Patent Document ID: 7961876
Application ID: 11323597
Patent Flag: 1

Claim One:
1. A cryptographic method for application to a multivariate public key cryptosystem (MPKC) to produce new multivariate public key cryptosystems or asymmetric cryptographic communication processes, wherein said multivariate public key cryptosystem is a cryptographic communication process comprising: a) a public transformation which transforms a value (X) represented by a vector of k n , a set or space of (n) elements of a finite field, or ring (k), X=(x 1 ,. .. , x n ), into another value (Y) represented by a vector of k m , a set or space of (m) elements of the finite field or ring (k), Y=(y 1 ,. .. , Y m ), through a set of (m) multivariate polynomials, (f 1 (x 1 ,. .. , x n ),. .. , f m (x 1 ,. .. , x n )) over (k) which are publicly available, have a low degree (d) and the transformation is computed as (f 1 (x 1 ,. .. , x n ),. .. , f m (x 1 ,. .. , x n ))=(y 1 ,. .. , y m ); wherein the transformation is used by anyone for encrypting a message or verifying the authenticity of a digital signature or a digital authentication code for a document; and b) a secret transformation for obtaining the value (X) from the value (Y) by means of inverting the transformation defined by (f 1 (x 1 ,. .. , x n ),. .. , f m (x 1 ,. .. , x n )), with the knowledge of a cryptographic secret, wherein the secret transformation is used by a legitimate user, who has the knowledge of the cryptographic secret, to decrypt a message, or produce a digital signature for a document or an authentication code for a document; and c) wherein producing a family of new multivariate public key cryptosystems or new asymmetric cryptographic communication process over any prior existing MPKC, which refers to any existing or future MPKC that does not use the method in its design, comprising the steps: i) adding directly into the prior MPKC internal perturbation through a small number (r) of randomly or specially chosen new internal variables z i = ∑ j = 1 n ⁢ a ij ⁢ x j + b i , i=1,. .. , r whose linear part without the constant term b i , a fixed value in k and not a variable, are linearly independent as linear functions of variables x i in the public transformation; and ii) appending (α) more components, which are randomly or specially chosen polynomials to the already perturbed MPKC, and composing randomly or specially chosen invertible affine or linear transformations, such that a newly produced MPKC improved by the method, has a new public transformation for transforming the value (X) represented by (n) elements of a finite field, or ring (k), X=(x 1 ,. .. , x n ) into another value (Y + ) represented by (m+α) elements of the finite field or ring (k), Y + =(y 1 ,. .. y m+α ), through this newly produced set of (m+α) multivariate polynomials (f + 1 (x 1 ,. .. , x n ),. .. , f + m+α (x 1 ,. .. , x n )) over (k); and iii) a secret transformation for obtaining the value (X) from the value (Y + ) by means of inverting the transformation defined by (f + 1 (x 1 ,. .. , x n ),. .. , f + m+α (x 1 ,. .. , x n )), with the knowledge of the prior cryptographic secret and the secrets in the adding step and appending step.