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.
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.
Module lattices have many advantages over traditional number theory to construct security schemes. Especially, module lattice-based security schemes are potentially able to resist to quantum attacks which can break traditional number theory based ones. In this vein, this paper designed an extremely fast identity-based encryption (for short IBE) scheme from module lattices. Although the security proof has been conducted in the random oracle (for short RO) model, the keys and the ciphertext expansion rate of our scheme are comparatively small. Moreover, the main idea behind the scheme can be easily understood: combining the provably secure NTRU signature of Stehle and Steinfeld [19] with the CPA secure El Gamal-like encryption scheme proposed by Lyubashevsky, Peikert and Regev [15].
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.
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.
Identity-based cryptography is a type of public key cryptography with simple key management procedures. To our knowledge, till now, the existing identity-based cryptography based on NTRU is all over power-of-2 cyclotomic rings. Whether there is provably secure identity-based cryptography over more general fields is still open. In this paper, with the help of the results of collision resistance preimage sampleable functions (CRPSF) over cyclotomic fields, we give concrete constructions of provably secure identity-based encryption schemes (IBE) and identity-based signature schemes (IBS) based on NTRU over any cyclotomic field. Our IBE schemes are provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks, meanwhile, our IBS schemes are existentially unforgeable against adaptively chosen message and adaptively chosen identity attacks for any probabilistic polynomial time (PPT) adversary in the random oracle model. The securities of both schemes are based on the worst-case approximate shortest independent vectors problem (SIVPγ) over corresponding ideal lattices. The secret key size of our IBE (IBS) scheme is short—only one (two) ring element(s). The ciphertext (signature) is also short—only two (three) ring elements. Meanwhile, as the case of NTRUEncrypt, our IBE scheme could encrypt n bits in each encryption process. These properties may make our schemes have more advantages for some IoT applications over postquantum world in theory.
Under the standard model, an IND-sID-CPA secure IBE (Identity Based Encryption) scheme is proposed, which is based on an improved trapdoor generation function over ring and decisional R-LWE (ring-learning with errors) assumption, thus the hardness of recovering system master key can be reduced to solve the Ideal-SIS (small integer solution) problem, and the attack to the ciphertext is equivalent to solving the SVP (the shortest vector problem) in the worst case on ideal lattice to within a fixed poly( n ) factor. Moreover, the proposed scheme has advantages of high encryption and decryption speed and low encryption blowup factor compared with all known IBE scheme from the standard lattice under the standard model.