Virtual Labs

What is the result of 23 mod 6?

a: 3 Explanation

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b: 4 Explanation

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c: 5 Explanation

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d: 6 Explanation

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Which property makes RSA encryption secure?

a: It uses very large prime numbers that are difficult to factor Explanation

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b: It uses complex polynomial equations Explanation

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c: It relies on the difficulty of solving linear equations Explanation

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d: It uses random number generation for each message Explanation

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In the RSA key generation process, what is the relationship between the public exponent e and Euler's totient function φ(n)?

a: e must be a factor of φ(n) Explanation

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b: e must be greater than φ(n) Explanation

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c: e and φ(n) must be coprime (gcd(e, φ(n)) = 1) Explanation

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d: e must equal φ(n) - 1 Explanation

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If p = 11 and q = 13, and we choose e = 7, what is the value of the private exponent d?

a: 103 Explanation

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b: 23 Explanation

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c: 31 Explanation

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d: 67 Explanation

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What is the result of 3^10 mod 11?

a: 1 Explanation

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b: 3 Explanation

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c: 9 Explanation

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d: 5 Explanation

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In RSA, if you encrypt a message m with the public key (e, n) to get ciphertext c, and then encrypt c again with the same public key, what mathematical property ensures you don't get back the original message m?

a: The commutative property of modular arithmetic Explanation

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b: The fact that (m^e)^e ≢ m (mod n) in general Explanation

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c: The irreversibility of prime factorization Explanation

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d: The randomness in the encryption process Explanation

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Using the Extended Euclidean Algorithm, what is the modular multiplicative inverse of 25 modulo 31?

a: 5 Explanation

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b: 6 Explanation

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c: 25 Explanation

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d: 30 Explanation

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In an RSA system with n = 77, e = 13, if the ciphertext is c = 23, what is the original message m?

a: 9 Explanation

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b: 12 Explanation

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c: 15 Explanation

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d: 18 Explanation

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What would happen to RSA security if quantum computers capable of running Shor's algorithm became widely available?

a: RSA would become slightly less secure but still usable Explanation

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b: RSA would be completely broken as Shor's algorithm can efficiently factor large integers Explanation

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c: RSA would become more secure due to quantum encryption Explanation

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d: Only the key generation process would need to be modified Explanation

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Modular Arithmetic and Applications