Cryptanalysis of schemes based on polynomial symmetrical decomposition

Abstract

Advances in quantum computation threaten to break public key cryptosystems such as RSA, ECC, and ElGamal that are based on the difficulty of factorization or taking a discrete logarithm, although up to now, no quantum algorithms have been found that are able to solve certain mathematical problems on non-commutative algebraic structures. Against this background, some novel public key cryptography based on Polynomial symmetrical decomposition (PSD) problem have been proposed. We find that these schemes are not secure. We present that they are vulnerable to structural attack, linearization equations attack, overdefined systems of multivariate polynomial equations attack and that, they only require polynomial time complexity to retrieve the same secret key for some given public keys respectively. We also propose an improvement to enhance public key cryptography based on PSD problem. In addition, we discuss possible lines of future work.