Non-invertible key exchange protocol

Luis Adrian Lizama-Perez
2020 SN Applied Sciences  
We investigate a cryptosystem through what we call non-invertible cryptography. As a result of a continuous refinement process, we present a new key exchange method to establish a secret key between two remote parties. Non-invertible KEP is supported by Euler's theorem as RSA, it uses exponentiation to exchange a secret key as Diffie-Hellman, and it encrypts/decrypts through invertible multiplication as ElGamal. This method is public key; it allows secret key exchange and performs secret
more » ... cation. Most remarkably, since it does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured, non-invertible KEP becomes a promising candidate to protect communication in the quantum era. By contrast, the algorithm is supported on indistinguishability of public key and ciphertext so it achieves perfect secrecy. The protocol demonstrates minimum required time for encryption/ decryption processes when is compared with the main public key algorithms as Diffie-Hellman, ElGamal or RSA. Even so, it is possible to continue using the algorithms RSA, ECDSA and DH, since their properties has been studied over the past years. The downside to this approach is that it can lead to increase the size of the keys to an impractical level in the quantum era. However, although quantum principles have threatened the security of major cryptographic systems, they have raised a new technology known as quantum key distribution (qkd) that allows remote secret key establishment [2, 3] . Post-quantum cryptosystems under evaluation for public-key quantumresistant [4] include cryptography based on lattices, multivariate-based, hash-based [5, 6] or code-based [7]. We will describe them in the next section, for now let us briefly summarize some of the main algebraic cryptosystems used today which are based on integer factoring and discrete logarithm computational problems: 1. The key exchange protocol introduced by Diffie and Hellman [8]. The asymmetric key encryption algorithm for public-key cryptography of Taher ElGamal [9]. Both of them are based on the Diffie-Hellman assumption. 2. Cryptosystems that rely on the difficulty of the integer factorization problem: the RSA method for obtaining digital signatures by Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman [10]. Also, it can be cited the digitalized signatures by Rabin, Michael O Rabin [11]. 3. Schemes based on the discrete logarithm with elliptic curve groups known as ECC developed by Miller and Koblitz [12, 13].
doi:10.1007/s42452-020-2791-3 fatcat:u3owvhttb5du5cbmx5qzuqex6y