Method for generating pseudo-random numbers

A method of providing message encryption using an output of a pseudo-random number generator wherein the pseudo-random number generator is defined by a modular exponential function xi=gxi−1 mod p, where xi is a value comprising m bits, p is a prime number comprising k bits, g is a generator of integer mod p, and 1<i ≦n, and wherein m and k are selected to achieve a desired security threshold level c, and m is further selected to cause the difference term m−2c to be greater than log2m+1, the method comprising the steps of:

• receiving a seed value x0 for the pseudo-random number generator;
• generating a value xi, using the pseudo-random number generator, wherein an initial value of the xi−1 term for the generator is the seed value x0;
• outputting from the generator a pseudo-random number zi constituted as j−1 bits of the generated value xi, the pseudo-random number zi including a second least significant bit of the value xi and excluding a least significant bit of the value xi, the value j being greater than log2m and no larger than m−2c;
• and
• combining the pseudo-random number zi with a message segment to produce an encrypted message segment.