Transmission of geometric algebra encrypted signals

Abstract

Cryptographic systems of information encryption use hypercomplex numbers: quaternions and octonions. A quaternion is used as a key, which rotates a group of information samples. Quaternions and biquaternions are special cases of Clifford’s geometric algebra. Using vectors and multivectors of geometric algebra to encrypt information allows us to expand the diversity of these vectors. To encrypt information represented by a set of geometric algebra vectors, these vectors are multiplied by multivectors that perform the rotor operation. A multivector (rotor) is used as a key. An operation corresponding to the reverse rotor is used to decrypt the information. Geometric algebra algorithms increase the security of information encryption by increasing the dimension of the algebra. To improve the encryption performance, it is proposed to select the coefficients of the information vector and the multivector of rotation from field Z256. It is proposed to add a vector of information with coefficients from Z256 to a random vector with coefficients from Z256 and consider these coefficients as encryption keys. The article presents reference vectors of the applied geometric algebras and tables of geometric products of reference vectors.