Security

SHA-256 is a cryptographic hash function that produces a fixed-size 256-bit (32-byte) hash. It is deterministic, collision-resistant, and designed for security-critical applications. !assets/hashing-algorithm-sha256.png How SHA-256 Works Preprocessing: Pad the input to a multiple of 512 bits. Append a 1, then add k zeros, and finally append the original message length (64 bits). Initialize Hash Values: Use constants derived from the fractional parts of square roots of the first 8 primes (eight 32-bit words). Example: h0 = 0x6a09e667, h1 = 0xbb67ae85, .... Process Blocks: Split the padded message into 512-bit blocks. For each block: Expand the block into 64 words using a message schedule. Perform 64 rounds of compression using bitwise operations (e.g., XOR, AND, modular addition). Compression Function A compression function is applied to each block, creating a new hash value. This function involves mixing the bits of the current hash value and the message block. Iteration Repeat the compression function for each block, using the output of each iteration as input for the next. Final Hash: Combine the intermediate hash values to produce the final 256-bit digest. Example: SHA-256 for String “Hello” Input: “Hello” → ASCII 48656C6C6F. Padding: Length = 40 bits (5 bytes). Pad with 1, 407 zeros, and 0000000000000028 (hex for 40 bits). Hash Computation: After processing, the final hash is: 185f8db32271fe25f561a6fc938b2e264306ec304eda518007d1764826381969. Use Cases SHA-256 Cryptographic security in: Digital signatures (SSL/TLS certificates). Password storage (hashed+salted). Blockchain (Bitcoin transactions). File integrity verification (e.g., software downloads). Guarantees: Pre-image resistance, collision resistance.

CRC is an error-detection code used to detect accidental changes to raw data (e.g., during transmission or storage). It works by treating the data as a polynomial and performing polynomial division with a predefined generator polynomial. The remainder of this division becomes the CRC value. How CRC is Calculated Convert data to binary: Treat the data as a sequence of bits. Append zeros: Add n zeros to the end of the data, where n is the degree of the generator polynomial (e.g., CRC-32 uses a 33-bit polynomial, so append 32 zeros). Polynomial division: Divide the data + zeros by the generator polynomial using modulo-2 arithmetic (XOR operations). CRC value: The remainder of this division is the CRC checksum. Example: CRC-8 for String “Hi” Data: “Hi” in ASCII is 01001000 01101001. Generator Polynomial: CRC-8 (e.g., x⁸ + x² + x + 1), represented as 100000111. Append 8 zeros: Data becomes 010010000110100100000000. Perform division: Divide 010010000110100100000000 by 100000111 using XOR. Remainder: Let’s assume the remainder is 00110110 (hex 0x36). Final CRC: 0x36. Use Cases Error detection in: Network protocols (Ethernet, Wi-Fi). Storage systems (hard drives, ZIP files). Quick checksums for small data transfers. Not secure against intentional tampering.