Computational cryptography › Public-key encryption and key exchange › Post-quantum public-key › Codes and noisy equations
PUBLIC-KEY ENCRYPTIONPrimitiveHistorically broken

Niederreiter with Reed-Solomon codes

In plain words

A 1986 code-based encryption scheme that hid a Reed-Solomon code, broken in 1992.

The idea: Instead of encoding the message and adding errors (McEliece), Niederreiter turns the message into the error pattern itself and publishes a short summary of it (the syndrome). The owner, who can decode, recovers the errors and so the message. The weakness was the choice of code, not the construction.

Why it matters: Its construction survives in Classic McEliece, which hides a different kind of code.

The details

On the map: ✗ proposed 1986

Harald Niederreiter's 1986 code-based encryption, the "dual" form of McEliece: the message is encoded as the error pattern itself, and the ciphertext is its syndrome. It is as secure as McEliece for the same code[1] and gives shorter ciphertexts.

The construction lives on: Classic McEliece is built in Niederreiter form[2], with binary Goppa codes. The Reed-Solomon version was broken in 1992.

Rests on

If any of these breaks, this breaks too.

If it falls

If this breaks, these break with it.

Nothing on the map depends on it: it is an end point, something people use directly.

References

  1. Yuan Xing Li, R.H. Deng and Xin Mei Wang. On the equivalence of McEliece's and Niederreiter's public-key cryptosystems. IEEE Transactions on Information Theory, 1994. doi:10.1109/18.272496
  2. Martin R. Albrecht, Daniel J. Bernstein, Tung Chou and Carlos Cid. Classic McEliece: conservative code-based cryptography. Classic McEliece team, 2022. classic.mceliece.org