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In RSA public key cryptosystem suppose $n=p*q$ where $p$ and $q$ are primes. $(e,n)$ and $(d,n)$ are public and private keys respectively. Let $M$ be an integer such that $o< M< n$ and $\phi(n)=(p-1)(q-1)$.

Which of the following equations represent RSA public key cryptosystem?

- $\begin{array}{} C \equiv M^{e} \text{(mod n)} \\ M \equiv C^{d} \text{(mod n)} \end{array} \\$
- $ed\equiv1 \text{(mod n)} \\$
- $ed\equiv1 ( \text{mod } \phi( n)) \\$
- $\begin{array}{} C\equiv M^{e} ( \text{mod } \phi(n)) \\ M \equiv C^{d}( \text{mod } \phi (n)) \end{array}$

- I and II
- I and III
- II and III
- I and IV

3 votes

Comparing it with RSA algorithm , I and III is correct ahere...see the example

- Choose p = 3 and q = 11
- Compute n = p * q = 3 * 11 = 33
- Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
- Choose e such that 1 < e < φ(n) and e and n are coprime. Let e = 7
- Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3 [(3 * 7) % 20 = 1]
- Public key is (e, n) => (7, 33)
- Private key is (d, n) => (3, 33)
- The encryption of
*m = 2*is*c = 2*^{7}% 33 = 29 - The decryption of
*c = 29*is*m = 29*^{3}% 33 = 2

so B is correct answer here

1 vote

Comparing it with RSA algorithm , I and III is correct ahere...see the example

- Choose p = 3 and q = 11
- Compute n = p * q = 3 * 11 = 33
- Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
- Choose e such that 1 < e < φ(n) and e and n are coprime. Let e = 7
- Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3 [(3 * 7) % 20 = 1]
- Public key is (e, n) => (7, 33)
- Private key is (d, n) => (3, 33)
- The encryption of
*m = 2*is*c = 2*^{7}% 33 = 29 - The decryption of
*c = 29*is*m = 29*^{3}% 33 = 2

so B is correct answer here