Poly-Dragon: an efficient multivariate public key cryptosystem

Abstract

In this paper we propose an efficient multivariate public key cryptosystem. Public key of our cryptosystem contains polynomials of total degree three in plaintext and ciphertext variables, two in plaintext variables and one in ciphertext variables. However, it is possible to reduce the public key size by writing it as two sets of quadratic multivariate polynomials. The complexity of encryption in our public key cryptosystem is O(n 3 ), where n is bit size, which is equivalent to other multivariate public key cryptosystems. For decryption we need only four exponentiations in the binary field. Our Public key algorithm is bijective and can be used for encryption as well as for signatures.

Using Poly-Dragon Cryptosystem in a Pseudorandom Number Generator Mstg

“…Firstly, we start this section by introducing basic terminology and definitions, which have been borrowed from [5].…”

“…We will follow the authors' suggestion in [5] for the choice of parameters, which is as follows. We set r = 0, n = 2m…”

“…The private key of the cryptosystem consists of parameters α, β, γ and of two affine transformations (s, t). Now we will describe the encryption and decryption algorithm as it was proposed in [5].…”

“…This problem belongs to the category of NP-complete problems, therefore we assume that with a correct choice of parameters this cryptosystem is secure against the brute-force attack. Additionally, authors argue in [5] that this cipher is also secure against linearization equation attacks, differential cryptanalysis, Gröbner basis attacks and XL and FXL algorithms.…”

“…Poly-Dragon is a cryptosystem which was proposed in 2010 in [5]. It is a multivariate cryptosystem and its security is based on the problem of solving a system of multivariate quadratic equations over a finite field.…”