Error-correcting codes were invented to clean static noise from radio broadcasts; Elwyn Berlekamp and Robert McEliece proved that deliberately scrambling error-correcting codes creates an NP-complete cryptographic lock. Published in 1978 and sidelined for decades due to large key sizes, the McEliece code-based cryptosystem has never been broken in nearly fifty years, standing today as NIST’s premier quantum-resistant encryption standard (Classic McEliece).

In 1978, when public-key cryptography was born, every system relied on prime number mathematics that could theoretically be reversed by quantum computers. Cryptographers needed a totally different branch of mathematics with proven, unbreakable computational hardness.
Information theorists realized that the math used to clean static noise from satellite radio could be turned into a lock. They proved that decoding a scrambled linear radio code is mathematically NP-complete—creating a system where the receiver can effortlessly remove injected noise using a private mathematical secret, while eavesdroppers face an impossible static maze.
While RSA dominated the commercial web, McEliece's code-based cipher quietly survived five decades of attacks. By resisting Shor’s quantum algorithm completely, by offering sub-microsecond decryption speeds, and by anchoring NIST’s post-quantum security suite, code-based cryptography protects government and financial networks.
On the inherent intractability of certain coding problems (Corresp.)
MEMBER, IEEE, AND HENK C. A. V~ TILBORG The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.
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