DH, Exercise 8
? p = 10007;
? g = Mod(5,p);
? g^2
%4 = Mod(25, 10007)
? lift(g^3)
%5 = 125
? lift(g^4)
%6 = 625
? i = 1; x = g;
? i = i+1; x = x*g; lift(x)
%8 = 25
? i = i+1; x = x*g; lift(x)
%9 = 125
? i = i+1; x = x*g; lift(x)
%10 = 625
? i = i+1; x = x*g; lift(x)
%11 = 3125
? i = i+1; x = x*g; lift(x)
%12 = 5618
? i = i+1; x = x*g; lift(x)
%13 = 8076
? i = i+1; x = x*g; lift(x)
%14 = 352
? i = i+1; x = x*g; lift(x)
%15 = 1760
? i = i+1; x = x*g; lift(x)
%16 = 8800
? i = i+1; x = x*g; lift(x)
%17 = 3972
? i
%18 = 11


DH, Exercise 14
? p = 73; n1 = 8; n2 = 9; g = Mod(5,p); x = Mod(70,p);
? g1 = g^n1; x1 = x^n1; lift(x1)
%20 = 64
? g1
%21 = Mod(2, 73)
? lift([ g1^2, g1^3, g1^4, g1^5, g1^6, g1^7])
%22 = [4, 8, 16, 32, 64, 55]
? lift(g1^5)
%23 = 32
? lift(g1^6)
%24 = 64
? g2 = g^n2; x2 = x^n2;
? for(i=0,7,if(x2 == g2^i, print(i);break()));
2
? chinese(Mod(6,9), Mod(2,8))
%27 = Mod(42, 72)
? lift(g^42)
%28 = 70


PKE, Exercise 33
? n = 2573;
? f = x -> (x^2+1)%n;
? s = 2; t = 2;
? s = f(s); t = f(f(t)); gcd(s-t,n)
%35 = 1
? s = f(s); t = f(f(t)); gcd(s-t,n)
%36 = 31