Interactive E2EE (Diffie-Hellman & Signal Double Ratchet) Simulator (2026)

While modular exponentiation (computing A = g^a mod p) takes only milliseconds using square-and-multiply, reversing the operation to find the private exponent 'a' from g^a mod p is the Discrete Logarithm Problem (DLP). For a 2048-bit prime or Curve25519 elliptic curve (ECDLP), no known classical algorithm can recover 'a' in feasible time.

Base Diffie-Hellman does not authenticate who generated a public key. If an active attacker (Mallory) sits on the network or server, she can intercept Alice's public key A, replace it with her own public key M, and send M to Bob. Alice shares secret S1 with Mallory, and Mallory shares secret S2 with Bob—allowing Mallory to decrypt, read, and re-encrypt every message unless Alice and Bob compare out-of-band Safety Numbers.

Designed by Trevor Perrin and Moxie Marlinspike, the Double Ratchet combines two cryptographic ratchets: (1) a Symmetric-Key KDF Ratchet that hashes the Chain Key (CK_n+1 = HMAC(CK_n)) after every single message to derive a throwaway Message Key (MK_n), and (2) an Asymmetric Diffie-Hellman Ratchet that attaches a new ephemeral DH public key whenever a party replies, feeding a fresh DH secret into the Root Key.

Forward Secrecy guarantees that if an attacker steals your current keys today, they cannot go backward to decrypt past recorded ciphertexts because the old Chain Keys and Message Keys were overwritten via one-way HMAC functions. Post-Compromise Security (PCS) guarantees that if an attacker steals your session state today, as soon as Alice and Bob exchange one new ephemeral Diffie-Hellman reply, the Root Key is re-seeded with fresh entropy that locks the attacker out of future messages.

Because Shor's algorithm on a sufficiently powerful quantum computer could solve elliptic-curve discrete logarithms (X25519), modern E2EE protocols now hybridize classical X25519 Diffie-Hellman with a post-quantum Key Encapsulation Mechanism (ML-KEM / Kyber-1024) so an attacker must break both lattice cryptography and elliptic curves simultaneously.