Number Theory and Mathematical Foundations ECES Practice Questions (Page 1)

Questions 1–5

1. 1application · easy

   An analyst is examining a number n = 143 to determine whether it is suitable as an RSA modulus. The analyst needs to factor n into its prime components. What is the correct factorization?

   • A7 × 21
   • B9 × 16
   • C3 × 47
   • D11 × 13
   Reveal Solution Discussion Select an answer first
2. 2foundation · easy

   What is the value of 5^φ(12) mod 12, given that GCD(5, 12) = 1?

   • A5
   • B0
   • C1
   • D11
   Reveal Solution Discussion Select an answer first
4. 3expert · easy

   A system administrator is configuring a rotation schedule for two cryptographic keys: one rotates every 12 days, the other every 18 days. The administrator wants to know when both keys will rotate on the same day to plan maintenance. What is the interval between simultaneous rotations?

   • A6 days
   • B24 days
   • C36 days
   • D72 days
   Reveal Solution Discussion Select an answer first
5. 4foundation · easy

   What is the greatest common divisor of 100 and 35?

   • A5
   • B20
   • C10
   • D15
   Reveal Solution Discussion Select an answer first
6. 5foundation · easy

   In the context of cryptography, what is a discrete logarithm?

   • AThe base g such that x^g ≡ h (mod p), given x, h, and p
   • BThe exponent x such that g^x ≡ h (mod p), given g, h, and p
   • CThe modulus p that makes g^x ≡ h (mod p) true
   • DThe product of all exponents that satisfy g^x ≡ h (mod p)
   Reveal Solution Discussion Select an answer first