🧠Algorithms

Tychi Wallet leverages a suite of backend-driven algorithms to streamline Web3 operations while maintaining maximum decentralization, efficiency, and user privacy. These algorithms power critical infrastructure such as gas fee abstraction, cross-chain bridging, and secure recovery.

🔁 Multi-Chain Bridging Protocol

Tychi Wallet supports token mobility across 50+ blockchains using a deterministic bridging system combining:

• Relay Node Validation: Confirms lock events on source chains before executing mint/release.

• Merkle Proof Verification: Proves transaction inclusion within source chain blocks.

• Signature Authentication: Uses cryptographic signing to authorize bridge actions.

• Liquidity Routing: Maintains on-demand liquidity through integrated liquidity sources.

• Smart Contract Enforcement: Manages token minting, burning, and lock mechanics.

Formulaic Trigger:

T_B = T_A - F
F = T_A * r

Where:

• T_A: Tokens locked

• T_B: Tokens released

• F: Fee deducted as T_A * r, where r is fee rate

🌐 Components of Multi-Chain Bridging

Component	Purpose
Optimized Relay Nodes	Enhance transaction speed and reliability
Blockchain Bridges	Facilitate secure asset movement between chains
Merkle Proofs	Verify transaction integrity during cross-chain execution
Cryptographic Signatures	Ensure authenticity and tamper-proof communication
Automated Liquidity Pools	Maintain sufficient liquidity across chains
Smart Contracts	Handle locking, minting, and token verification processes automatically

⛽ Gas Fee Optimization – AI Powered

Tychi Wallet features an AI-based system that continuously monitors network congestion trends to suggest the optimal time to transact—when gas fees are lower and network usage is minimal.

✅ Privacy Focused: This logic uses historical and public data, never tracking the user’s transaction history.

🛠️ Gas Fee Abstraction Flow Diagram

---

💱 Fee Abstraction Engine

Tychi allows users to pay gas fees using TYI or BNB—removing the burden of managing native tokens.

Conversion Workflow

1. Input: User pays with TYI or BNB

2. Chain Detection: System identifies the origin blockchain

3. Gas Estimation: Calculates required native token fee

4. Price Aggregation: Fetches rates from Chainlink, CoinGecko, CoinMarketCap

5. Slippage Check: Applies tolerance formulas to validate risk

6. Conversion: Executes off-chain via internal or third-party liquidity sources

7. Finalization: Submits transaction using converted native token

🔁 This creates a frictionless, chain-agnostic gas payment system.

🧮 Slippage Calculation

effectivePrice = priceFeedAvg * (1 ± ε)

Where:

• priceFeedAvg is the median of prices from Chainlink, CoinMarketCap, and CoinGecko

• ε = predefined slippage threshold (1-2%), adjusted by volatility metrics

The abstraction system only proceeds when:

priceChainlink - priceOther| < ε * priceFeedAvg

This ensures consistent pricing without user overpayment.

🔐 Social Recovery Algorithm

Tychi’s recovery module utilizes Shamir’s Secret Sharing. A user's private key is split across n guardians. A threshold t (e.g. 3 of 5) must approve to reconstruct the key.

Recovery Flow:

1. User initiates recovery

2. Guardians confirm identity and submit encrypted shares

3. Backend reconstructs key securely

4. Key is returned to user in encrypted format

Model Basis:

Key = SSS(k, t, n)

Where:

• SSS = Shamir’s Secret Sharing

• k = private key

• t = threshold required

• n = total guardians

All shares are encrypted and transported over secure channels.