# Number of Limbs in CKKS-RNS

**URL:** <https://openfhe.discourse.group/t/number-of-limbs-in-ckks-rns/957>\
**Category:** Library Questions\
**Created:** [December 7, 2023, 12:05pm UTC](https://openfhe.discourse.group/t/number-of-limbs-in-ckks-rns/957 "2023-12-07T12:05:36Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![jomivaan](https://avatars.discourse-cdn.com/v4/letter/j/53a042/32.png) [@jomivaan](https://openfhe.discourse.group/u/jomivaan)\
**Post date:** [December 7, 2023, 12:05pm UTC](https://openfhe.discourse.group/t/number-of-limbs-in-ckks-rns/957/1 "2023-12-07T12:05:36Z")

</div>

Hello,  
How is the number of limbs decided in OpenFHE? Is there a paper with a theoretical explanation?  
Thank you

---

<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:** [December 7, 2023, 2:38pm UTC](https://openfhe.discourse.group/t/number-of-limbs-in-ckks-rns/957/2 "2023-12-07T14:38:23Z")

</div>

Yes, the paper is [Approximate Homomorphic Encryption with Reduced Approximation Error](https://eprint.iacr.org/2020/1118)

At a high level, for `FLEXIBLEAUTOEXT`, the number of RNS limbs is multiplicative depth + 2. For all other modes, it is multiplicative depth + 1.