add readme

README.md

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-Circomkit template
+# HKDF Circuit Implementation
+
+## Overview
+
+Implementation of HKDF (HMAC-based Key Derivation Function) using SHA-256 in Circom 2.1.8. The circuit follows [RFC 5869](https://www.rfc-editor.org/rfc/rfc5869.html)'s extract-then-expand paradigm.
+
+
+## Components
+
+### 1. HKDFSha256 Template
+Main template that combines Extract and Expand operations.
+
+```circom
+template HKDFSha256(s, i, k, m, n)
+```
+
+Parameters:
+- `s`: Salt length
+- `i`: Info length
+- `k`: Input key length
+- `m`: Number of output keys
+- `n`: Output key length
+
+Signals:
+- Input: `salt[s]`, `info[i]`, `key[k]`
+- Output: `out[m][n]`
+
+### 2. Extract Template
+Implements HKDF-Extract using HMAC-SHA256.
+
+```circom
+template Extract(s, k)
+```
+
+Parameters:
+- `s`: Salt length
+- `k`: Key length
+
+Signals:
+- Input: `salt[s]`, `key[k]`
+- Output: `out[32]` (fixed 32-byte SHA-256 output)
+
+### 3. Expand Template
+Implements HKDF-Expand using HMAC-SHA256.
+
+```circom
+template Expand(i, k, m, n)
+```
+
+Parameters:
+- `i`: Info length
+- `k`: Key length (PRK)
+- `m`: Number of output keys
+- `n`: Length per output key
+
+Signals:
+- Input: `info[i]`, `key[k]`
+- Output: `out[m][n]`
+
+## Implementation Details
+
+### Extract Operation
+1. Uses HmacSha256 component
+2. Sets input key material as message
+3. Uses salt as HMAC key
+4. Produces 32-byte PRK (Pseudorandom Key)
+
+### Expand Operation
+1. Calculates required rounds: `rounds = ceil((m*n)/32)`
+2. First round:
+   - Message = info || 0x01
+   - Key = PRK
+3. Subsequent rounds:
+   - Message = prev_hash || info || counter
+   - Key = PRK
+   - Counter increments each round
+4. Output mapping:
+   - Maps expanded keys to output array
+   - Uses byte-wise indexing for proper output arrangement
+
+### Signal Flow
+```
+Input Key Material → Extract → PRK → Expand → Output Key Material
+        ↑              ↑        ↑       ↑
+       Salt           HMAC    Info    HMAC[rounds]
+```
+
+## Dependencies
+
+- HMAC circuit (`./hmac/circuits/hmac.circom`)
+- Circom 2.1.8 or higher