The HighRank attack was designed to attack Rainbow or Rainbow-like MPKC schemes .
The core essence of Linearization Equation attack is to construct a potential linear relationship between the input and the output of MPKC public system.
In fact, rotating relations are hard to use in cryptanalysis of MPKC .
give a Streaming SIMD Extensions (SSE) implementation of MPKC on x86 CPUs .
It was used to enhance the security of many MPKC schemes such as MI and HFE .
The fastest known MPKC signature schemes are Rainbow and Gui.
The UOV scheme is a well-known and deeply studied scheme in MPKC. This scheme uses a trapdoor one-way function whose security relies both on the MQ problem and on the isomorphism of polynomials (IP) problem (which will be described in the next section).
There exists other attacks besides the above algebraic attacks in MPKC, such as the Thomae-Wolf attack, linearization equation attack and differential attack.
The good keys are a generalization of equivalent keys in a MPKC scheme, and the Thomae-Wolf attack is a generalization of the Rainbow Band Separation attack.
In this attack, one uses the fact that the differential of the public key of any MPKC is an affine map, and the dimension of the kernel of the differential is invariant.
The result shows that HS-Sign is competitive with all the current promising MPKC schemes, so we think it is a promising MPKC scheme.
The public key size and the private key size is much larger than that of both the RSA and ECDSA scheme, but considering that these keys do not need to update frequently, and this result is acceptable in the field of MPKC. Also we can see that the signature size of HS-Sign is smaller than that of RSA, and a little larger than that of ECDSA.