NTRU Public Key Cryptosystem Research Articles

Proposed Development of NTRU Public Key Cryptosystem

As life progresses and develops, cryptography has become an indispensable science. The development of this science has given flexibility and security in exchanging information and data of various kinds by making it difficult for unauthorized persons to access them. In this paper, we proposed a new NTRU-like encryption scheme using a different mathematical structure for the public key, as well as for text encryption and decryption to have more resistance to attacks, which makes this method suitable for many applications.

Comparison and intelligent analysis of NTRU and ETRU signature algorithms for public key digital signature

Three American mathematicians made the NTRU public-key cryptosystem in 1996, it has a fast speed, small footprint, and also it is easy to produce key advantages. The NTRU signature algorithm is based on an integer base, the performance of the signature algorithm will change when the integer base becomes other bases. Based on the definition of “high-dimensional density” of lattice signatures, this paper chooses the ETRU signature algorithm formed by replacing the integer base with the Eisenstein integer base as a representative, and analyzes and compares the performance, security of NTRU and ETRU signature algorithms, SVP and CVP and other difficult issues, the speed of signature and verification, and the consumption of resources occupied by the algorithm.

Novel public-key cryptosystems based on NTRU and algebraic structure of group rings

In this paper, we propose two novel public-key cryptosystems by combining the well-known NTRU public-key cryptosystem with the algebraic structure of group rings. We discuss the security analysis of these cryptosystems and show their enhanced security in comparison to the NTRU public-key cryptosystem. To be more precise, we show that the security of our novel cryptosystems is based on solving some recently discovered hard problems, for instance, Discrete logarithm problems in group rings, Inverse computation problems etc. We also discuss two examples to show the encryption and decryption procedure for both the cryptosystems.

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks.

Wireless sensor networks (WSNs) are the core of the Internet of Things and require cryptographic protection. Cryptographic methods for WSN should be fast and consume low power as these networks rely on battery-powered devices and microcontrollers. NTRU, the fastest and secure public key cryptosystem, uses high degree, N, polynomials and is susceptible to the lattice basis reduction attack (LBRA). Congruential public key cryptosystem (CPKC), proposed by the NTRU authors, works on integers modulo q and is easily attackable by LBRA since it uses small numbers for the sake of the correct decryption. Herein, RCPKC, a random congruential public key cryptosystem working on degree polynomials modulo q, is proposed, such that the norm of a two-dimensional vector formed by its private key is greater than . RCPKC works as NTRU, and it is a secure version of insecure CPKC. RCPKC specifies a range from which the random numbers shall be selected, and it provides correct decryption for valid users and incorrect decryption for an attacker using LBRA by Gaussian lattice reduction. RCPKC asymmetric encryption padding (RAEP), similar to its NTRU analog, NAEP, is IND-CCA2 secure. Due to the use of big numbers instead of high degree polynomials, RCPKC is about 27 times faster in encryption and decryption than NTRU. Furthermore, RCPKC is more than three times faster than the most effective known NTRU variant, BQTRU. Compared to NTRU, RCPKC reduces energy consumption at least thirty times, which allows increasing the life-time of unattended WSNs more than thirty times.

A new NTRU cryptosystem outperforms three highly secured NTRU-analog systems through an innovational algebraic structure

NTRU public key cryptosystem relies on computations that are efficiently performed with insignificant storage and time complexity. Many researchers were motivated to improve NTRU performance by replacing the original polynomial ring and mathematical structure with new modified algebraic structures, such as QTRU, OTRU, BITRU, and many others. In this work, a new NTRU-analog cryptosystem called QOBTRU is proposed based on a newly designed algebraic structure called Carternion algebra. QOBTRU is at least quadratic higher than the original NTRU in terms of computational and space complexity. It is intended to have an alternative security and performance attribute upon three chosen highly performed multidimensional NTRU-like cryptosystems, which are QTRU, OTRU, and BITRU. Their comparison with QOBTRU highlighted its strength over them. Some statistical and security analysis is performed to demonstrate its efficiency.

Dynamic keys generation for internet of things

<span>In several aspects, interest in IoT has become considerable by researchers and academics in recent years. Data security becomes one of the important challenges facing development of IoT environment. Many algorithms were proposed to secure the IoT applications. The traditional public key cryptographic are inappropriate because it requires high computational. Therefore, lattice-based public-key cryptosystem (LB-PKC) is a favorable technique for IoT security. NTRU is one of a LB-PKC that based on truncated polynomial ring, it has good features, which make it to be an effective alternative to the RSA and ECC algorithms. But, there is LLL algorithm can success to attack it under certain conditions. This paper proposes modifications to NTRU public key cryptosystem to be secure against the lattice-based attack by using LLL algorithm, as well as a method for generating a new keys sequence dynamically. The results from simulations show that the performance of these modifications gives more secure from NTRU. </span>

On the distribution of Low Hamming Weight products

Jeffrey Hoffstein et al. (Discrete Appl. Math. 130:37–49, 2003) introduced the Low Hamming Weight products (LHWP) X=x_{1}x_{2}x_{3} as random exponent of elements in a group or a ring to improve the operational efficiency, where each x_{i} has Hamming Weight operatorname{Ham}(x_{i}) in its binary representation. The random power or multiple be used in many cryptographic constructions, such as Diffie–Hellman key exchange, elliptic curve ElGamal variants, and NTRU public-key cryptosystem. But their randomness is just a conjecture, which lacks of the security proof. The main purpose of this paper is using the analytic method and the properties of the character sums to prove the distribution of the Hamming weight products, which is related to their pseudorandomness and unpredictability. It is important to research the application of LHWP in cryptographic constructions. Our theory shows that the LHWP are exponentially close to the uniform distribution, namely, an attack on algorithm (Hoffstein et al. in Discrete Appl. Math. 130:37–49, 2003) needs polynomial time to reach exponentially close probabilities of success.

A MULTI-DIMENSIONAL ALGEBRA FOR DESIGNING AN IMPROVED NTRU CRYPTOSYSTEM

The NTRU public key cryptosystem is essentially based on the Nth degree trun- cated polynomial ring Z[X]/XN−1 . By altering the Z[X]/XN−1 or its mathematical con- struction, many researchers have worked to improve NTRU. In this paper, we present a new multi-dimensional public key cryptosystem which depends on a commutative quaternion al- gebra with a new structure. The new structure is an alternative to NTRU called NTRTE. Some data are used for comparing the key security and message security of NTRTE with the original NTRU and QTRU cryptosystems. Based on a security assessment, the comparison reveals that NTRTE is more resistant to them.

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.

A Logical XOR Operation for NTRU Cryptosystem

The NTRU public key cryptosystem was first presented by J. Hoffstein, J. H. Silverman and J. Pipher in 1996. This system is based on shortest and closest vector problem in a lattice and operations based on objects in a truncated polynomial ring. In this paper we propose new variant of NTRU cryptosystem which is based on logical exclusive operator. This system works under the same general principles as that of the NTRU cryptosystem except the logical operators “exclusive OR with the different bit size for encryption and decryption which are used in place of truncated polynomial in NTRU cryptosystem. We also calculate the time complexity which shows that this system is faster than NTRU cryptosystem.

Proposal for Scrambled Method based on NTRU

Scrambling is widely used to protect the security of data files such as text, image, video or audio files; however, it is not the most efficient method to protect the security of the data files. This article uses NTRU public key cryptosystem to increase the robustness of scrambling of sound files. In this work, we convert the sound file into text, and then scramble it in the following way: first, we encrypt the header of the sound file then, scramble the data of the file after the header in three stages. In each stage we scramble the data of the sound file and keep the original order of data in an array then, the three arrays are encrypted by the sender and sent with the encrypted header to the receiver in one file, while the scrambled data of the sound file is sent to the receiver in another file. We have tested the proposed method on several sound files; the results show that the time of encryption and decryption is reduced to approximately one-third, or less, compared to encrypting the file using NTRU.

Enhanced Provably Secure NTRU Encryption Based on Hard Learning over Rings

Since the presentation of NTRU public-key cryptosystem by Hoffstein, Pipher and Silverman, its favorable properties, such as easily created keys, high speed, excellent performance and conjectured resistance to quantum computers, have made it to be of great use. This paper proposes an enhanced scheme based on the hard learning with error over ring (R-LWE) problem to improve the security of the modified NTRUEncrypt presented by Stehle and Steinfled. We used part of the padding ideas of Fujisaki and Okamoto to obtain this scheme. It is semantically secure in strong sense of indistinguishability against adaptive chosen-ciphertext attacks in the random oracle model assuming the quantum hardness of standard worst-case problem over ideal lattices. It is also possible to arbitrarily decrease the error probability, and even to eliminate it completely. We gave the detailed analysis using the known results from classic works. Furthermore, this scheme owns many advantages such as the uniformity of public key, usual assumptions and the freedom for coding messages.

Fault Analysis of the NTRUEncrypt Cryptosystem

In this paper, we present a fault analysis of the original NTRU public key cryptosystem. The fault model in which we analyze the cipher is the one in which the attacker is assumed to be able to fault a small number of coefficients of the polynomial input to (or output from) the second step of the decryption process but cannot control the exact location of injected faults. For this specific original instantiation of the NTRU encryption system with parameters (N,p,q), our attack succeeds with probability ≈ 1 - 1/p and when the number of faulted coefficients is upper bounded by t, it requires O((pN)t) polynomial inversions in Z/pZ[x]/(xN - 1).

A New Attack on NTRU Public Key Cryptosystem Depend on Using Public Key and Public Information

A New Attack on NTRU Public Key Cryptosystem Depend on Using Public Key and Public Information

Countermeasures against Power Analysis Attacks for the NTRU Public Key Cryptosystem

The NTRU cryptosystem is a public key system based on lattice problems. While its theoretical security has been well studied, little effort has been made to analyze its security against implementation attacks including power analysis attacks. In this paper, we show that a typical software implementation of NTRU is vulnerable to the simple power analysis and the correlation power analysis including a second-order power attack. We also present novel countermeasures to prevent these attacks, and perform experiments to estimate the performance overheads of our countermeasures. According to our experimental results, the overheads in required memory and execution time are only 8.17% and 9.56%, respectively, over a Tmote Sky equipped with an MSP430 processor.

Breaking the NTRU Public Key Cryptosystem Using Self-Assembly of DNA Tilings

Computation by self-assembly of DNA is an efficient method of executing parallel DNA computing where information is encoded in DNA tiles and a large number of tiles can be self-assembled via sticky end associations.This paper shows how the DNA self-assembly process can be used for breaking the NTRU public key cryptosystem.In order to achieve this,a method for implementing the cyclic convolution product of two polynomials using self-assembled DNA computing is expounded.Then,a non-deterministic algorithmic is provided to break efficiently the NTRU public key cryptosystem.By creating billions of billions of copies of the participating DNA tiles,the algorithmic will run in parallel on all possible private keys.The computation takes advantage of non-determinism,but theoretically,each of the non-deterministic paths is executed in parallel,yielding the solution in time polynomial in the size of the input,with high probability.It presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.

Parallel Symmetric Attack on NTRU using Non-Deterministic Lattice Reduction

Currently, the most efficient passive attack on the NTRU public-key cryptosystem, proposed by Coppersmith and Shamir l1r, is based on finding a short enough vector in an integral lattice. An NTRU lattice possesses a cyclic automorphism group whose symmetry may be exploited. We have designed methods for reducing bases of NTRU integral lattices based on this symmetry. In addition to these methods, we use hill-descending techniques to combine new and proposed lattice-reduction algorithms. This approach includes deterministic and non-deterministic components which may be efficiently parallelized.