# For the SingleKey Architecture, I only achieve a 128 security level with a ring dimension of 31k

**URL:** <https://openfhe.discourse.group/t/for-the-singlekey-architecture-i-only-achieve-a-128-security-level-with-a-ring-dimension-of-31k/1279>\
**Category:** Library Questions\
**Created:** [May 18, 2024, 10:34pm UTC](https://openfhe.discourse.group/t/for-the-singlekey-architecture-i-only-achieve-a-128-security-level-with-a-ring-dimension-of-31k/1279 "2024-05-18T22:34:37Z")\
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**Author:** ![Caesar](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/caesar/32/63_2.png) [@Caesar](https://openfhe.discourse.group/u/Caesar)\
**Post date:** [May 19, 2024, 12:28am UTC](https://openfhe.discourse.group/t/for-the-singlekey-architecture-i-only-achieve-a-128-security-level-with-a-ring-dimension-of-31k/1279/2 "2024-05-19T00:28:07Z")

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Question 1. The minimum ring dimension that can satisfy a certain security level depends primarily on the multiplicative depth. It seems the multiplicative depth in your use case is large necessitating a ring dimension of 128K to achieve a 128-bit security level. Try to reduce the multiplicative depth which would allow for a smaller ring dimension while maintaining the desired security level. You can use bootstrapping to evaluate deep circuits if needed.

Question 2. This is not straightforward to answer. In a nutshell, the ring dimension does affect the precision as it affects the noise growth for certain CKKS operations (See Table 3 in this [paper](https://eprint.iacr.org/2022/162.pdf)).

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