SHA-3 and Keccak

Cryptography · Axiom Academy

Understanding the sponge construction and the next generation of cryptographic hashing 1. NIST Competition and Design Philosophy Following concerns about SHA-1 vulnerabilities, NIST launched the SHA-3 competition in 2007. After five years of cryptanalysis, Keccak was selected in 2012 as SHA-3. Diversification: Avoid single point of failure if SHA-2 is broken Novel Construction: Different mathematical foundation than Merkle-Damgård Future-Proofing: Design resilient to emerging cryptanalytic techniques Sequential compression function applied to padded blocks. Vulnerable to length extension attacks. Absorbing and squeezing phases with permutation function. Naturally resistant to length extension. The sponge construction divides the internal state into two parts: the rate (r) which interacts with input/output, and the capacity (c) which remains internal, providing security. Total state size: b = r + c (for SHA-3: b = 1600 bits) Rate (r): Portion that absorbs input and produces output Capacity (c): Internal security buffer (never directly exposed) Security level: c/2 bits (e.g., c=512 gives 256-bit security) 3. Absorbing and Squeezing Phases The sponge operates in two distinct phases that enable flexible input processing and arbitrary-length output generation. Pad and split message into r-bit blocks XOR each block with the rate portion of state Apply permutation function f after each block Continue until all input is processed Extract r bits from the rate portion

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