# Converting OpenFHE parameters to lattice parameters

**URL:** <https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389>\
**Category:** Library Questions\
**Created:** [June 28, 2024, 7:24am UTC](https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389 "2024-06-28T07:24:37Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![andoni](https://avatars.discourse-cdn.com/v4/letter/a/f05b48/32.png) [@andoni](https://openfhe.discourse.group/u/andoni)\
**Post date:** [June 28, 2024, 7:24am UTC](https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389/1 "2024-06-28T07:24:37Z")

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Several posts in the forum suggest using [this lattice estimator](https://github.com/malb/lattice-estimator) to estimate the security level, but how do OpenFHE parameters relate with the ones in the estimator?

| | |
| --- | --- |
| `n` | the dimension of the LWE sample vector (Z/qZ)^n. |
| `q` | the modulus of the space Z/qZ of integers the LWE samples are in. |
| `Xs` | the distribution on Z/qZ from which the LWE secret is drawn |
| `Xe` | the distribution on Z/qZ from which the error term is drawn |

I assume `n` is `BatchSize`, `q` is `ModSize`, and `Xs` is related to `SecretKeyDist`? How can I extract the correct parameters from OpenFHE?

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**Author:** ![ypolyakov](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/ypolyakov/32/47_2.png) [@ypolyakov](https://openfhe.discourse.group/u/ypolyakov)\
**Post date:** [June 30, 2024, 6:20pm UTC](https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389/2 "2024-06-30T18:20:02Z")

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n either corresponds to ring dimension (for RingLWE schemes, like BGV, BFV, abd CKKS) or lattice dimension for (TFHE/FHEW).

q is the maximum modulus used for encryption. It can either be the ciphertext modulus Q or PQ (in hybrid key switching for the schemes in the pke module). See [openfhe-development/src/pke/examples/advanced-real-numbers.cpp at v1.2.0 · openfheorg/openfhe-development · GitHub](https://github.com/openfheorg/openfhe-development/blob/v1.2.0/src/pke/examples/advanced-real-numbers.cpp) for more explanations on Q and QP and how to output them in OpenFHE.

\chi\_e by default uses 3.19 as the distribution parameter. The parameter can be changed (but this is uncommon for OpenFHE applications).

You are correct abour \chi\_s.

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<div class="post-metadata">

**Author:** ![andoni](https://avatars.discourse-cdn.com/v4/letter/a/f05b48/32.png) [@andoni](https://openfhe.discourse.group/u/andoni)\
**Post date:** [July 4, 2024, 3:48am UTC](https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389/3 "2024-07-04T03:48:39Z")

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Thank you for your reply.

My understanding is that OpenFHE uses the Homomorphic Encryption Standard, and the Standard uses this estimator, so the two should be consistent?

I set these parameters in OpenFHE:

```auto
parameters.SetSecretKeyDist(UNIFORM_TERNARY);
parameters.SetMultiplicativeDepth(17);
parameters.SetScalingModSize(33);
parameters.SetScalingTechnique(FLEXIBLEAUTO);
parameters.SetSecurityLevel(HEStd_128_classic);
parameters.SetNumLargeDigits(3);
parameters.SetKeySwitchTechnique(HYBRID);

```

Which gives me:

```auto
ring dimension of 32768
Q = 8811260159874699672336486180796396406243869077359646715352840075916900504413241269164695376404013045805703256871370210283196107117288933764274398464130413565444208105643075409269856534529 (bit length: 622)
P = 1532495540823465179097654646454320532079704299659657217 (bit length: 180)

```

But when I this this on the estimator:

```auto
n=2**15,
q=[Q above]*[P above],
Xs=estimator.nd.NoiseDistribution.UniformMod(3),
Xe=estimator.nd.NoiseDistribution.DiscreteGaussian(stddev=3.19),

```

I get less than 128-bit:

```auto
usvp :: rop: ≈2^106.9, red: ≈2^106.9, δ: 1.004234, β: 366, d: 63121, tag: usvp
dual_hybrid :: rop: ≈2^106.9, red: ≈2^106.9, guess: ≈2^53.2, β: 366, p: 3, ζ: 0, t: 0, β': 366, N: ≈2^43.0, m: ≈2^15.0

```

Any ideia why?

Thank you.

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<div class="post-metadata">

**Author:** ![ypolyakov](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/ypolyakov/32/47_2.png) [@ypolyakov](https://openfhe.discourse.group/u/ypolyakov)\
**Post date:** [July 5, 2024, 8:52pm UTC](https://openfhe.discourse.group/t/converting-openfhe-parameters-to-lattice-parameters/1389/4 "2024-07-05T20:52:50Z")

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It does not seem right. According to Table 1 of [https://homomorphicencryption.org/wp-content/uploads/2018/11/HomomorphicEncryptionStandardv1.1.pdf](https://homomorphicencryption.org/wp-content/uploads/2018/11/HomomorphicEncryptionStandardv1.1.pdf), one can use n=2^{15} up to \log q = 881. Even more refined estimates using the latest lattice estimator (and MATZOV cost model) suggest one can use n=2^{15} up to \log q = 868. So I suspect you are not using the lattice estimator correctly. I am not an expert in the lattice estimator, but I typically specify the uniform ternary distribution not as `Xs=estimator.nd.NoiseDistribution.UniformMod(3)` but using Xs = ND.Uniform(-1,1,n) instead

I would run the test using the following command (I started it on my machine but it is taking too long - I will add it here if I get a result later).

```auto
params1 = LWE.Parameters(n=2^15, q=13503216904043430132322375130323520686726597922127692329036916273626067969416451343520467627876120344481929085215823190265452525616489335894869259632143756391813518830548262609950752986418758718499434014407188181502236786143292803727664545793, Xs = ND.Uniform(-1,1,n), Xe=ND.DiscreteGaussian(3.19))
LWE.estimate(params1)

```