def main():
x = readinput("x")
y = readinput("y")
if y > x:
x, y = y, x
ans = gcd(x, y)
print("GCD of %d and %d = %d" % (x, y, ans))
def main():
x = readinput("x")
y = readinput("y")
if y > x:
x, y = y, x
ans = gcd(x, y)
print ("GCD of %d and %d = %d" % (x, y, ans))
def main():
print ("X^Y % N")
x = readinput("X")
y = readinput("Y")
N = readinput("N")
ans = modular_exp(x, y, N)
print ("(%d^%d) %% %d = %d" % (x, y, N, ans))
def main():
print("X^Y % N")
x = readinput("X")
y = readinput("Y")
N = readinput("N")
ans = modular_exp(x, y, N)
print("(%d^%d) %% %d = %d" % (x, y, N, ans))
def test_numpower():
while True:
x = readinput("X")
n = readinput("N")
ans = numpower(x, n)
print("%d^%d is: %d\n" % (x, n, ans))
print("press \"n\" to exit, any other key to cont.")
inp = input()
if inp.strip() == 'n':
break
def main():
num = readinput()
clist = findconstant(num)
print("showing c values: ")
print(clist)
ch = input("based on above c values. enter c: ")
c = float(ch)
# c = clist[-1]
print("Now Lets verify if for c=%0.2f the equation Fn <= 2^(c*n) holds" %
(c))
print("First lets choose \"n\" value")
num = readinput()
verifyc(c, num)
def main():
num = readinput()
clist = findconstant(num)
print ("showing c values: ")
print (clist)
ch = input("based on above c values. enter c: ")
c = float(ch)
# c = clist[-1]
print ("Now Lets verify if for c=%0.2f the equation Fn <= 2^(c*n) holds" %
(c))
print ("First lets choose \"n\" value")
num = readinput()
verifyc(c, num)
def send_message(e, N):
print ("Alish wishes to send message x to Bob")
print ("She looks up his public key (N, e) and sends him message"
" y = x^e mod N")
x = readinput("message x")
y = modular_exp(x, e, N)
return y
def main():
clist = [0.5, 1, 2]
print ("Please enter \"n\" value below")
n = readinput()
for c in clist:
theta = calc_theta(c, n)
print("for c:%0.2f and n:%d, theta is: %0.2f" % (c, n, theta))
def main():
num = readinput()
for n in range(num+1):
fib = findfibonacci(n)
sys.stdout.write(str(fib) + " "),
sys.stdout.write("\n")
print ("Finding fibonacci through expression 2**(0.694*n)")
for n in range(num):
fib = findfibexpr(n)
sys.stdout.write(str(fib) + " "),
sys.stdout.write("\n")
print ("Enter number for fast fibonacci")
num = readinput()
fib = findfibopoly(num)
print ("fib %d is: %d" % (num, fib))
def send_message(e, N):
print("Alish wishes to send message x to Bob")
print("She looks up his public key (N, e) and sends him message"
" y = x^e mod N")
x = readinput("message x")
y = modular_exp(x, e, N)
return y
def main():
num = readinput()
for n in range(num + 1):
fib = findfibonacci(n)
sys.stdout.write(str(fib) + " "),
sys.stdout.write("\n")
print("Finding fibonacci through expression 2**(0.694*n)")
for n in range(num):
fib = findfibexpr(n)
sys.stdout.write(str(fib) + " "),
sys.stdout.write("\n")
print("Enter number for fast fibonacci")
num = readinput()
fib = findfibopoly(num)
print("fib %d is: %d" % (num, fib))
def main():
print("Fermat's little theorem for primality")
print("If p is prime then for every 1 <= a < p")
print("a^(p-1) ≡ 1 (mod) p")
p = readinput("prime candidate")
if isprime(p):
print("%d is Prime Number" % p)
else:
print("%d is Not a Prime Number" % p)
def main():
print ("Fermat's little theorem for primality")
print ("If p is prime then for every 1 <= a < p")
print ("a^(p-1) ≡ 1 (mod) p")
p = readinput("prime candidate")
if isprime(p):
print ("%d is Prime Number" % p)
else:
print ("%d is Not a Prime Number" % p)
def main():
a = readinput("x value")
b = readinput("y value")
x = bin(a)
y = bin(b)
x = x[2:]
y = y[2:]
xlen = len(x)
ylen = len(y)
diff = abs(xlen - ylen)
z = "0" * diff
if xlen < ylen:
x = z + x
elif ylen < xlen:
y = z + y
ans = multiply(x, y)
print ("x in bin: ", x)
print ("y in bin: ", y)
print ("x * y = ", ans)
def main():
print("Fermat's little theorem for primality")
print("If p is prime then for every 1 <= a < p")
print("a^(p-1) ≡ 1 (mod) p")
p = readinput("prime candidate")
if isprime(p):
print("%d is Prime Number" % p)
else:
print("%d is Not a Prime Number" % p)
for i in range(100000):
if isprime(4):
print("we are getting 4 as prime")
print("Done!")
def main():
print ("Fermat's little theorem for primality")
print ("If p is prime then for every 1 <= a < p")
print ("a^(p-1) ≡ 1 (mod) p")
p = readinput("prime candidate")
if isprime(p):
print ("%d is Prime Number" % p)
else:
print ("%d is Not a Prime Number" % p)
for i in range(100000):
if isprime(4):
print("we are getting 4 as prime")
print ("Done!")
def main():
num = readinput("n >= 2")
p = random_prime(num)
print ("Random Prime less than %d: %d" % (num, p))
test_random_prime()
def main():
x = readinput("X")
y = readinput("Y")
ans = division(x, y)
print("%d / %d = Quotient: %d, Remainder: %d" % (x, y, ans[0], ans[1]))
def main():
num = readinput("n >= 2")
p = random_prime(num)
print("Random Prime less than %d: %d" % (num, p))
test_random_prime()
def main():
num = readinput("which fibonacci number")
fib = fibonacci(num)
print("fib digit len: ", len(str(fib[0])))
print("%d fibonacci is: %d" % (num, fib[0]))
print("log(fib): ", math.log(fib[0], 2))
def main():
a = readinput("a")
b = readinput("b")
(x, y, d) = extended_euclid(a, b)
print("ax + by = d")
print("x=%d, y=%d, d=%d" % (x, y, d))
def main():
n = readinput("n value")
count = checkinverses(n)
print("%d integers have inverses with modulo %d" % (count, n))
def main():
num = readinput("which fibonacci? ")
fib = get_fibonacci(num)
print ("%d fibonacci: %d" % (num, fib))
def main():
x = readinput("X: ")
y = readinput("Y: ")
ans = french_mult(x, y)
print("%d x %d: %d" % (x, y, ans))
def main():
num = readinput("n value for series")
harmonic_series(num)
def main():
x = readinput("X: ")
y = readinput("Y: ")
ans = french_mult(x, y)
print ("%d x %d: %d" % (x, y, ans))
def main():
a = readinput("a")
b = readinput("b")
(x, y, d) = extended_euclid(a, b)
print ("ax + by = d")
print ("x=%d, y=%d, d=%d" % (x, y, d))
def main():
print("empirical study of log(n!) = Θ(nlog(n))")
n = readinput("n value")
test_expression(n)
def main():
print("To calculate: X^(-1) mod N")
x = readinput("X")
n = readinput("N")
ans = inverse_modulo(x, n)
print("Ans: ", ans)
def test_binary_converter():
num = readinput("decimal number")
bnum = tobinary(num)
print ("binary: ", bnum)
def main():
n = readinput("n value")
count = checkinverses(n)
print("%d integers have inverses with modulo %d" % (count, n))
def main():
x = readinput("X")
y = readinput("Y")
ans = division(x, y)
print("%d / %d = Quotient: %d, Remainder: %d" % (x, y, ans[0], ans[1]))
def main():
num = readinput("n value for series")
harmonic_series(num)
def main():
print ("To calculate: X^(-1) mod N")
x = readinput("X")
n = readinput("N")
ans = inverse_modulo(x, n)
print ("Ans: ", ans)
def main():
num = readinput("which fibonacci number")
fib = fibonacci(num)
print ("fib digit len: ", len(str(fib[0])))
print ("%d fibonacci is: %d" % (num, fib[0]))
print ("log(fib): ", math.log(fib[0], 2))
