2.3. Substitution Ciphers 83 15. The mixing property of an affine cipher can be utilized in a linear con- gruential pseudorandom number generator (LCPNG). Choose a modulus m, two coefficients a and b in the range 0 to m-1, and a seed value zo also in the range 0 to m - 1. Then the sequence of integers 20, 21, 22, 23, ..., given by In = (axn-1 + b) MOD m, n = 1, 2, 3,... may satisfy some statistical tests for randomness. Indeed, the "ran- dom" number generators built into some computers are of this type. (a) Compute several values produced by a LCPNG with the following choices of parameters. (i) m = 13, a = 7, b = 0, = 1 (ii) m = 13, a = 3, b = 0,20 = 1 (iii) m = 11, a = 6, b = 1,20 = 1 (iv) m = 11, a = 6, b = 6, 30 = 1 (b) Explain why an LCPNG produces a sequence that eventually re- peats a pattern. (c) Suppose that an LCPNG with modulus m = 23 produces the three successive numbers 22, 7, and 5. Determine the coefficients a and b