Public Key Cryptography Questions and Answers

Q: In RSA given two prime numbers p = 19 and q = 23, find n and φ ?

The values are n = 437, φ = 396.\[ \begin{aligned} n &= p \times q = 19 \times 23 = 437 \\ \phi(n) &= (p - 1)(q - 1) = 18 \times 22 = 396 \end{aligned} \]n is the public modulus, and \(\phi(n)\) is used to choose the public exponent e (coprime to 396) and compute the private exponent d. The other options do not come from these formulas: 38 and 52 are neither product, and 19 and 23 are just p and q.

In RSA given two prime numbers p = 19 and q = 23, find n and φ ?

A.n = 437, φ = 396
B.n = 381, φ = 231
C.n = 38, φ = 52
D.n = 19, φ = 23

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: A

The values are n = 437, φ = 396.

\[ \begin{aligned} n &= p \times q = 19 \times 23 = 437 \\ \phi(n) &= (p - 1)(q - 1) = 18 \times 22 = 396 \end{aligned} \]

n is the public modulus, and \(\phi(n)\) is used to choose the public exponent e (coprime to 396) and compute the private exponent d. The other options do not come from these formulas: 38 and 52 are neither product, and 19 and 23 are just p and q.

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