# Vector Component-Wise Modular Multiplications in FHEW/AP & TFHE/GINX Bootstrapping

**URL:** <https://openfhe.discourse.group/t/vector-component-wise-modular-multiplications-in-fhew-ap-tfhe-ginx-bootstrapping/348>\
**Category:** FHE Questions\
**Created:** [February 10, 2023, 9:33am UTC](https://openfhe.discourse.group/t/vector-component-wise-modular-multiplications-in-fhew-ap-tfhe-ginx-bootstrapping/348 "2023-02-10T09:33:19Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Shiuan](https://avatars.discourse-cdn.com/v4/letter/s/3bc359/32.png) [@Shiuan](https://openfhe.discourse.group/u/Shiuan)\
**Post date:** [February 10, 2023, 9:33am UTC](https://openfhe.discourse.group/t/vector-component-wise-modular-multiplications-in-fhew-ap-tfhe-ginx-bootstrapping/348/1 "2023-02-10T09:33:19Z")

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Hi, there!  
Does anyone know why the numbers of “vector component-wise modular multiplications” for FHEW/AP & TFHE/GINX bootstrapping estimated in [https://dl.acm.org/doi/pdf/10.1145/3474366.3486924](https://dl.acm.org/doi/pdf/10.1145/3474366.3486924) would be the numbers marked in the figure below?

Suppose that in this case, the “vector component-wise modular multiplications” is defined as the multiplication of two Ring-LWE ciphertexts. (in evaluation format)

Besides, the matrix size in a Ring-GSW ciphertext is `(2*d_g)*2`, so what I supposed for the estimated number is `4*(1-(1/B_r))*n*d_r*d_g` and `4*n*|U|*d_g` (the monomial multiplications are not calculated in TFHE/GINX case).

I also traced the code in the function AddToAccCGGI but still not figure out the reason for the difference between my estimated numbers and the marked numbers.

![image](https://canada1.discourse-cdn.com/flex031/uploads/openfhe/original/1X/d0e3475d1e1c181d83374c072269b03b5b344ab6.png)

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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:** [February 12, 2023, 11:23pm UTC](https://openfhe.discourse.group/t/vector-component-wise-modular-multiplications-in-fhew-ap-tfhe-ginx-bootstrapping/348/2 "2023-02-12T23:23:43Z")

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Hi @Shiuan,

You are correct. These are typos in the paper (note that these expressions were not used in the complexity analysis/comparison). For FHEW/AP, there should be an extra factor of 2. Same for TFHE/GINX. So your expressions are accurate. Thanks for pointing this out.