Range Proof (Bit Decomposition)

Prove v ≥ T by showing delta = v - T is non-negative. A non-negative value can be written as a sum of bits, each 0 or 1. The full ZK version commits to each bit; here we visualize the decomposition.

Inputs

v (your value) T (threshold) num_bits

For the full check (random blinding per bit, Pedersen commitments, Schnorr-OR per bit, homomorphic product), set g, h, p below and run Full ZK check — same path as Bit-OR demo + Ex3.

g h p

Decomposition

delta = v − T —

bits (LSB first) —

Σ b_i · 2ⁱ —

—

Why this proves v ≥ T

BigUint arithmetic refuses to compute v - T when v < T (would underflow). So just being able to produce delta and its bit decomposition is the proof. In a true ZK protocol, the prover commits to each bit, and the verifier checks the homomorphic recombination without ever seeing the bits.

Range Proof (Bit Decomposition)

Inputs

Decomposition

Full ZK pipeline (browser)

Why this proves v ≥ T