1. Write a program in language that simulates an LFSR. It should take an initial state vector x1, ..., xk) and the coefficients a0, a1, ..., ak-1 of the recurrence

xn k ak-1 xn+k-1 ak-2 xn+k-2 .... a0x0(mod

the number of terms l of pseudo-random bit sequence as input and output l terms of the pseudo-random bit sequence. Use it to generate first 20 terms of the sequence given by xn+6 xn xn+2 xn+3 xn+5 and initial vector

Write a program in GP that performs Rabin Miller test. Use it to check whether the number n =12083810075737055857 is a prime number.

Write a function in GP that converts a text to a number by considering the text as a number in base 27 with A B ..., Z =26. Use this function to convert the text "THISISATEST" into a number.

Then, encrypt the number using RSA algorithm with

p 15838626342085188689

q =12648755071576652143

e 27628987

Find decrypt and check your answer.