RA2

Question 1

value of Φ of any prime number

Answer 1

the number minus 1

Question 2

for primes p&q, let N = pq. What is Φ(N)?

Answer 2

(p-1)(q-1)

Question 3

Φ(a*b) =

Answer 3

Φ(a) * Φ(b)

Question 4

conditions for choosing e (encryption key)

Answer 4

1 < e < Φ(N)

e must be coprime with N, Φ(N)

Question 5

conditions for choosing d (decryption key)

Answer 5

any d such that:

(d*e) mod Φ(N) = 1

Question 6

lecture definition of d

Answer 6

modular inverse of e (mod Φ(N))

Question 7

youtube calculation of d

Answer 7

1. Take various multiples of Φ(N)
2. add 1 to each of these multiples
3. choose whichever of these values which is evenly divisible by e
4. d = the quotient from evenly dividing by e

Question 8

Eulers Theorem

Answer 8

for any N, a which are relatively prime to one another, a^Φ(N) is congruent to 1 mod N

Question 9

When do we know there is NOT an inverse for some A, B?

Answer 9

When the GCD is not 1.

Question 10

When to use Φ(N) and N in RSA process?

Answer 10

N used in encryption and decryption of message.

Φ(N) used for calculating modular inverse

Question 11

What is smallest value of e possible?

Answer 11

smallest number which is greater than 1 and coprime to Φ(N)