Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Asymmetric key cryptography is significant slower than symmetric key cryptography. Reason R: Asymmetric key cryptography is based on complex mathematical structure to secure data. In the light of the above statements, choose the most appropriate answer from the options given below
Analysis of Assertion A and Reason R
This question evaluates understanding of the performance characteristics and underlying principles of asymmetric versus symmetric key cryptography.
Assertion A: Performance Comparison
- Assertion A states that asymmetric key cryptography is significantly slower than symmetric key cryptography.
- This is generally true. Asymmetric algorithms (like RSA, ECC) involve complex mathematical operations (e.g., modular exponentiation with very large numbers) that require more computational resources and time compared to the simpler substitution and permutation operations used in symmetric algorithms (like AES).
- Therefore, Assertion A is correct.
Reason R: Underlying Principles
- Reason R states that asymmetric key cryptography is based on complex mathematical structures to secure data.
- This is also true. The security of asymmetric cryptography relies on the difficulty of solving certain mathematical problems, such as factoring large numbers or computing discrete logarithms. These problems form the basis of its complex mathematical foundation.
- Therefore, Reason R is correct.
Relationship between Assertion A and Reason R
- The complex mathematical structures mentioned in Reason R are precisely what necessitate computationally intensive operations, leading to the slower performance described in Assertion A.
- The complexity of calculations, such as those involving large prime factorization or elliptic curve equations, directly causes the performance difference.
- Thus, Reason R provides the fundamental explanation for why Assertion A is true.
Conclusion
Both statements are factually correct, and the reason adequately explains the assertion.
The most appropriate answer is: Both A and R are correct and R is the correct explanation of A.
Important Questions from Cryptography - Teaching
- In symmetric key cryptography, if every person in a group of 12 people needs to communicate with every other person in the group, how many secret keys are required?
- Match the following:
Match correctly the cryptographic algorithm with their corresponding key-length.1. DES a. 128-256 bits 2. Rj indeal b. 1-448 bits 3. RC4 c. 56 bits 4. Blowfish d. 1-2048 bits - Decryption of the ciphertext "Z" with the key pair (7, 2) in modulus 26 is
In the RSA public key cryptosystem, the private and public keys are $(e, n)$ and $(d, n)$ respectively, where $n = p \times q$ and $p$ and $q$ are large primes. Besides, $n$ is public and $p$ and $q$ are private. Let M be an integer such that $0 <M< n$ and $\phi(n) = (p-1)(q - 1)$. now consider the following equations.
I. M’ =\( M^e\) mod n M =\( (M')^d\) mod nII. ed ≡1 mod n
III. ed ≡1 mod f(n)
IV. M’ = \(M^e \)mod f(n)
M = \( (M')^d\) mod
Which of the above equations correctly represent RSA cryptosystem?- Let M be a message consisting of 50 AES blocks. Alice encrypts using CBC mode and transmits the resulting ciphertext to Bob. Due to a network error, ciphertext block number 45 is corrupted during transmission. All other ciphertext blocks are transmitted and received correctly. Once Bob decrypts the received ciphertext, number of plaintext blocks corrupted is
