I slightly changed the advanced CKKS example by replacing the ring dimension and the security level by

```
parameters.SetRingDim(1 << 16);
parameters.SetSecurityLevel(HEStd_128_classic);
```

Since I chose the security level as 128 bits and N=2^{16}, I should have the integer modulus (the product of the prime factors) with around 1750 bits. However, it seems that it has 2371 bits, which gives me much less than 128 bits of security.

Do you know what is going wrong here? I thought that by using parameters.SetSecurityLevel(HEStd_128_classic), openFHE would choose the parameters correctly already…

**More detail:**

`std::cout << "Parameters " << parameters << std::endl << std::endl;`

outputs this

Parameters scheme: CKKSRNS; ptModulus: 0; digitSize: 0; standardDeviation: 3.19; secretKeyDist: UNIFORM_TERNARY; maxRelinSkDeg: 2; ksTech: HYBRID; scalTech: FLEXIBLEAUTO; batchSize: 0; firstModSize: 60; num LargeDigits: 3; multiplicativeDepth:29; scalingModSize: 59; securityLevel: HEStd_128_classic; ringDim: 65536; evalAddCount: 0; keySwitchCount: 0; encryptionTechnique: STANDARD; multiplicationTechnique: HPS; multiHopModSize: 0; PREMode: INDCPA; multipartyMode: FIXED_NOISE_MULTIPARTY; executionMode: EXEC_EVALUATION; decryptionNoiseMode: FIXED_NOISE_DECRYPT; noiseEstimate: 0; desiredPrecision: 25; statisticalSec urity: 30; numAdversarialQueries: 1

I wrote this function to print the modulus chain:

```
void print_moduli_chain(const DCRTPoly& poly){
int num_primes = poly.GetNumOfElements();
double total_bit_len = 0.0;
for (int i = 0; i < num_primes; i++) {
auto qi = poly.GetParams()->GetParams()[i]->GetModulus();
std::cout << "q_" << i << ": "
<< qi
<< ", log q_" << i <<": " << log(qi.ConvertToDouble()) / log(2)
<< std::endl;
total_bit_len += log(qi.ConvertToDouble()) / log(2);
}
std::cout << "Total bit length: " << total_bit_len << std::endl;
}
```

and when I run it on the public key, that is,

```
const std::vector<DCRTPoly>& ckks_pk = keyPair.publicKey->GetPublicElements();
std::cout << "Moduli chain of pk: " << std::endl;
print_moduli_chain(ckks_pk[0]);
```

I get this

q_0: 1152921504606584833, log q_0: 60

q_1: 576460752395173889, log q_1: 59

q_2: 576460752386129921, log q_2: 59

q_3: 576460752405135361, log q_3: 59

q_4: 576460752395960321, log q_4: 59

q_5: 576460752399106049, log q_5: 59

q_6: 576460752284418049, log q_6: 59

q_7: 576460752347332609, log q_7: 59

q_8: 576460752286253057, log q_8: 59

q_9: 576460752319414273, log q_9: 59

q_10: 576460752289005569, log q_10: 59

q_11: 576460752347201537, log q_11: 59

q_12: 576460752289529857, log q_12: 59

q_13: 576460752315482113, log q_13: 59

q_14: 576460752289923073, log q_14: 59

q_15: 576460752342876161, log q_15: 59

q_16: 576460752298180609, log q_16: 59

q_17: 576460752340123649, log q_17: 59

q_18: 576460752321642497, log q_18: 59

q_19: 576460752337502209, log q_19: 59

q_20: 576460752325705729, log q_20: 59

q_21: 576460752331210753, log q_21: 59

q_22: 576460752329113601, log q_22: 59

q_23: 576460752329900033, log q_23: 59

q_24: 576460752328327169, log q_24: 59

q_25: 576460752329506817, log q_25: 59

q_26: 576460752298835969, log q_26: 59

q_27: 576460752319021057, log q_27: 59

q_28: 576460752300015617, log q_28: 59

q_29: 576460752308273153, log q_29: 59

q_30: 1152921504598720513, log q_30: 60

q_31: 1152921504597016577, log q_31: 60

q_32: 1152921504595968001, log q_32: 60

q_33: 1152921504592822273, log q_33: 60

q_34: 1152921504592429057, log q_34: 60

q_35: 1152921504589938689, log q_35: 60

q_36: 1152921504586530817, log q_36: 60

q_37: 1152921504583647233, log q_37: 60

q_38: 1152921504581419009, log q_38: 60

q_39: 1152921504580894721, log q_39: 60

Total bit length: 2371