Cryptology Exam - October 25, 2024

A cipher that uses a key consisting of two integers (j and k) to encrypt a message. It encrypts each letter in a message by multiplying it by the first key (j) and adding the second key (k) modulo 26.

The key length of a Vigenere cipher should be the length of a common English word. This range is typically considered to be between 30,000 and 100,000 words, representing approximately 15-16 bits of information.

Breaking Vigenere involves finding the key length and then identifying the individual Caesar shifts used for each letter position. This is done by analyzing repeating patterns in the ciphertext and calculating the greatest common divisor (GCD) of their distances. Once the key length is found, you can identify the individual Caesar shifts by looking at the letter frequencies in each block corresponding to each letter of the key.

Redundancy in a language is the amount of information that can be removed from a written text without losing its meaning. It's measured by comparing the actual length of the written text to the amount of information it actually carries.

A system for representing characters using numerical values. In English, this system makes use of 7-bit codes for each character, but it is known to be inefficient due to redundancies.

A type of cipher that operates on single characters or a group of characters at a time, transforming them into a ciphertext. It relies on a predetermined key and algorithm to encrypt and decrypt the message using a specific mathematical operation or sequence.

The process of generating pseudo-random sequences used in cryptography. This involves creating sequences that appear random but are actually generated using a deterministic algorithm and a seed value.

A method used in cryptography to create nonces, which are random, unpredictable values used to protect security against certain attacks. They are usually used one time only. One-time pad (OTP) is an example.

The average entropy of English text is approximately 1 bit per letter. Entropy is a measure of randomness or uncertainty in a system.

Stream ciphers address the drawback of one-time pad (OTP) by using a short secret key to generate a longer keystream. This allows secure transmission without needing a key as long as the message itself.

A cryptosystem has perfect secrecy if the conditional entropy of the plaintext given the ciphertext is equal to the entropy of the plaintext. This means that the ciphertext reveals no information about the plaintext.

Real-world pseudo-random number generators (PRNGs) generate sequences that are periodic due to the deterministic nature of their algorithms and the finite size of their internal state. This means the sequences eventually repeat.

In a generic block cipher, the number of possible keys is determined by the factorial of 2 raised to the power of the block size (n). This number grows exponentially with the block size, making generic block ciphers impractical due to the immense number of possible keys.

Solving for x in the RSA encryption equation (xe = c mod n) is computationally equivalent to factoring the modulus (n = pq). This is because the Chinese Remainder Theorem can be used to transform these problems into equivalent forms.

The RSA parameters are chosen as follows:

1. p, q: Large prime numbers, preferably with similar bit lengths.
2. n: The product of p and q, called the modulus.
3. e: The public key exponent, chosen as an odd number greater than 1 and relatively prime to the totient of n (φ(n)).
4. d: The private key exponent, calculated as the modular multiplicative inverse of e modulo φ(n).

The Diffie-Hellman key exchange is a protocol for establishing a shared secret key between two parties over an insecure channel. The protocol relies on modular exponentiation and the difficulty of the discrete logarithm problem.

A method for encrypting messages where the key is a string of random bits of the same length as the message, used only once and then discarded.

A cryptographic system where the same key is used for both encryption and decryption.

A cryptographic system that uses separate keys for encryption and decryption.

A digital signature that is created for a message whose content is hidden from the signer.

A technique for proving knowledge of a secret without revealing it.

A method for securely storing a secret by dividing it into multiple parts, each of which is given to a different party.

A process used to generate sequences of numbers that appear random but are actually generated using a deterministic algorithm.

A way to prove ownership of a digital asset without revealing the asset itself.