Reza Ebrahimi Atani; Shahabaddin Ebrahimi Atani; Amir Hassani Karbasi
Abstract
\emph{ Smooth Projective Hash Functions } ( SPHFs ) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient cryptographic schemes and protocols. As an application of SPHFs, \emph { Password - Based Authenticated Key Exchange } ( PAKE ) protocol is well-studied ...
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\emph{ Smooth Projective Hash Functions } ( SPHFs ) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient cryptographic schemes and protocols. As an application of SPHFs, \emph { Password - Based Authenticated Key Exchange } ( PAKE ) protocol is well-studied area in the last few years. In 2009, Katz and Vaikuntanathan described the first lattice-based PAKE using the Learning With Errors ( LWE ) problem. In this work, we present a new efficient \emph { ring-based } smooth projectice hash function `` ( Ring - SPHF ) " using Lyubashevsky, Peikert, and Regev's dual-style cryptosystem based on the Learning With Errors over Rings ( Ring - LWE ) problem. Then, using our ring-SPHF, we propose the first efficient password-based authenticated key exchange ` ` ( Ring - PAKE ) " protocol over \emph{ rings } whose security relies on ideal lattice assumptions.
Reza Ebrahimi Atani; Shahabaddin Ebrahimi Atani; A. Hassani Karbasi
Abstract
In this paper we present a new finite field-based public key cryptosystem(NETRU) which is a non-commutative variant of CTRU. The original CTRU is defined by the ring of polynomials in one variable over a finite field F2. This system works in the ring R = F2[x]=hxN 1i and is already broken ...
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In this paper we present a new finite field-based public key cryptosystem(NETRU) which is a non-commutative variant of CTRU. The original CTRU is defined by the ring of polynomials in one variable over a finite field F2. This system works in the ring R = F2[x]=hxN 1i and is already broken by some attacks such as linear algebra attack. We extend this system over finite fields Zp, where p is a prime (or prime power) and it operates over the non-commutative ring M = Mk(Zp)[T; x]=hXn Ikki, where M is a matrix ring of k by k matrices of polynomials in R = Zp[T; x]=hxn 1i. In the proposed NETRU, the encryption and decryption computations are non-commutative and hence the system is secure against linear algebra attack as lattice-based attacks. NETRU is designed based on the CTRU core and exhibits high levels of security with two-sided matrix multiplication.
R. Ebrahimi Atani; Sh. Ebrahimi Atani; A. Hassani Karbasi
Abstract
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public ...
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GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive cube root of unity. EEH applies representations of polynomials to the GGH encryption scheme and we discuss its key size and parameters selection. We also provide theoretical and experimental data to compare the security and efficiency of EEH to GGH with comparable parameter sets and show that EEH is an improvement over GGH in terms of security and efficiency.