A McEliece-type Cryptosystem using a Random Inverse Matrix and an Error Vector with Large Hamming Weight

The McEliece cryptosystem has emerged as a finalist in Round 4 of the NIST Post-Quantum Cryptography (PQC) competition. The Shor algorithm underscores the potential vulnerability of cryptographic primitives to quantum attacks. The McEliece cryptosystem has been shown to be resistent to these attacks. Currently, no known attack is capable of breaking this cryptosystem in polynomial time. Despite this, the McEliece cryptosystem has received little attention in practical applications primarily due to the large public key size. Recent progress to address this issue has reduced the size of the public key by approximately $\mathbf{3 8 \%}$. This paper introduces a McEliece-type cryptosystem which incorporates a large weight error vector and a random inverse matrix to improve security. A key generation algorithm is presented that employs a random matrix to construct the public and private keys. This increases the difficulty of attacks and allows for smaller key sizes than with the McEliece cryptosystem.