Network Security: Random Numbers and Hashing

Network Security: Random Numbers and Hashing

• This document details random numbers and hashing, core concepts in network security.
• It covers true random number generators (TRNGs) and pseudorandom number generators (PRNGs), exploring their uses and characteristics.
• The document also discusses cryptographic hash functions, their requirements, and potential attacks.

Random Numbers

• Randomness Criteria: Two key criteria are uniform distribution (frequency of bits is approximately equal) and independence (no subsequence can be inferred from another).
• Unpredictability Criteria: Forward unpredictability (next output is unpredictable if the seed is unknown), and backward unpredictability (seed is not predictable from any output value).
• Random Number Generation: A diagram illustrates the process, differentiating between true random number generators (TRNGs) drawing from real-world randomness (e.g., thermal noise), and pseudorandom number generators (PRNGs) that produce deterministic sequences using algorithms and seeds.
• TRNG Entropy Sources: Various sources of entropy for TRNGs are listed, including sound/video input, thermal noise, fluctuations in disk drive speeds, and clock timings.

Hashing

• Goal of a Hash Function: To map long messages to short, fixed-size hash values (digests). These are useful for integrity checks and digital signatures.
• Hashing Using XOR: A simplified method initially used for integrity checks and block-level hash function generation; XOR operations across blocks and bits are emphasized. This type is not as complex or secure when compared to more established hashing functions.
• Cryptographic Hash Function Requirements: Emphasis is on variability in input size, fixed output size, and efficiency for hardware and software implementations.
• Security Requirements for Cryptographic Hash Functions: Includes: pre-image resistance (one-way property), 2nd pre-image resistance (weak collision resistance), and strong collision resistance.
• Relationship among Hash Function Properties: A Venn diagram visually shows relationships between collision resistance, 2nd pre-image resistance and preimage resistance.
• Brute-Force Attacks on Cryptographic Hash Functions: Effort for these attacks corresponds to the number of possible hash values; 1st pre-image resistance is 2^m; 2nd pre-image resistance is 2^m; collision resistance is 2^m/2.

PRNGs

• Linear Congruential Generators (LCGs): Details of LCG parameters including modulus (m), multiplier (a), increment (c), and seed (x₀), are provided.
• Blum Blum Shub Generator: The generation method is outlined—initializing with a seed, calculating (x² mod n), and selecting the least significant bit.
• PRNGs using Block Cipher Modes of Operation: Two cipher modes are described (counter mode and output feedback mode), using pseudo-random bits to generate random values.
• PRNG based on RSA: The method uses RSA to encrypt the seed and generate pseudo-random bits in a cyclic fashion, emphasizing the use of encryption/decryption procedures for cryptographic security.

PRNG Comparison:

• Efficiency & Determinism of PRNGs vs. TRNGs: PRNGs are very efficient, deterministic, and periodic; TRNGs are generally inefficient, non-deterministic, and aperiodic.

Hashing Applications

• Message Authentication Code (MAC): Methods of adding MACs to messages are introduced, along with diagrams illustrating the processes involved. Different methods include encrypt-then-MAC, encrypt-and-MAC, and MAC-then-Encrypt.
• Digital Signatures: The use of a hash function and associated cryptographic functions to generate and verify digital signatures is illustrated, using one-way functions.
• Message Digest Implementation (e.g., MD5): Steps involved are outlined (padding to a fixed length, appending length information, initializing a buffer, and processing in blocks).
• MD5 Implementation Details: Specific details about the MD5 algorithm are provided, outlining how parameters are initialized and manipulated for various rounds of processing.
• Iteration Function(f) for SHA-3: Various cryptographic functions used are discussed (theta, rho, pi, chi, iota) focusing on the different functionalities each performs. This function takes various inputs and outputs results based on the current values.
• SHA-3 Sponge Construction: A detailed outline of the SHA-3 structure emphasizing the sponge construction, showing input message processing, the state, and the output value, with illustrations of the absorption and squeezing phases.