CRT Key Exchange

Diffie-Hellman over Z/970200Z. 5 CRT channels = 5 independent key components. CC0.

How It Works

PUBLIC PARAMETERS:
  Ring: Z/970200Z = Z/8 x Z/9 x Z/25 x Z/49 x Z/11
  Generator: g = 137 (ADDRESS). order(137) = 420 = lambda(N).

PROTOCOL (Diffie-Hellman variant):
  1. Alice picks secret a, computes A = g^a mod N
  2. Bob picks secret b, computes B = g^b mod N
  3. Alice sends A (public). Bob sends B (public).
  4. Alice computes S = B^a mod N. Bob computes S = A^b mod N.
  5. S = g^(a*b) mod N = SHARED SECRET.

WHY CRT MAKES THIS INTERESTING:
  - g^a decomposes into 5 INDEPENDENT exponentiations (one per channel)
  - Each channel has its own discrete log problem
  - Attacker must solve ALL 5 simultaneously to recover the secret
  - L=11 channel provides built-in authentication (parity check)
  - CRT structure allows per-channel key derivation

SECURITY NOTE: This is a DEMONSTRATION of the CRT structure applied to
key exchange. Z/970200Z is too small for real cryptographic use.
The PATTERN (CRT-decomposed DH) scales to larger rings.

Key Exchange Demo

Alice

Secret key a:

Bob

Secret key b:

Alice ---[ A = g^a mod N ]---> Bob

Alice <---[ B = g^b mod N ]--- Bob

Channel-by-Channel View

Watch the key exchange happen independently in each CRT channel.

Brute Force Attack Simulation

Try to find Alice's secret from her public key. Shows why CRT helps.

L=11 Authentication Channel

The L=11 channel acts as a built-in parity check / authentication tag.

Key Space Explorer

Map all g^k for k=0..419. The generator visits every element with gcd(element, N) coprime structure.

CC0 1.0 Universal - No Rights Reserved. CRT-based key exchange using Z/970200Z = Z/8 x Z/9 x Z/25 x Z/49 x Z/11.
Diffie-Hellman variant with 5-channel CRT decomposition. Generator g=137, order=420=lambda(N).
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