Abstract: A public key cryptographic mechanism provides a measurable degree of minimum security, in an ensemble sense, for two Parties, A and B, to establish a commonly held private cryptographic keying variable between them for establishing communications. Both parties randomly generate m-bit vectors vec.sub.-- A and vec.sub.-- B, store the vectors, then copy the vectors and add m-bit vectors containing n ones. The vectors thus modified are exchanged between the parties. Both parties then respectively bit-by-bit combine, by Exclusive-Or logic, their stored m-bit vectors vec.sub.-- A and vec.sub.-- B with a received vector, denoted rec.sub.-- B and rec.sub.-- A, to generate respective vectors W.sub.-- A and W.sub.-- B. Parties A and B then generate all ##EQU1## vectors at a Hamming distance n from W.sub.-- A and W.sub.-- B respectively. These ##EQU2## vectors are each bit-by-bit added, using Exclusive-Or logic, with their encryptions under a publicly known keying variable K.sub.1, forming image vectors.