v4v-4k: A 32,768-Bit Memory-Hard Key Derivation Function with 4096-Block Pyramid Architecture.

Abstract

Abstract This paper presents V4V-4K, a 32,768-bit memory-hard cryptographic Key Derivation Function (KDF) engineered around a native Add-Rotate-Xor (ARX) core architecture with a 4096-block pyramid network structure. Designed to mitigate parallel hardware attacks, GPU cracking rigs, and side-channel vulnerabilities, V4V-4K combines deep sequential memory filling, non-linear memory looping, multi-stride permutation rounds with 12 main rounds and 256 golden rounds, and an overarching binary pyramid architecture of 4096 interconnected blocks of 4096 bytes each. Through an exhaustive empirical validation suite, including Shannon entropy analysis, NIST SP 800-22 statistical evaluations (MonoBIT, Runs), Strict Avalanche Criterion (SAC), differential propagation tests, linear and non-linear cryptanalysis, Pearson correlation, collision resistance, length-extension resistance, and comprehensive fuzzing, V4V-4K demonstrates near-ideal avalanche characteristics of 49.99% to 50.41%, complete bit diffusion across 32,768 bits within 3 rounds, entropy of 7.9590 bits per byte, and absolute immunity against collisions and length-extension attacks. Comparative analysis against industry-standard KDFs including Argon2id, scrypt, bcrypt, and PBKDF2 establishes V4V-4K as a superior solution in terms of memory-hardness, ASIC/GPU resistance, side-channel immunity, and cryptographic diffusion. The 1024-bit salt, 256-word × 128-bit state, and dynamic pyramid structure provide unprecedented resistance to parallel hardware acceleration while maintaining deterministic consistency through secure memory zeroization. Comparative Table Feature, V4V-4K, Argon2id, scrypt, bcrypt, PBKDF2 Block Size, 4096 bytes, 1024 bytes, 1024 bytes, 512 bytes, 64 bytes Word Size, 128 bits, 64 bits, 64 bits, 32 bits, 64 bits Memory-Hard, Yes, Yes, Yes, No, No ASIC/GPU Resistant, Yes, Yes, Yes, No, No ARX Core, Yes, No, Yes, No, No Rounds, 12 + 256, 3 + passes, 1 + passes, 2^rounds, iterations Salt Size, 1024 bits, 128 bits, 128 bits, 128 bits, 128 bits Zeroize, Yes, Yes, Yes, Yes, Yes Unique Value of V4V-4K Feature, V4V-4K, Argon2id, scrypt, bcrypt, PBKDF2 128-bit ARX, Yes, No, No, No, No Binary Pyramid, Yes, No, No, No, No 128-bit Golden Ratio, Yes, No, No, No, No Footer Verification, Yes, No, No, No, No 1024-bit Salt, Yes, No, No, No, No SAC Validated, Yes, No, No, No, No.