How to support 55 (q_0) + 40 (q_i), i>0 in OpenFHE

Library Questions
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1

Dear developers

Might I seek guidance on how to implement the following security parameters inside OpenFHE and make it able to pass the 128-bit security checking?

I’m using this example to test the bootstrapping openfhe-development/src/pke/examples/advanced-ckks-bootstrapping.cpp at main · openfheorg/openfhe-development · GitHub

I change following configurations

parameters.SetRingDim(1 << 16);

#else
    // All modes are supported for 64-bit CKKS bootstrapping.
    ScalingTechnique rescaleTech = FLEXIBLEAUTO;
    usint dcrtBits               = 40;
    usint firstMod               = 55;
#endif

    cryptoContext->EvalBootstrapSetup(levelBudget, bsgsDim, numSlots, 16);

To make sure the log2(Degree) is <= correct_factor, which is 16.

But value of decrypted results are super far off than the original input value. (The same setup in lattigo would give better performance).

root@f8525abf3eae:/work/build# ./bin/examples/pke/advanced-ckks-bootstrapping 
CKKS scheme is using ring dimension 65536

Input: (0.28982194, 0.36697159, 0.50791944, 0.086401449, 0.66832224, 0.621857, 0.94061381, 0.60058416, ... ); Estimated precision: 40 bits

Initial number of levels remaining: 1
Number of levels remaining after bootstrapping: 11

terminate called after throwing an instance of 'lbcrypto::OpenFHEException'
  what():  /work/src/pke/lib/encoding/ckkspackedencoding.cpp:l.453:Decode(): The decryption failed because the approximation error is too high. Check the parameters. 
Aborted (core dumped)

Might I seek guidance on how to correctly set the parameters correctly to match lattigo’s setup in orion?

Thank you!

Best
Jianming

2

The parameter set you are trying to use is not good for single-iteration CKKS bootstrapping in OpenFHE. Typically, the scaling factor has to be at least 50 to get meaningful accuracy after one bootstrapping, or the two-iteration bootstrapping can be used if you want to achieve a better accuracy for a smaller scaling factor. The CKKS implementations in Lattigo and OpenFHE are based on different low-level algorithms. The CKKS implementation in OpenFHE is based on 2020/1118. The Lattigo CKKS implementation is based on 2020/1203. Each of them has different tradeoffs both in terms of both usability and efficiency.

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