Randomness

The things that we call random are not entirely “random”. For example, we often think that flipping a coin and guess which face will be up should be a random result. However, we know there are several factors that could influence the result from a flipped coin: the force applied, the strength of the wind, air resistance etc. If we can obtain the accurate value about these data, we can predict which face will be up once the coin have been flipped.

From here we know that randomness, is the ignorance of the initial condition(s) of a chaotic system. Randomness can be predicted and known in advance. For instance, there are many programming languages implemented their own random generator (pseudorandom number generator, PRNG). If we can know what’s the formulae that’s behind the function generating random numbers, we can predict what random numbers will be generated in sequence. Therefore, attempting to encrypt a data with random number generated by the computer which mostly operated in a deterministic manner is a #cryptography and #security disaster.

There are many use cases in Cryptography# relies on random numbers such as Nonce# in authentication protocols, session keys, public key generation, and keystream for One-Time Pad.

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Transport Layer Security (TLS)

a pseudo-random function expands secrets into blocks of data
TNS3131 Chapter 2: Conventional Encryption and Message Confidentiality

Randomness
Pretty Good Privacy (PGP)

Authentication, that is validation of the sender, is done by involving the sender’s private key \(KR_a\) and public key \(KU_a\), and comparing the hashed message \(H(M)\)and the decrypted plaintext \(M\). The confidentiality of the message is done through the compression \(Z\) and encryption of the message using a randomly generated session key \(K_S\) (with ANSI X12.17 generator) which will be distributed together with the message encrypted by the receiver public key \(KU_b\).
One-Time Pad

One-Time Pad, or sometimes called One-Time Vernam Cipher#, is a #Substitution Cryptographic #algorithm that uses a single-use secret key for encrypting. It requires the key to be as long as the plaintext and random. Thus, guarantees an Unconditional Security# to the ciphertext. However, it does face some security concerns over secure key distribution and key generation for randomness. It is only used for low bandwidth and very high security purposes.
Nonce

Nonce is a random number generated to used just once during a communication session. The main purpose of it is to prevent Replay Attack#.
Monoalphabetic Cipher

Monoalphabetic Cipher is a #Substitution Cryptographic #algorithm that shuffle the letters arbitrarily (random) which has a key size of 26 letters. The total number of keys are \(26! = 4.03 \times 10^{26}\). However, since in Monoalphabetic Cipher the relationship between the letter in a plaintext to the letter in a ciphertext is always one-to-one, it is vulnerable to Frequency Analysis# due to the fact the frequency of the letters is not altered.
Hash Function

pseudorandomness#

Hash Function, denoted as \(h = H(M)\), is an unkey function that condense arbitrary lengths of value into a fixed size output (fingerprint). It could be used as a mapping function of #Hash Table key into an appropriate cell, in #Digital Signature for authentication#, creating one-way password, detecting intrusion or virus, or construct pseudorandom# function (PRF) or a pseudorandom number generator (PRNG).

#math #physics #statistics #chaos #cryptography #security