Which of the following best describes a finite field?

An infinite set of integers with standard addition and multiplication

A set of elements with addition and multiplication operations that satisfy specific axioms and has a finite number of elements

A set of polynomials with coefficients in a finite field

A group under addition only, with no multiplication operation

A security analyst is evaluating the security of a Diffie-Hellman key exchange. The public parameters are a prime p = 23 and a generator g = 5. An attacker intercepts the public value A = 10 (which is g^a mod p). The analyst wants to estimate the difficulty of recovering the private exponent a. What is the primary computational problem the attacker must solve?

The integer factorization problem: factor 23 into its prime components.

The discrete logarithm problem: find a such that 5^a ≡ 10 mod 23.

The square root problem: find a number whose square is 10 modulo 23.

The modular inverse problem: compute the inverse of 10 modulo 23.

EC-CouncilCertified Encryption Specialist

Domain 3Objective 1

Number Theory and Mathematical Foundations ECES Practice Questions (Page 4)

Part of the Asymmetric Cryptography and Number Theory domain, which makes up ~17% of our current practice bank. EC-Council does not publish an official question count, but from its 120-minute exam (~50–80 total, ~9–14 in this domain), expect 3–5 from this objective — we provide 44 practice questions to prepare you well beyond it. (estimate)

44questions here

9free pages

11concepts

Questions 16–20

16expert · medium
A cryptographic library implements RSA with modulus n = 35 and public exponent e = 5. To compute the private exponent, the library must find d such that e*d ≡ 1 mod φ(n). What is the correct private exponent d?
Select an answer first
17foundation · easy
Which of the following best describes a finite field?
Select an answer first
18application · medium
A security analyst is evaluating the security of a Diffie-Hellman key exchange. The public parameters are a prime p = 23 and a generator g = 5. An attacker intercepts the public value A = 10 (which is g^a mod p). The analyst wants to estimate the difficulty of recovering the private exponent a. What is the primary computational problem the attacker must solve?
Select an answer first
19foundation · easy
What is the value of Euler's totient function φ(9)?
Select an answer first
20application · medium
A cryptographic engineer is reviewing a list of candidate numbers for use as an RSA modulus. The engineer needs a composite number that is the product of two distinct primes. Which of the following numbers meets this requirement?
Select an answer first

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Number Theory and Mathematical Foundations ECES Practice Questions (Page 4)

Questions 16–20

A cryptographic library implements RSA with modulus n = 35 and public exponent e = 5. To compute the private exponent, the library must find d such that e*d ≡ 1 mod φ(n). What is the correct private exponent d?

Which of the following best describes a finite field?

What is the value of Euler's totient function φ(9)?

A cryptographic engineer is reviewing a list of candidate numbers for use as an RSA modulus. The engineer needs a composite number that is the product of two distinct primes. Which of the following numbers meets this requirement?

Keep studying — Asymmetric Cryptography and Number Theory