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 (C.sub.1,C.sub.2) derived independently from the parameters where p is a pseudocomplement of a key c with respect to s. The derived conjugate pseudocomplements are C.sub.1 =T.sub.S *(M) and C.sub.2 =T.sub.p.sup.+ (M) where T.sub.s * and T.sub.p.sup.

Abstract: A division A/B where A and B are represented in a radix D can be accomplished by evaluating a power series. It is very important not only for the power series to converge but also to converge quickly in practical application. Thus, the convergence rate of the power series must be small in order to obtain a reasonably good approximation of the quotient by evaluating the first few terms. The acceleration method that guarantees to give a small convergence rate, 1/(2D-3 ), of the power series (see the section of the related application) was proposed with at most three successive applications of acceleration constants. This invention reduces the convergence rate, 1/(2D-3), to a smaller convergence rate, 1/(2mD-3), in the worst case where m=1,2,2.sup.2,2.sup.3,2.sup.4, . . . and the three successive applications of acceleration constants to at most the two successive applications of the constants. These two reductions promise to yield faster division in digital computer.

Abstract: A division A/B where A and B are represented in a radix D (assuming the absolute value of D is greater than one) can be accomplished by evaluating a power series. It is very important not only for the power series to converge but also to converge quickly in practical application. When the convergence rate of the power series is close to one, the convergence is slow. Usually it results in lengthy and time-consuming computation to obtain a reasonably good approximation of the reciprocal of the divisor B. The invention that accelerates the convergence could be used in a digital computation system for performing a faster division A/B. In digital system, the dividend A and the divisor B are stored in digital registers. This invented apparatus determines acceleration constants from the stored digits of the divisor B and the determinate constants are multiplied to the stored numbers A and B.