google / google/heir

BGV: Support the original BGV scheme parameter generation

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dialect: bgv
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MLIR
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Description

In #1379, the primes are generated to be congruent to 1 mod `m`, the cyclotomic order. However, this will introduce scaling factor for messages and we have to do scaling factor management (see #1169).

We may also support the original BGV scheme that primes are congruent to 1 mod `m` and mod `t`. Openfhe supports the generation in FIXEDMANUAL mode by mod `lcm(m, t)`

Code ref: https://github.com/openfheorg/openfhe-development/blob/7b8346f4eac27121543e36c17237b919e03ec058/src/pke/lib/scheme/bgvrns/bgvrns-parametergeneration.cpp#L501-L514

We would also need to track which variant we are using in `bgv::SchemeParam`

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