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Verifiable Delay Functions (VDF) & Wesolowski Proofs Studio
Model time-lock cryptographic puzzles and non-parallelizable sequential computing. Simulate modular squaring chains \(x^{2^T} \pmod N\), Wesolowski \(O(1)\) succinct proofs, Fiat-Shamir prime challenges, and sub-millisecond verification.
Time-Lock Crypto
Wesolowski Proofs
O(1) Verification
Non-Parallelizable
Number of non-parallelizable modular squarings
Mathematical group with hidden order \(|G|\)
Zero-knowledge succinct argument of delay
Evaluator sequential multiplier hardware class
VDF Sequential Evaluation & Verification Pipeline
Sequential Steps
262,144
T = 2^18 Squarings
Evaluation Latency
4.77 sec
Enforced Sequential Delay
Verification Latency
0.64 ms
7,450x Asymmetric Speedup
Proof Size (π)
256 Bytes
1 Group Element (O(1))
Parallelism Gain
1.00x
0% GPU Speedup (Safe)
Fiat-Shamir Prime (ℓ)
128-bit
Soundness 2^-128
Live Wesolowski Proof Mathematical State Trace
| Cryptographic Parameter | Mathematical Symbol | Value / Formula | Role in Security Protocol |
|---|---|---|---|
| Input Entropy Seed | x ∈ G | 0x7a89f3...b4c2 | Beacon seed from RANDAO or lottery hash |
| Sequential Output | y = x^(2^T) mod N | 0x3d91ea...7f01 | Result of 262,144 non-parallelizable squarings |
| Fiat-Shamir Prime | ℓ = H_prime(x, y) | 0xFFFFFFFFFFFF...C7 | Random challenge prime drawn from random oracle |
| Quotient & Remainder | 2^T = q · ℓ + r | q = ⌊2^T / ℓ⌋, r = 2^T mod ℓ | Long integer polynomial division |
| Succinct Proof | π = x^q mod N | 0x82f091...a54e (256 bytes) | Verifier verifies: π^ℓ · x^r ≡ y (mod N) in 0.64 ms |
Production VDF Implementation (Rust & Python)
VDF Cryptographic Design & Attack Resistance
1. Strict Non-Parallelizability
Unlike PoW mining (hash guessing), where 1,000 GPUs compute 1,000 hashes in parallel, calculating \(x^{2^T} = ((((x^2)^2)^2)...)\) has an inherent depth of \(T\). Parallelization yields 0 speedup because step \(k+1\) cannot start until step \(k\) is fully resolved.
2. Soundness Under Unknown Order
If an attacker knows the group order \(\phi(N)\), they can compute \(e = 2^T \bmod \phi(N)\) via Euler's totient theorem and evaluate \(x^e \pmod N\) in \(O(\log T)\) time! Hence, the RSA trusted setup must discard \(p\) and \(q\), or Class Groups with mathematically intractable orders must be used.
3. Sub-Millisecond Verification
The verifier only performs two fast exponentiations \(\pi^\ell\) and \(x^r\) mod \(N\). This asymmetric property allows smart contracts on Ethereum L1 to verify a multi-hour proof in a single EVM transaction consuming fewer than 120,000 gas.
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