The bet that a disguised Reed-Solomon code looks random. It didn't: in 1992 the disguise was stripped in polynomial time.
The idea: McEliece-style encryption needs a code its owner can decode fast, disguised so it looks random. Reed-Solomon codes are easy to decode but very structured: their codewords are values of polynomials. Sidelnikov and Shestakov showed that this algebraic structure survives the disguise, so the hidden code can be read off the public key.
Why it matters: Shows that which code you hide matters, the same question now facing McEliece's Goppa codes.
On the map: ✗ broken 1992 (Sidelnikov-Shestakov)
Niederreiter's 1986 variant of McEliece[1] hid a generalized Reed-Solomon code, which decodes efficiently and gives much smaller keys than Goppa codes. In 1992 Sidelnikov and Shestakov showed[2] how to recover the hidden code's structure from the public key in polynomial time.
The disguise failed. The underlying decoding problem was never solved. Many later attempts to hide other structured codes met the same fate, which is why the Goppa disguise (the amber box next to it) is the one that matters for McEliece today.
If any of these breaks, this breaks too.
If this breaks, these break with it.