Exercise · ZW-RSA-CRYPTOSYSTEM-009 · ★★☆ Intermediate
With p = 5 and q = 11, compute φ(n) and the smallest valid exponent e = 3.
Choose one option.
Show answer
- B. 40
Explanation
Since φ(n) = 4·10 = 40 and gcd(3, 40) = 1, the exponent e = 3 is valid. Confusing φ(n) with n = 55 is the typical error.
Review the concept: RSA cryptosystem
The RSA cryptosystem is a public-key encryption method based on the difficulty of factoring the product of two large primes. It uses Euler's theorem and modular inverses to encrypt and decrypt messages.
\[c \equiv m^{e} \pmod{n}, \quad m \equiv c^{d} \pmod{n}\]
More practice problems: rsa cryptosystem
- ZW-RSA-CRYPTOSYSTEM-001 Which modulus is used to compute the exponent d in RSA?
- ZW-RSA-CRYPTOSYSTEM-002 If p = 5 and q = 7, what is the value of n?
- ZW-RSA-CRYPTOSYSTEM-003 For p = 5 and q = 7, what is the value of φ(n)?
- ZW-RSA-CRYPTOSYSTEM-004 What condition must the public exponent e satisfy in RSA?
- ZW-RSA-CRYPTOSYSTEM-005 Which theorem guarantees that m^ed ≡ m pmodn in RSA?
- ZW-RSA-CRYPTOSYSTEM-006 With p = 3, q = 11 and e = 3, find d such that 3d ≡ 1 (mod 20).
- ZW-RSA-CRYPTOSYSTEM-007 With n = 33 and d = 7, what is the decryption of c = 31?
- ZW-RSA-CRYPTOSYSTEM-008 If e = 5 and φ(n) = 24, what is the modular inverse d of e?