Symmetric Key Cryptography: Calculating Required Secret Keys
The question asks for the total number of secret keys needed in a group of 12 people, where each person must be able to communicate securely with every other person using symmetric key cryptography.
Understanding Symmetric Key Cryptography Needs
In symmetric key cryptography, a unique shared secret key is required for every pair of individuals who need to communicate. If there are 'n' people in a group, and each person needs to communicate with every other person, we need to find the number of unique pairs that can be formed from this group.
Applying the Combination Formula
This is a classic combination problem. We need to choose 2 people from a group of 'n' to form a pair, and each pair requires one secret key. The formula for combinations is:
$ C(n, k) = \frac{n!}{k!(n-k)!} $
In our case, we are forming pairs (k=2) from a group of 12 people (n=12). So, the formula simplifies to:
$ \text{Number of keys} = C(n, 2) = \frac{n \times (n-1)}{2} $
Step-by-Step Calculation
- Identify the number of people (n): In this group, $ n = 12 $.
- Apply the combination formula for pairs: We need to find the number of ways to choose 2 people from 12, which is $ C(12, 2) $.
- Calculate the number of keys: $ \text{Number of keys} = \frac{12 \times (12-1)}{2} $ $ \text{Number of keys} = \frac{12 \times 11}{2} $ $ \text{Number of keys} = \frac{132}{2} $ $ \text{Number of keys} = 66 $
Conclusion
Therefore, 66 unique secret keys are required for every person in a group of 12 to communicate with every other person using symmetric key cryptography.
Important Questions from Cryptography - Teaching
- 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
- Match the type of attack and its prevention mechanism:
1. Brute-Force Attack a. Change of keys 2. Statistical Attack b. Number of possible keys are large 3. Pattern Attack c. Hide the characteristics of the
language4. Known - Plain Text Attack d. Ciphertext is as random as
possible
