Patent ID: 7764785

Claim:
A method for communicating securely over an insecure communication channel between a pair of correspondents using a cryptographic protocol that involves implementing respective ones of a pair of complimentary mathematical operations said method comprising the steps of: assembling a data string including information to be transferred from a sending correspondent to a receiving correspondent; performing a complimentary mathematical operation that incorporates finite field elements and operations and generating a corresponding cipher-text; providing security against side channel attacks and cryptanalysis by a dynamic transformation of elements between objects that share a category; forwarding the cipher-text over a communication channel to the receiving correspondent and performing other mathematical cryptographic operations to decrypt the cipher-text; in which objects that share the same category are mapped to each other through homomorphic transformations; wherein object hopping is facilitated using a floating object which is defined as a combination of a base object and a one-to-one parametric transformation function τ that is used to map elements of the base object to elements of homomorphic objects; and wherein field hopping is facilitated using a floating finite field which is defined as a combination of a base finite field and a transformation function of the form τ( x ,κ)= xμ −κ = κ {tilde over (x)} where x, κ and μ are field elements, and where κ {tilde over (x)} denotes the resulting element.