# Evaladd does not add after EvalMult

**URL:** <https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560>\
**Category:** FHE Questions\
**Created:** [May 17, 2023, 7:10am UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560 "2023-05-17T07:10:43Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![Cesare](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@Cesare](https://openfhe.discourse.group/u/Cesare)\
**Post date:** [May 17, 2023, 7:10am UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/1 "2023-05-17T07:10:43Z")

</div>

I’m using the CCKS algorithm. After each Evalmult, I have to rescale so that EvalAdd will work. But the plaintext I multiply may be a unit vector(only one element is 1). If I rescale every time after a plaintext-ciphertext multiplication, it seems to waste the multiplication depth.  
In my opinion, homomorphic addition should work after homomorphic multiplication, especially for plaintext-ciphertext multiplication.  
I want to know why EvalAdd doesn’t work after Evalmult. Thanks in advance!

---

<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:** [May 18, 2023, 10:10pm UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/2 "2023-05-18T22:10:22Z")

</div>

Could you post the full example, including the parameters you are using? It is hard to understand what specifically you are asking about.

---

<div class="post-metadata">

**Author:** ![Cesare](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@Cesare](https://openfhe.discourse.group/u/Cesare)\
**Post date:** [May 21, 2023, 6:39am UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/3 "2023-05-21T06:39:35Z")

</div>

I apologize for my expression. This is an example.

```auto
    uint32_t multDepth = 2;
    uint32_t scaleModSize = 40;
    uint32_t batchSize = 128;
    ScalingTechnique rescaleTech = FIXEDMANUAL;
// 
    CCParams<CryptoContextCKKSRNS> parameters;
    parameters.SetMultiplicativeDepth(multDepth);
    parameters.SetScalingModSize(scaleModSize);
    parameters.SetBatchSize(batchSize);
	parameters.SetScalingTechnique(rescaleTech);

    CryptoContext<DCRTPoly> cc = GenCryptoContext(parameters);
    cc->Enable(PKE);
    cc->Enable(KEYSWITCH);
    cc->Enable(LEVELEDSHE);
    auto keys = cc->KeyGen();

	std::vector<double> x1 = {0.25, 0.5, 1, 2, 4};
    std::vector<double> x2 = {4, 2.0, 1.0, 0.5, 0.25};
	
    Plaintext ptxt1 = cc->MakeCKKSPackedPlaintext(x1);
    Plaintext ptxt2 = cc->MakeCKKSPackedPlaintext(x2);

    auto c1 = cc->Encrypt(keys.publicKey, ptxt1);
    Ctx c3;
	c3 = cc->EvalMult(c1, ptxt2);
    Ptx ptxt3;
    cc->Decrypt(keys.secretKey, c3, &ptxt3);
	ptxt3->SetLength(8);
	std::cout << ptxt3 <<std::endl;
	c3 = cc->EvalAdd(c3, ptxt1);
    cc->Decrypt(keys.secretKey, c3, &ptxt3);
	ptxt3->SetLength(8);
	std::cout << ptxt3 <<std::endl;

	c3 = cc->EvalMult(c1, ptxt2);
	cc->RescaleInPlace(c3);
    cc->Decrypt(keys.secretKey, c3, &ptxt3);
	ptxt3->SetLength(8);
	std::cout << ptxt3 <<std::endl;
	c3 = cc->EvalAdd(c3 ,ptxt1);
    cc->Decrypt(keys.secretKey, c3, &ptxt3);
	ptxt3->SetLength(8);
	std::cout << ptxt3 <<std::endl;

```

I think the fourth and second outputs should be the same. But the output is

```auto
(1, 1, 1, 1, 1, -2.09141e-10, 4.27276e-10, -9.01037e-10, ... ); Estimated precision: 30 bits

(1, 1, 1, 1, 1, -5.85196e-10, -9.59139e-10, -3.23153e-10, ... ); Estimated precision: 30 bits

(1, 1, 1, 1, 1, 2.80713e-10, 3.63784e-10, -1.00066e-09, ... ); Estimated precision: 30 bits

(1.25, 1.5, 2, 3, 5, -8.32482e-10, 2.66915e-10, 8.11207e-10, ... ); Estimated precision: 30 bits

```

EvalAdd without rescaling did not work after EvalMult.

---

<div class="post-metadata">

**Author:** ![Cesare](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@Cesare](https://openfhe.discourse.group/u/Cesare)\
**Post date:** [May 22, 2023, 8:06am UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/4 "2023-05-22T08:06:03Z")

</div>

The Ctx is the Ciphertext and the Ptx is the Plaintext.

```auto
using Ctx = lbcrypto::Ciphertext<lbcrypto::DCRTPoly>;
using Ptx = lbcrypto::Plaintext;

```

---

<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:** [May 22, 2023, 9:48pm UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/5 "2023-05-22T21:48:02Z")

</div>

The `FIXEDMANUAL` mode does not do automated rescaling/modulus switching (see Page 6 of [https://eprint.iacr.org/2022/915.pdf](https://eprint.iacr.org/2022/915.pdf)). This is why the second output is `incorrect` (behavior by design). All other modes automatically call rescaling. If you want to do it without rescaling (in this example), `MakeCKKSPackedPlaintext` should be called the noise scale degree of 2 (second parameter = 2 should be supplied).

Yes, the rescaling is not required after a plaintext-ciphertext multiplication (in contrast to ciphertext-ciphertext multiplication, where the approximation error grows very fast if no rescaling is applied). However, there is still an increase in the noise growth even for a ciphertext-plaintext multiplication. See the intro of [Approximate Homomorphic Encryption with Reduced Approximation Error](https://eprint.iacr.org/2020/1118) for more information.

---

<div class="post-metadata">

**Author:** ![Cesare](https://avatars.discourse-cdn.com/v4/letter/c/dfb087/32.png) [@Cesare](https://openfhe.discourse.group/u/Cesare)\
**Post date:** [May 23, 2023, 3:55am UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/6 "2023-05-23T03:55:58Z")

</div>

Thanks for your explanation!  
In simple terms, the plaintext that is evaluated with fresh ciphertext is \Delta\cdot m. And the plaintext that is evaluated with ciphertext after k times EvalMult is \Delta^{k+1} \cdot m.  
Is there a problem with my understanding?

---

<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:** [May 26, 2023, 6:24pm UTC](https://openfhe.discourse.group/t/evaladd-does-not-add-after-evalmult/560/7 "2023-05-26T18:24:14Z")

</div>

Yes, this is correct.