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Official PYQ · 2009Q46Concept of Layering: OSI and TCP/IP Protocol StacksMCQ1 mark

GATE CS 2009 Q46 — Concept of Layering: OSI and TCP/IP Protocol Stacks

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In the RSA public key cryptosystem, the private and public keys are (e,n)(e, n) and (d,n)(d, n) respectively, where n=p×qn=p \times q and pp and qq are large primes. Besides, nn is public and pp and qq are private. Let MM be an integer such that 0<M<n0<M<n and ϕ(n)=(p−1)(q−1)\phi(n) = (p-1)(q-1). Now consider the following equations. 

  1. M’=Me mod nM’ = M^e \text{ mod } n
    M=(M’)d mod nM = (M’)^d \text{ mod } n

  2. ed≡1 mod ned \equiv 1 \text{ mod } n

  3. ed≡1 mod ϕ(n)ed \equiv 1 \text{ mod } \phi(n)

  4. M’=Me mod ϕ(n)M’ = M^e \text{ mod } \phi(n)
    M=(M’)d mod ϕ(n)M = (M’)^d \text{ mod }\phi( n)

Which of the above equations correctly represents RSA cryptosystem?

Choose one option
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Answer: B

In the RSA cryptosystem, the operations are defined as follows:

  1. Encryption and Decryption: The plaintext message MM (where 0<M<n0 < M < n) is encrypted to ciphertext M′M' using the public exponent ee modulo nn: M′=Me(modn)M' = M^e \pmod n The ciphertext M′M' is decrypted back to the plaintext MM using the private exponent dd modulo nn: M=(M′)d(modn)M = (M')^d \pmod n Thus, Equation I is correct and Equation IV is incorrect.

  2. Relation between Keys: The public exponent ee and private exponent dd are multiplicative inverses of each other modulo ϕ(n)\phi(n), where ϕ(n)=(p−1)(q−1)\phi(n) = (p-1)(q-1): ed≡1(modϕ(n))ed \equiv 1 \pmod{\phi(n)} Thus, Equation III is correct and Equation II is incorrect.

Since equations I and III are correct, the correct option is B.

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