A matrix formulation for NTRU cryptosystem

Nayak, Rakesh; Sastry, Ch. V.; Pradhan, Jayaram

doi:10.1109/icon.2008.4772602

Cited by 14 publications

(6 citation statements)

References 8 publications

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“…When m = 1 and deg(f) > 1, we capture standard NTRU [27] along with NTRU Prime [8] and many other variants when taking g(X) an integer; in addition, we have the Mersenne low Hamming ratio (MLHR) problem [1] when g(X) = X − 2. Furthermore, for m > 1 and g ∈ ℤ, we have the basic matrix formulation of NTRU [42] when deg(f) = 1, while MaTRU [18] uses deg(f) > 1. Ideal-SIS.…”

Section: A Catalogue Of Problemsmentioning

confidence: 99%

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A framework for cryptographic problems from linear algebra

Bootland

Castryck

Szepieniec

et al. 2020

Journal of Mathematical Cryptology

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We introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also problems coming from code-based cryptography. The framework allows to easily instantiate new hard problems and to automatically construct plausibly post-quantum secure primitives from them. As a first basic application, we introduce two new hard problems and the corresponding encryption schemes. Concretely, we study generalisations of hard problems such as SIS, LWE and NTRU to free modules over quotients of {\mathbb{Z}[X]} by ideals of the form {(f,g)} , where f is a monic polynomial and {g\in\mathbb{Z}[X]} is a ciphertext modulus coprime to f. For trivial modules (i.e. of rank one), the case {f=X^{n}+1} and {g=q\in\mathbb{Z}_{>1}} corresponds to ring-LWE, ring-SIS and NTRU, while the choices {f=X^{n}-1} and {g=X-2} essentially cover the recently proposed Mersenne prime cryptosystems. At the other extreme, when considering modules of large rank and letting {\deg(f)=1} , one recovers the framework of LWE and SIS.

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Section: A Catalogue Of Problemsmentioning

confidence: 99%

“…The definition of what exactly "small" means and what a distribution of small elements is, is left to the next section. 4 See also[42], where this is elaborated in more detail. 5 Recall we have (f, g) = (a, r) for some a ∈ ℤ.…”

mentioning

confidence: 99%

A framework for cryptographic problems from linear algebra

Bootland

Castryck

Szepieniec

et al. 2020

Journal of Mathematical Cryptology

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“…In 2008, Nayak et al presented a matrix formulation of NTRU cryptosystem and showed that a matrix form of NTRU is much faster than the polynomial form of NTRU.…”

Section: Variants Of Ntrumentioning

confidence: 99%

“…Nayak et al proposed matrix formulation of NTRU cryptosystem in 2008 . Key generation, encryption and decryption are described in the following discussions.…”

Section: Variants Of Ntrumentioning

confidence: 99%

Generalisations of NTRU cryptosystem

Singh

Padhye

2016

Security Comm Networks

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“…This latter problem is equivalent to finding a short vector in a certain 2N dimensional lattice, a commonly known and also widely studied hard problem. [2] Since NTRU is a ring based public key cryptosystem and is therefore quite different from the group based cryptosystems whose security relies on the integer factorization problem or the discrete logarithm problem. This extra structure can be exploited to obtain a very fast cryptosystem; to encrypt/decrypt a message block of length N, NTRU only requires O(N 2 ) time, whereas the group based schemes like RSA etc.…”

Section: Introductionmentioning

confidence: 99%

Proposal for Two Enhanced NTRU

Sadiq¹,

Hussein²,

Khoja³

2014

IJACSA

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Abstract-Sound is very widely used in communication. In order to ensure secure communication a cryptographic data scheme is used. Secure sound is needed in many fields such as military, business, banking and electronic commerce. There is also an increasing demand for secured sound in network communication. Several symmetric and asymmetric algorithms are used for sound encryption. In this work, NTRU, the last in line public key cryptosystem is enhanced in two methods and used for encrypting sound files after converting the sound into text. In the proposed methods the message is encrypted one character at a time, since NTRU encrypts only prime numbers, thus 7 bits of each character is encrypted and the eighth bit is left without encryption. In method I NTRU algorithm is enhanced by adding the result obtained from calculating a mathematical equation of one variable to the message and then the resulted encrypted bit is fed-back and added to the next bit of the message in the next step; this procedure is repeated for the subsequent bits of the message. In method II NTRU algorithm is enhanced by adding the subsequent states of LFSR (Linear Feedback Shift Register) to the subsequent bytes of the message. The proposed methods are tested on several sound files; the results show that the proposed methods I and II maintain approximately the same original method encryption and decryption time while generating more complex encryption.

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A matrix formulation for NTRU cryptosystem

Cited by 14 publications

References 8 publications

A framework for cryptographic problems from linear algebra

A framework for cryptographic problems from linear algebra

Generalisations of NTRU cryptosystem

Proposal for Two Enhanced NTRU

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