme is designed by using the framework structure of the encryption algorithm based on the LWE problem. Under the condition that the NTRU difficulty hypothesis and the LWE difficulty hypothesis hold simultaneously, the scheme is proved to have indistinguishability under chosen plaintext attack with identity-based encryption (IND-ID-CPA). The software implementation of the scheme and the efficiency under the specific parameter settings are given, and the experimental results show that the new scheme has higher encryption and decryption efficiency and shorter ciphertext length than the typical lattice IBE scheme.
The identity-based encryption (IBE) scheme takes the user's identity as the public key, which avoids the disadvantages of digital certificate management. Lattice-based IBE scheme has the advantages of resistant to quantum attack, high efficiency and simple structure, and has become a research hotspot in the field of post-quantum information security. In this paper, an IBE scheme is designed based on NTRU lattice, and the hybrid sampling algorithm proposed by Ducas and Prest is used in the private key extraction algorithm of the scheme, which improves the implementation efficiency of the key generation algorithm while ensuring the security of the private key. The encryption and decryption algorithm of the IBE scheme is designed by using the framework structure of the encryption algorithm based on the LWE problem. Under the condition that the NTRU difficulty hypothesis and the LWE difficulty hypothesis hold simultaneously, the scheme is proved to have indistinguishability under chosen plaintext attack with identity-based encryption (IND-ID-CPA). The software implementation of the scheme and the efficiency under the specific parameter settings are given, and the experimental results show that the new scheme has higher encryption and decryption efficiency and shorter ciphertext length than the typical lattice IBE scheme.
Authentication has been adopted in many areas, but most of these authentication schemes are built using traditional cryptographic primitives. It is widely believed that such primitives are not resistant to quantum algorithms. To deal with those quantum attacks, lattice-based cryptography was introduced by Ajtai in 1996. To the best of our knowledge, the existing lattice-based authentication schemes are based on a lattice-based public key encryption called NTRU: a ring-based public key cryptosystem, proposed by Hoffstein, Pipher, and Silverman in 1998. However, these schemes only support the case of a single user. In view of the aforementioned issue, we propose the first lattice-based group authentication scheme. The proposed scheme is secure against replay attacks and man-in-the-middle attacks. Moreover, compared with the existing lattice-based authentication schemes, ours provides the most efficient method to agree upon a session key among a group of users after mutual authentication.