Decryption Failure Research Articles

New rank codes based encryption scheme using partial circulant matrices

We propose a new rank metric code based encryption based on the hard problem of rank syndrome decoding problem. We consider a generator matrix for Gabidulin codes in the form of k-partial circulant matrix. We distort the matrix G by adding it with another random k-partial circulant matrix and multiplying the product with a random circulant matrix. We also convert our encryption into an IND-CCA2 secured encryption scheme under assumption of Rank Syndrome Decoding problem. Our encryption has the smallest key size (of 4.306 KB) at 256-bit security level as compared to all the other rank code based encryption schemes with zero decryption failure and hidden structure for the decodable codes.

Порівняльний аналіз алгоритмів шифрування NTRUEncrypt та NTRUCipher

The asymmetric encryption scheme NTRUEncrypt proposed in 1996 and is one of the fastest post-quantum encryption schemes. It is included in the ANSI X9.98-2010 standard and is the prototype of cryptosystems’ wide class with the same name, which security is based on the difficulty of finding short vectors in some lattices. The cryptographic properties of NTRUEncrypt encryption scheme are sufficiently explored and its latest modifications are presented at the current NIST competition to standardize post-quantum asymmetric encryption, key encapsulation and digital signature.One of the most important problem in the field of cryptology is the design of symmetric encryption schemes, whose security, similarly to the asymmetric one, is based on the complexity of solving only one particular problem (for example, for RSA this is the problem of factorization of numbers). Due to this, in 2017 the symmetric encryption scheme NTRUCipher based on NTRUEncrypt was proposed. For it, a preliminary security analysis was performed and a parameter selection algorithm was proposed. At the same time, there are essential errors in the proof of CPA-se­curity of the encryption algorithm NTRUCipher. Moreover, the problem of comparative analysis of NTRUCipher and NTRUEncrypt encryption schemes is not solved for security and practicality.The purpose of this article is to conduct a comparative analysis of the abovementioned encryption schemes and to prove correctly the conditions that ensure the CPA-security of the NTRUCipher encryption scheme. A certain result is analytical bounds of decryption failure probability in NTRUCipher encryption scheme. This result is important for the proper parameters’ choice of the encryption scheme in its practical implementation. It is shown that the decryption failure probability in the NTRUCipher varies from to while the value of this probability for the NTRUEncrypt encryption scheme varies from to . In addition, the obtained bounds are not based on any heuristic assumptions.

A Secure and Verifiable Access Control Scheme for Big Data Storage in Clouds

Due to the complexity and volume, outsourcing ciphertexts to a cloud is deemed to be one of the most effective approaches for big data storage and access. Nevertheless, verifying the access legitimacy of a user and securely updating a ciphertext in the cloud based on a new access policy designated by the data owner are two critical challenges to make cloud-based big data storage practical and effective. Traditional approaches either completely ignore the issue of access policy update or delegate the update to a third party authority; but in practice, access policy update is important for enhancing security and dealing with the dynamism caused by user join and leave activities. In this paper, we propose a secure and verifiable access control scheme based on the NTRU cryptosystem for big data storage in clouds. We first propose a new NTRU decryption algorithm to overcome the decryption failures of the original NTRU, and then detail our scheme and analyze its correctness, security strengths, and computational efficiency. Our scheme allows the cloud server to efficiently update the ciphertext when a new access policy is specified by the data owner, who is also able to validate the update to counter against cheating behaviors of the cloud. It also enables (i) the data owner and eligible users to effectively verify the legitimacy of a user for accessing the data, and (ii) a user to validate the information provided by other users for correct plaintext recovery. Rigorous analysis indicates that our scheme can prevent eligible users from cheating and resist various attacks such as the collusion attack.

A Survey on Secure and Verifiable Access Control Scheme for Enormous Information Storage In Clouds

A secure and verifiable access control scheme for enormous information storage in cloud is based on open source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data .To overcome the decryption failures of the original LLL, the NTRU decryption algorithm is analysed. It allows to analyze it correctness, accuracy, security qualities and computational effectiveness. When a new entry permission is granted by the data users. It allows the cloud main system to update the cipher method details. It also able to update the counter against the hacking behavior on the cloud. It includes the data holder and eligible users who need to check the data user for accessing the data, the user check the content given by the next user for accurate plain text recovery. Through test shows, this scheme can prevent qualified user against hacking together with some other different raid such as scam attacks.

Bounds of decryption failure probability in NTRUEncrypt encryption scheme for a fixed key

The asymmetric encryption scheme NTRUEncrypt is one of the fastest post-quantum encryption schemes. To date, there are several versions of this encryption scheme but all of them have an unwanted feature that assumes decryption failure. Besides the inconvenience for authorized users, this feature leads to specific attacks on the encryption scheme and consequently reduces its security. The traditional approach to estimating the decryption failure probability assumes that this probability is determined by random selection of all elements used to form the encrypted message: the plain text, the key and so-called randomizing polynomial. At the same time, from a practical point of view, a more adequate indicator of the failure frequency is the set of probabilities calculated for each fixed value of the secret key. In this article, we get upper bounds for the decryption failure probability for a fixed key for one of the most extensive versions of the NTRUEncrypt encryption scheme. The first of two obtained bounds is approximate in the sense that, when it is proved, the replacement of the probability distribution of certain independent random variables sum by the limit (normal) distribution is carried out. The second obtained bound is due to Hoeffding's inequality and it is not based on any heuristic assumptions. In general, the obtained results provide more adequate information about the frequency of decryption failure for the considered version of NTRUEncrypt and can be used later in choosing the parameters of this encryption scheme to optimize it for security or practicality.

Efficient Encryption From Random Quasi-Cyclic Codes

We propose a framework for constructing efficient code-based encryption schemes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight. We depart somewhat from Alekhnovich’s approach and propose an encryption scheme based on the difficulty of decoding random quasi-cyclic codes. We propose two new cryptosystems instantiated within our framework: the hamming quasi-cyclic cryptosystem (HQC), based on the hamming metric, and the rank quasi-cyclic cryptosystem (RQC), based on the rank metric. We give a security proof, which reduces the indistinguishability under chosen plaintext attack security of our systems to a decision version of the well-known problem of decoding random families of quasi-cyclic codes for the hamming and rank metrics (the respective $\mathsf {QCSD}$ and $\mathsf {RQCSD}$ problems). We also provide an analysis of the decryption failure probability of our scheme in the Hamming metric case: for the rank metric there is no decryption failure. Our schemes benefit from a very fast decryption algorithm together with small key sizes of only a few thousand bits. The cryptosystems are very efficient for low encryption rates and are very well suited to key exchange and authentication. Asymptotically, for $\lambda $ the security parameter, the public key sizes are respectively in $\mathcal {O}({\lambda }^{2})$ for HQC and in $\mathcal {O}\left({\lambda ^{\frac {4}{3}}}\right)$ for RQC. Practical parameter compares well to the systems based on ring-learning parity with noise or the recent moderate density parity check codes system.

SPA on Rabin variant with public key $$N=p^2q$$ N = p 2 q

Variants of the Rabin cryptosystem are built to overcome the decryption failure problem encountered by the cryptosystem. In this paper, we perform a theoretical simple power analysis on one of the variants that operates its decryption procedure via modular multiplication where the moduli \(N_1=pq\) is kept secret while the moduli \(N=p^2q\) is public. The attack utilizes Legendre’s theorem of continued fraction to successfully retrieve the secret key of the cryptosystem. An example of the attack is also included in this paper.

BITRU: Binary Version of the NTRU Public Key Cryptosystem via Binary Algebra

New terms such as closest vector problem (CVP) and the shortest vector problem (SVP), which have been illustrated as NP-hard problem, emerged, leading to a new hope for designing public key cryptosystem based on certain lattice hardness. A new cryptosystem called NTRU is proven computationally efficient and it can be implemented with low cost. With these characteristics, NTRU possesses advantage over others system that rely on number-theoretical problem in a finite field (e.g. integer factorization problem or discrete logarithm problem). These advantages make NTRU a good choice for many applications. After the adaptation of NTRU, many attempts to generalize its algebraic structure have appeared. In this study, a new variant of the NTRU public key cryptosystem called BITRU is proposed. BITRU is based on a new algebraic structure used as an alternative to NTRU-mathematical structure called binary algebra. This commutative and associative. Establishing two public keys in the proposed system has distinguished it from NTRU and those similar to NTRU cryptosystems. This new structure helps to increase the security and complexity of BITRU. The clauses of BITRU, which include key generation, encryption, decryption, and decryption failure, are explained in details. Its suitability of the proposed system is proven and its security is demonstrated by comparing it with NTRU.

Simple Matrix – A Multivariate Public Key Cryptosystem (MPKC) for Encryption

Multivariate cryptography is one of the main candidates to guarantee the security of communication in the presence of quantum computers. While there exist a large number of secure and efficient multivariate signature schemes, the number of practical multivariate encryption schemes is somewhat limited. In this paper we present our results on creating a new multivariate encryption scheme, which is an extension of the original SimpleMatrix encryption scheme of PQCrypto 2013. Our scheme allows fast en- and decryption and resists all known attacks against multivariate cryptosystems. Furthermore, we present a new idea to solve the decryption failure problem of the original SimpleMatrix encryption scheme.

Efficient Broadcast Authentication using TSG Algorithm for WSN

Wireless Sensor Networks (WSN) is an emerging technology that has a wide range of applications including environment monitoring, medical systems, robotic exploration and smart places. In most of the sensor network sink node send broadcast information to all other sensor nodes. Broadcast authentication is an important security mechanism in a Wireless Sensor Network. . Base station broadcast the public key to all the sensor nodes. Broadcast message authenticated by using public key. If single key is used throughout the life time, adversaries can easily listen to the communication between the sensor nodes and the base station. To overcome this short term keys are introduced. In shortPK, the base stations broadcast a set of many short length encrypted keys for all the sensor nodes for every short term. The encrypted key contains message and next phase key. Due to long propagation of encrypted keys throughout the network causes propagation delay, decryption failure and packet loss. To overcome this problem we proposed Tree based Short term Group key Algorithm (TSGA) to reduce packet loss and enhance security mechanism by using short term group key in wireless sensor networks. The basic idea of the project is to use many short length group keys to provide the broadcast authentication in wireless sensor networks. The overall network is constructed as tree from base station and the parent and child nodes are established for different levels. Depends on level in tree network group will be formed. The encryption and decryption takes place within the group itself so the propagation delay of public key and packet loss will be reduced. Our simulation result shows that the packet loss is reduced and the data transmission also more secured than previous schemes.. General Terms Wireless sensor networks, security, broadcast, authentication, ECC.

NTRU over rings beyond $${\mathbb{Z}}$$

The NTRU cryptosystem is constructed on the base ring $${\mathbb{Z}}$$ . We give suitability conditions on rings to serve as alternate base rings. We present an example of an NTRU-like cryptosystem based on the Eisenstein integers $${\mathbb{Z}[\zeta_3]}$$ , which has a denser lattice structure than $${\mathbb{Z}}$$ for the same dimension, and which furthermore presents a more difficult lattice problem for lattice attacks, for the same level of decryption failure security.

Enhanced NTRU cryptosystem eliminating decryption failures

An enhaned NTRU cryptosystem eliminating decryption failures is proposed without using padding schemes and can resist the oracle model andchosen-ciphertext attacks. Because lattice reduction is the main threat to lattice-based cryptosystems, lattice reductionalgorithms are analyzed to evaluate the security of this scheme. Furthermore, the new scheme remains the advantage of high efficiency of original NTRU.