secure join (cpz)

[cpz2024]

Pull Request

What problem does this PR solve?

Issue Number: Fixed #

Possible side effects?

• Performance:

• Backward compatibility:

[gemini-code-assist]

Code Review

This pull request introduces secure join operations (join_uu_ss, join_uu_vv, and join_un) to the HAL layer, supported by new MPC kernels and extensive unit tests. Key improvements include an O(1) lookup optimization for permutation solving in the MPC utility layer. Feedback identifies a potential shape mismatch bug in the associative_reduce utility, significant code duplication between join variants that warrants refactoring, and several instances of dead or commented-out code that should be addressed for better maintainability.

[gemini-code-assist]

The early return here can lead to a shape mismatch. The function is expected to return a tensor with the last dimension reduced, but when N < 2, it returns the input tensor in unmodified. For example, if in has a shape of (M, 1), the expected output shape is (M), but this will return a tensor of shape (M, 1). This can be fixed by reshaping the output before returning.

Suggested change

	return in;
	return hal::reshape(ctx, in, out_shape);

[gemini-code-assist]

There is significant code duplication between join_uu_ss and join_uu_vv. For example, steps 3 through 7 (permuting tables, comparison, handling payload, and final result aggregation) are nearly identical. This duplication makes the code harder to maintain.

Consider refactoring the common logic into a helper function to reduce duplication and improve maintainability. This helper could be parameterized (e.g., with lambdas) to handle the minor differences between the two functions, such as how values are created (hal::seal vs hal::_p2v).