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BITCOIN_MINING

The document, "Hardware Implementation of Hash Functions," provides an overview of cryptographic hash functions, their properties, common constructions like the Merkle-Damgård model, and applications such as verifying data integrity and generating digital signatures.

**Cryptographic Hash Functions**

  * A hash algorithm takes an arbitrary-length message (M) as input and produces a fixed-size hash or message digest (h) as output, denoted as $h = H(M)$.
  * Key properties include preimage resistance, second preimage resistance, and collision resistance.
  * Common algorithms are MD5 and SHA-2.

**Construction of Hash Functions**

  * The Merkle-Damgård model pads the message, divides it into uniform blocks, and processes them sequentially using a compression function F. The security of the hash function relies on the security of F. MD5 and SHA-2 are designed using this model.
  * A hash function can also be constructed from a symmetric-key cipher, such as DES or AES, using schemes like Davies-Meyer, Matyas-Meyer-Oseas, and Miyaguchi-Preneel. The Whirlpool hash function is constructed with the Miyaguchi-Preneel scheme.

**Hardware Implementation**

  * **MD5:** A Merkle-Damgård-based function with a 512-bit message block and a 128-bit internal hash state. Optimization techniques include pipelining, which can take advantage of data forwarding or the independency among the four rounds. Other optimizations include using Carry Save Adders (CSA) and Block RAM in FPGA implementations. FPGA implementations have reached throughputs up to 32 Gbps.
  * **SHA-2:** Includes variants like SHA-224, 256, 384, and 512. SHA-256 uses a 512-bit message block and eight state variables, while SHA-512 has a 1,024-bit block size with 64-bit words. SHA-2 is generally slower than MD5 due to increased interdependency and complexity. Optimization techniques include Iterative Bound Analysis (IBA) to find the theoretical performance limit, which involves retiming and unfolding a Data Flow Graph (DFG). Loop unrolling has also been applied to SHA-512.
  * **Optimization for Area:** Techniques like folding, the opposite of unrolling, can be used for platforms with limited resources, such as RFID tags.

**SHA-3 Candidates**
The final round of the NIST SHA-3 competition included five algorithms:

  * **Keccak:** Based on sponge construction. It has shown to have higher throughput and smaller area in FPGA implementations compared to other candidates and SHA-2.
  * **BLAKE:** Based on the HAIFA iteration mode with a compression function using a modified version of the stream cipher ChaCha. It has a local wide-pipe internal structure that makes local collisions impossible.
  * **Grøstl:** Based on the wide-pipe design and chop-Merkle-Damgård iterations, applying a final output transformation before truncation. It is based on AES, and its compression function uses two permutations P and Q.
  * **Skein:** A family of hash functions based on the tweakable block cipher Threefish and Unique Block Iteration (UBI). It is designed to be simple, secure, and efficient, excelling on 64-bit processors.
  * **JH:** An iterative hash algorithm with a compression function using generalized AES methodology. It is strong against differential attacks due to a large number of active S-Boxes.

**Performance Comparison**

  * Table 2.8 summarizes the best reported performance, showing that Skein has the highest throughput for ASIC implementations (58 Gbps for Skein-512) and Keccak has the highest throughput for FPGA implementations (8.5 Gbps for Keccak-1600).
  * Four out of the five SHA-3 candidates in the final rounds have implementations with higher throughput than SHA-256.