Prior to the discovery of any specific public-key schemes, such as RSA, an existence proof was developed whose purpose was to demonstrate that public-key encryption is possible in theory. Consider the functions fi(x1) = 21: f2(x2.72) = 22; f3(X3: Y3) = 23, where all values are integers with 1 Xi Yi, ZiN. Function f1 can be represented by a vector Mi of length N in which the kth entry is the value of f1(k). Similarly, f2 and fz can be represented by NxN matrices M2 and M3. The intent is to represent the encryption decryption process by table lookups for tables with very large values of N. Such tables would be impractically huge but in principle could be constructed. The scheme works as follows: construct M1 with a random permutation of all integers between 1 and N; that is, each integer appears exactly once in Mi. Construct M2 so that each row contains a random permutation of the first N integers. Finally, fill in M3 to satisfy the condition: f3(f2(f1(k), p), k) = p for all k, p with 1