# Linear shift of the hypercube and sumcheck

**URL:** <https://forum.aztec.network/t/linear-shift-of-the-hypercube-and-sumcheck/6253>\
**Category:** Honk!\
**Created:** [October 13, 2024, 11:34am UTC](https://forum.aztec.network/t/linear-shift-of-the-hypercube-and-sumcheck/6253 "2024-10-13T11:34:53Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![nicky](https://avatars.discourse-cdn.com/v4/letter/n/f0a364/32.png) [@nicky](https://forum.aztec.network/u/nicky)\
**Post date:** [October 13, 2024, 11:34am UTC](https://forum.aztec.network/t/linear-shift-of-the-hypercube-and-sumcheck/6253/1 "2024-10-13T11:34:53Z")

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Hi,

Is there a simple explanation and/or example to what Zac means by “shifting the boolean hypercube & sumcheck” in the ZK Summit 12, in the video link below?  
This is part of an upcoming paper about Honk!, as mentioned in the same video.

> **[Zero Knowledge Summit 12 - LIVESTREAM](https://www.youtube.com/live/lVvct93zJz0?feature=shared&t=26371)**
>
> This is the livestream from ZK12 - Zero Knowledge Summit 12 - happening on Oct 8th in Lisbon, Portugal.https://www.zksummit.com/-----------If you are looking...

Cheers!

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**Author:** ![careydanyele401](https://dub1.discourse-cdn.com/flex013/user_avatar/forum.aztec.network/careydanyele401/32/1899_2.png) [@careydanyele401](https://forum.aztec.network/u/careydanyele401)\
**Post date:** [November 18, 2024, 1:17pm UTC](https://forum.aztec.network/t/linear-shift-of-the-hypercube-and-sumcheck/6253/2 "2024-11-18T13:17:27Z")

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If I understood correctly, Zak in the ZK Summit 12 video discusses “moving the logical hypercube and summing checks” as a method to optimize zk-SNARKs. The technique aims to reduce computational complexity by reorganizing how data is structured and validated, improving efficiency in zero-knowledge proofs. This is part of the Honk! protocol, which focuses on improving zk-SNARK performance by simplifying these processes.

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**Author:** ![joshc](https://dub1.discourse-cdn.com/flex013/user_avatar/forum.aztec.network/joshc/32/20_2.png) [@joshc](https://forum.aztec.network/u/joshc)\
**Post date:** [November 18, 2024, 9:18pm UTC](https://forum.aztec.network/t/linear-shift-of-the-hypercube-and-sumcheck/6253/3 "2024-11-18T21:18:12Z")

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Not that I am aware of, might just have to wait until the Honk paper is published 😁