Use of a private key to encrypt and decrypt a message

A computer program product executable in computer recordable storage medium for transmitting a message with encryption from a sender at a first location to a recipient at a second location, wherein the message comprises a specified number M, and said computer program product comprises:

• instructions for selecting a first random number P and a second random number Q, wherein at least one of the numbers P and Q is a non-prime number;
• instructions for furnishing the numbers P and Q to both the sender at the first location and the recipient at the second location;
• instructions for operating a first data processing system at the first location to generate an encrypted value E that represents the message M, wherein E comprises the remainder which results when a modulus operator defined by a system of modular arithmetic is employed to divide a first quantity by a second quantity, the first quantity is equal to the product of M multiplied by P to the i power, wherein i is a selected number, and the second quantity is equal to the result obtained by subtracting one from the product of P multiplied by Q;
• instructions for transmitting a tuple comprising the values of E and i from the first location to the second location;
• and
• instructions for operating a second data processing system at the second location to determine the message M by selectively processing the values of E, i and Q.

A system for transmitting a message with encryption from a sender at a first location to a recipient at a second location, wherein the message comprises a specified number M, and said system comprises:

• means for selecting a first random number P and a second random number Q, wherein at least one of the numbers P and Q is a non-prime number;
• means for furnishing the numbers P and Q to both the sender at the first location and the recipient at the second location;
• a first data processing system operable at the first location to generate an encrypted value E that represents the message M, wherein E comprises the remainder which results when a modulus operator defined by a system of modular arithmetic is employed to divide a first quantity by a second quantity, the first quantity is equal to the product of M multiplied by P to the i power, wherein i is a selected number, and the second quantity is equal to the result obtained by subtracting one from the product of P multiplied by Q;
• means for transmitting a tuple comprising the values of E and i from the first location to the second location;
• and
• operating a second data processing system at the second location to determine the message M by selectively processing the values of E, i and Q.