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.