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Column openings in linear-code-based PCSs #65

@Antonio95

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@Antonio95

This issue is related to Arkworks' poly-commit library and not our codebase, but since we make crucial use of those PCSs here, I open this issue as a reminder.

As @mmagician noticed, the indices of columns opened in linear-code-based PCSs (Brakedown, Ligero) are not checked to be unique, potentially compromising (at least formally - and perhaps practically in the case of Brakedown) soundness. The fix should be relatively easy for a potentially non-negligible performance costs (searching each generated index in the list of previously generated ones). Although a separate discussion, performance would likely take a major hit in recursive settings.

@mmagician Let me know if you would prefer me to remove this issue from this repo, open it in Arkworks, both or neither :)

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