Virtual Labs

What is the result of 17 mod 5?

a: 2 Explanation

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b: 3 Explanation

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c: 4 Explanation

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d: 5 Explanation

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Which of the following statements about prime numbers is TRUE?

a: All prime numbers are odd Explanation

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b: A prime number has exactly two distinct positive divisors Explanation

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c: 1 is considered a prime number Explanation

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d: Prime numbers can be factored into smaller integers Explanation

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In RSA cryptography, what does the public key consist of?

a: The values (d, n) Explanation

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b: The values (e, n) Explanation

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c: The values (p, q) Explanation

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d: The values (φ(n), e) Explanation

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If p = 7 and q = 11, what is the value of Euler's totient function φ(n) where n = p × q?

a: 60 Explanation

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b: 72 Explanation

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c: 77 Explanation

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d: 84 Explanation

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In RSA, if e = 5 and φ(n) = 24, what condition must the private exponent d satisfy?

a: d × φ(n) ≡ 1 (mod e) Explanation

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b: e × d ≡ 1 (mod φ(n)) Explanation

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c: d ≡ e (mod φ(n)) Explanation

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d: e + d ≡ 1 (mod φ(n)) Explanation

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What is the result of 13^3 mod 7?

a: 6 Explanation

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b: 1 Explanation

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c: 3 Explanation

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d: 5 Explanation

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Using the Extended Euclidean Algorithm, what is the modular multiplicative inverse of 17 modulo 26?

a: 23 Explanation

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b: 15 Explanation

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c: 21 Explanation

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d: No inverse exists Explanation

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In an RSA system with n = 35, e = 5, what is the correct decryption of the ciphertext c = 12?

a: 2 Explanation

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b: 17 Explanation

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c: 23 Explanation

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d: Cannot determine without knowing d Explanation

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Why is the security of RSA based on the difficulty of factoring large numbers?

a: Because factoring determines the value of the public exponent e Explanation

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b: Because knowing p and q allows computation of φ(n) and thus the private key d Explanation

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c: Because factoring large numbers requires solving discrete logarithms Explanation

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d: Because the encryption process itself involves factoring Explanation

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Modular Arithmetic and Applications