Simple and effective public-key cryptosystem

A method of securely communicating over an insecure communication channel of the type wherein an original information signal is transformed into an encoded information signal according to an encryption algorithm, transmitted over said information channel between a transmitter and a receiver, received by said receiver and decoded to obtain said original information signal, said original information signal comprising at least two integers m.sub.1 and m.sub.2 where at least m.sub.1 represents information and 0<m.sub.1 <M.sub.1 and 0<m.sub.2 <M.sub.2, where M.sub.1 and M.sub.2 are integers, said method comprising the steps of:

• producing a cryptogram x from said original information signal and a public encryption key (c.sub.1, c.sub.2 r), where c.sub.1, c.sub.2 and r are all integers, r is the product of two relatively prime numbers p.sub.1 and p.sub.2, and c.sub.1 and r are well as c.sub.2 and r are relatively prime, said cryptogram x being defined by:
• x=c.sub.1 m.sub.1 +c.sub.2 m.sub.2 (mod r)
• where c.sub.1 m.sub.1 +c.sub.2 m.sub.2 (mod r) is defined as the remainder of (c.sub.1 m.sub.1 +c.sub.2 m.sub.2)/r;
• transmitting said cryptogram x as said encoded information signal from said transmitter to said receiver;
• receiving said encoded information signal at said receiver;
• generating two simultaneous linear equations from said encryption algorithm;
• and
• solving said two simultaneous linear equations using said received cryptogram x, to thereby obtain said integers m.sub.1 and m.sub.2 of said original information signal.