Enable field extension #4
Description
STARK security is defined in the ethSTARK paper under the security section. If you dig into the details, you'd see that in order to achieve an adequate amount of security we have to enable field extensions. This is because the field Miden uses only provides around 63 bits of security. With the extension, it won't be an issue.
You can in the codebase some references to "TODO FIELD_EXTENSION" which marks some of the areas where additional code needs to be added in order to support it.
A few useful code pointers:
- In the reference verifier code implemented in Winterfell, you can see the composer has to take into account field extensions: https://github.com/starkoracles/winterfell/blob/a2c9e8a21f66d6cba8d4073775e52406efdcceb2/verifier/src/composer.rs#L87.
- This is currently not implemented in our verifier: https://github.com/starkoracles/starknet-miden-verifier/blob/dbc5fea0d60d4b7e035df163bd631092b885847e/src/stark_verifier/composer.cairo#L81