Ambiguous notation in SNOVA docs.

[niux_d...@icloud.com]

Hi SNOVA team and all.

I'm trying to implement SNOVA using the carry-less multiplication instructions, and so far, I'm able to get finite field multiplication, vector dot product working, and determinant and matrix multiplication is written.

Now that I'm proceeding to higher level, I find a bit of frustration. There're 2 symbols used for multiplication: the ASCII * (asterisk) and \cdot (HTML entity ·). Although it's easy to infer the meaning of them based on data type context, I still hope this can be more consistent.

Since it's more easy to deduce the meaning of operators based on the data type context instead of depending on font faces that may not be easy to typeset and distinguish, I hope that the data type of elements such as P, A, B, Q, F, T, be clearly stated (e.g. at the beginning of the introduction section), and elements of F16[S] have subscripts on them (e.g. P_ij), and that combined matrices have brackets around them (e.g. [P], [T], etc.)

Hope we can get a consistent mathematical notation when (and if) we proceed to the next round(s). I see potential in this scheme, and I hope it can get standardized.

Thank you for your attention.
DannyNiu/NJF.

[Po-En Tseng]

Dear DannyNiu,

Thank you for bringing this to our attention. You are correct that the multiplication symbol differs between the mathematical expression and the algorithm description in our supporting document. We will address this inconsistency if we proceed to the next round.

We appreciate your careful review and helpful suggestion.

All the best,
Po-En Tseng
SNOVA Team

niux_d...@icloud.com 在 2025年9月19日 星期五下午3:32:39 [UTC+8] 的信中寫道：

[niux_d...@icloud.com]

Hi Dr. Tseng. I've noticed some other editorial issues, mostly with algorithm description. Some of which are major enough that I need to refer to the implementation for clarification.

I'll do some investigation after the week. In the mean time, I wonder if the SNOVA team could update the spec out-of-band at the website? 

Attached are my editorial observations and the PCLMUL-optimized field and matrix arithmetic part of my work-in-progress implementation.

[Jan Adriaan Leegwater]

Dear DannyNiu,

Thanks for pointing this out. We have updated the specification accordingly. 

We prefer to use github for the out-of-band updates to the specification. The updated specification can be found at:

1. https://github.com/vacuas/SNOVA/tree/documentation/Supporting_Documentation
2. https://github.com/vacuas/SNOVA/blob/documentation/Supporting_Documentation/SNOVA_prime_q_specification.pdf

This document also contains a description (not a proper specification yet) of the odd prime q variant of SNOVA. You can ignore this for your work.

Best wishes,

Jan Adriaan Leegwater

SNOVA team

Op za 20 sep 2025 om 06:21 schreef niux_dannyniu via pqc-forum <pqc-...@list.nist.gov>:

Hi Dr. Tseng. I've noticed some other editorial issues, mostly with algorithm description. Some of which are major enough that I need to refer to the implementation for clarification.

I'll do some investigation after the week. In the mean time, I wonder if the SNOVA team could update the spec out-of-band at the website? 

Attached are my editorial observations and the PCLMUL-optimized field and matrix arithmetic part of my work-in-progress implementation.

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