Question

Samantha uses the RSA signature scheme with primes p = 13 and q = 23 and public verification exponent v = 53. (a) What is Samantha’s public modulus? What is her private signing key? (b) Samantha signs the digital document D = 100. What is the signature?

Answer 1

Answer:-------------
a).
Samantha’s public modulus is n = pq = 13 · 23 = 299 .
Her private signing key is 1/53 (mod φ(299)). Since φ(299) = 12 · 22 = 264, we calculate 1/53 modulo 264: applying the Euclidean
algorithm, we have 264 = 4·53 +5 2 and 53 = 52 + 1, and so 1 = 53 − 52 = 53 − (264 − 4·53) = 5·53 − 264.
Therefore, Samantha’s private signing key is 1/53 ≡ 5 (mod 264) .

b).
Samantha signs D = 100 by evaluating D⁵ (mod 299).
Since D⁵ = 10¹⁰ ≡ 16 (mod 299),
the digital signature is (100, 16) .