Computer Security and Cryptography

15.9 THE MENEZES – VANSTONE ELLIPTIC CURVE CRYPTOSYSTEM

The system we describe appears in Menezes and Vanstone [1993]. Let p > 3 be a prime and _p(a, b) the elliptic group generated by y² = x³ + ax + b. The Menezes – Vanstone (public-key) elliptic curve cryptosystem is a variant of El Gamal's encipherment system to be described in Chapter 17. Its keys are

Private Key:

Public Keys: K₁, K₂ ∈ _p(a, b), K₂ = K_PK₁ ∈ _p(a, b).

The encipherment and decipherment processes are

Encipherment – Plaintext: .

1. Choose a secret (session key) .
2. Compute y₀ = k_SK₁ ∈ _p(a, b).
3. Compute (z₁, z₂) = k_SK₂ ∈ _p(a, b).
4. Compute .
5. Compute .

Ciphertext: .

Decipherment – Ciphertext: ,

1. Compute K_Py₀ = K_Pk_SK₁ = k_SK_PK₁ = k_SK₂ = ...