Cryptanalysis of Two Sparse Polynomial Based Public Key Cryptosystems
نویسندگان
چکیده
The application of sparse polynomials in cryptography has been studied recently. A public key encryption scheme EnRoot [4] and an identification scheme SPIFI [1] based on sparse polynomials were proposed. In this paper, we show that both of them are insecure. The designers of SPIFI proposed the modified SPIFI [2] after Schnorr pointed out some weakness in its initial version. Unfortunately, the modified SPIFI is still insecure. The same holds for the generalization of EnRoot proposed in [2].
منابع مشابه
EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
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...
متن کاملCryptanalysis of Rational Multivariate Public Key Cryptosystems
In 1989, Tsujii, Fujioka, and Hirayama proposed a family of multivariate public key cryptosystems, where the public key is given as a set of multivariate rational functions of degree 4[5]. These cryptosystems are constructed via composition of two quadratic rational maps. In this paper, we present the cryptanalysis of this family of cryptosystems. The key point of our attack is to transform a p...
متن کاملAlgebraic Attacks Galore!
Received: May 15, 2009 This is the first in a two-part survey of current techniques in algebraic cryptanalysis. After introducing the basic setup of algebraic attacks and discussing several attack scenarios for symmetric cryptosystems, public key cryptosystems, and stream ciphers, we discuss a number of individual methods. The XL, XSL, and MutantXL attacks are based on linearization techniques ...
متن کاملNonlinear Piece In Hand Matrix Method for Enhancing Security of Multivariate Public Key Cryptosystems
It is widely believed to take exponential time to find a solution of a system of random multivariate polynomials because of the NP-completeness of such a task. On the other hand, in most of multivariate public key cryptosystems proposed so far, the computational complexity of cryptanalysis is apt to be polynomial time due to the trapdoor structure. In this paper, we develop the concept, piece i...
متن کاملQuantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems
Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system F has a solution and compute one if F does have solutions with any given success probability. The complexity of the algorithm is polynomial in the size of F and the condition number of F . As a...
متن کامل