Question

Consider the above quadratic residue generator x_n+1 = x_n² mod m with m = 4783 × 4027. Write a program to generate pseudo-random numbers from this generator. Use this to determine the period of the generator starting with seed x₀ = 196, and with seed x₀ = 400?

Answer 1

The R program is

x={}

x0 = 196# seed

x[1]=x0

m =4783*4027

k=1 # how many next random numbers you want

for(n in 1:k){

x[n+1] =(x[n]^2)%%m

}

x

[1]   196 38416

#The Output is Seed and next random numbers

x0 = 400 # seed

x[1]=x0

m =4783*4027

k=1 # how many next random numbers you wants

for(n in 1:k){

x[n+1] =(x[n]^2)%%m

}

x

[1]    400 160000

# The output is Seed and next random numbers

x={}
x0 = 196
x[1]=x0
m =4783*4027
k=10
for(n in 1:k){
x[n+1] =(x[n]^2)%%m
}
x

 [1]      196    38416 11942340   179421  6528630 11496859 16561776  4718361
 [9] 17746035  3406856   543841

x0 = 400
x[1]=x0
m =4783*4027
k=10
for(n in 1:k){
x[n+1] =(x[n]^2)%%m
}
x

[1]      400   160000  1943611 13179555  2320953  1741316 15551072  3530790
 [9] 12690106 11484744 14234586