Introducing a Novel Quantum-Resistant Secret Key Establishment Method

TL;DR

The paper addresses the vulnerability of classical cryptography to quantum attacks by proposing a quantum-resistant secret key establishment method that does not rely on factoring or discrete logarithms. It introduces a public-key pair $(P_i,Q_i) = (g^{x_i+z_i}, g^{y_i+z_i})$ in a prime field with private keys $(x_i,y_i,z_i)$ and derives a shared secret $k_{js} = (g_{ij})^{w_i w_j} = g^{w_i w_j(x_i x_j+y_i y_j)} mod p$, ensuring both parties arrive at the same key. The authors provide security analyses across public-key, channel, and secret-key perspectives, arguing resilience against quantum adversaries and demonstrating Perfect Forward Secrecy (PFS). They also discuss practical considerations, including key-size efficiency, highlighting compact public/private keys and the feasibility of deployment. Overall, the work claims a viable, quantum-resistant alternative for secure key establishment with forward secrecy and favorable key size characteristics.

Abstract

We present a novel approach to secret key establishment that appears to be resistant to currently known quantum cryptanalytic algorithms. This quantum resistance arises because the security of our method does not rely on the difficulty of integer factorization or the discrete logarithm problem. Based on the analyses of Alice's public key, the communication exchange between Alice and Bob, and the scenario where Bob behaves as Eve, we can conclude that, even if Eve has access to a quantum computer capable of solving discrete logarithms, she is unable to determine Alice's private key. Additionally, our approach achieves Perfect Forward Secrecy (PFS), ensuring that the security of previously used keys is not compromised by any key that becomes compromised. Notably, our system offers competitive public and private key sizes compared to those currently available.

Figures (4)

• Figure 1: Diffie-Hellman protocol: Both keys are identical ($k_{ab} \equiv k_{ba}$) because modular exponentiation follows the same rules as conventional exponentiation.
• Figure 2: Elgamal cryptosystem: $P_b$ is Bob's public key, defined as $g^{x_b} \mod p$. Using $y_a$ as a different random value for each message, Alice sends an encrypted message by multiplying $m$ by $k_s$. Bob retrieves $m$ by applying the inverse of $k_s$, denoted as ${k_s}^{-1}$.
• Figure 3: A public key exchange precedes key establishment.
• Figure 4: Derivation of the secret key. Here, ${g}_{ab}$ represents ${g}^{x_a x_b + y_a y_b}$.