CRYPTOGRAPHIC SYSTEM USING PSEUDOCOMPLEMENTS OF VECTOR BOOLEAN ALGEBRA

Abstract

By using properties of pseudocomplements of vector Boolean algebra defined herein, a vector Boolean value which represents a plaintext of a message is converted to an enciphered text. The enciphered text consists of a pair of conjugate pseudocomplements of the plaintext with respect to a parameter which is a cipher key. In the deciphering process, the pair of the conjugate pseudocomplements is needed to recover the original plaintext. When a higher degree of message security is desired, both parties (a sender and a receiver) of a communication can establish two parameters (s,p) rather than one, and the sender can encipher a plaintext M into a pair of conjugate pseudocomplements (C1,C2) derived independently from the parameters where p is a pseudocomplement of a key c with respect to s. The derived conjugate pseudocomplements are C1 =TS *(M) and C2 =Tp + (M) where Ts * and Tp + represent the transformations of pseudocomplementing operations with respect to its suffixed parameters. The receiver performs a pseudocomplementing operation with respect to c on C1, namely Tc + (C1)=Tc + (Ts *(M))=Tp *(M)and recovers the original message M by deciphering Tp *(M) and Tp + (M) with respect to p. An advantage of this method is an increase of information entropy in each enciphered pseudocomplement over the one in a plaintext. Another advantage is an increase of the message length of an enciphered text. The first advantage can be applied to quickly establish a transient cipher key between a sender and a receiver through an insecure communication medium. The second advantage can strengthen a combinational complexity in an enciphered text so that in cryptanalysis, a decryption of the enciphered text becomes more difficult. Furthermore, when the two keys used in this system are enciphered by the third key, the decipher key used is different from its corresponding encipher key and is difficult to retrieve from the encipher key, which may be announced to general public. Thus this system becomes a public key system.

Source: Google Patents

35 USC §181 Secrecy Order

Inventor

• 1HITOHISA ASAI