Why is random number generation critical for secure cryptography?

1 What is randomness?

Randomness is the property of having no predictable pattern or order. In cryptography, randomness is needed to create unpredictability and diversity in the encryption and decryption processes, making them resistant to attacks. For example, if you use a fixed key to encrypt every message, an attacker could easily guess or brute-force the key by comparing the encrypted messages. However, if you use a different random key for every message, the attacker would have no clue about the key or the message content. Similarly, if you use a random initialization vector (IV) to encrypt each message block, you can prevent the same plaintext from producing the same ciphertext, which could reveal patterns or repetitions.

2 What are the sources of randomness?

Randomness can be derived from two main sources: physical and computational. Physical sources are based on natural phenomena that are inherently unpredictable, such as atmospheric noise, radioactive decay, thermal fluctuations, or human input. Computational sources are based on mathematical algorithms that produce pseudo-random numbers, which are not truly random but appear to be so for practical purposes. Physical sources are usually more secure and reliable than computational sources, but they are also slower, more expensive, and harder to access. Computational sources are faster, cheaper, and more convenient, but they require a good seed (a starting value) from a physical source to ensure their quality.

3 What are the challenges and risks of randomness?

Randomness is not easy to measure or verify. It is possible for a random number generator (RNG) to produce numbers that look random but have hidden biases, correlations, or patterns that could compromise the security of cryptographic operations. For example, a RNG could be faulty, tampered, or compromised by malware, producing weak or predictable numbers that could expose the keys or the data. Alternatively, a RNG could be misused or misconfigured, resulting in insufficient or inappropriate randomness for a given context. For example, a RNG that is suitable for statistical purposes may not be suitable for cryptographic purposes, or a RNG that is designed for one-time use may not be refreshed or reseeded frequently enough.

4 How to use different types of RNGs?

There are different types of RNGs that are suitable for different cryptographic purposes, such as True random number generators (TRNGs), Cryptographically secure pseudo-random number generators (CSPRNGs), and Non-cryptographic pseudo-random number generators (NPRNGs). TRNGs are physical devices that generate random numbers from unpredictable physical sources, such as quantum effects, optical noise, or thermal noise. They are the most secure and reliable type of RNGs, but they are also the most expensive and slowest. They are mainly used for generating long-term keys. CSPRNGs are computational algorithms that generate pseudo-random numbers from a seed and a state, using cryptographic functions. They are designed to produce numbers that are indistinguishable from true random numbers, even by an attacker with unlimited resources. They are faster and cheaper than TRNGs, but they still require a good seed from a TRNG or another CSPRNG. They are mainly used for generating short-term keys. NPRNGs are computational algorithms that generate pseudo-random numbers from a seed and a state, using simple mathematical functions. They are not designed to withstand cryptographic attacks and they may have biases, correlations, or patterns that could be exploited by an attacker. They are the fastest and cheapest type of RNGs, but they are also the least secure and reliable. They are mainly used for non-cryptographic purposes.

5 How to test and evaluate RNGs?

To ensure the quality and security of RNGs, it is important to test and evaluate them regularly, using a variety of methods and criteria. Statistical tests are mathematical tests that check whether the output of a RNG follows a uniform distribution and has no detectable patterns or anomalies. These tests can detect flaws or errors in the RNG design or implementation, but they cannot guarantee the cryptographic strength or unpredictability of the output. Entropy estimation is a measure of the amount of randomness or uncertainty in the output, usually expressed in bits. The higher the entropy, the more random and secure the output. Cryptanalysis is the process of trying to break or compromise a RNG by finding weaknesses or vulnerabilities in its design, implementation, or usage. It is the most rigorous and reliable way to evaluate the security and unpredictability of a RNG, but also the most complex and costly. Examples of statistical tests include NIST Statistical Test Suite, Dieharder Test Suite, and TestU01 Test Suite. Examples of entropy estimation methods are NIST Entropy Assessment, min-entropy, and Shannon entropy.