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Fix mathematical variable definitions consistency

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Standardize LaTeX notation for subscripts and superscripts:
- Use consistent braces for subscripts: K^{n}_{i} instead of K^{n}_i
- Fix malformed proof notation: pi^{K^{n}_{i}}_{Q}
- Use braces around mathbf arguments: \mathbf{K} instead of \mathbf K
- Add missing semicolons before "it also contains"
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Cofson
2025-12-23 10:10:22 +01:00
parent 60deaf642a
commit 6eb2ab4f46
1 changed files with 18 additions and 18 deletions
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nomos/raw/nomos-message-formatting.md
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@@ -90,16 +90,16 @@ class PublicHeader:
**Fields:**
- version=0x01 is version of the protocol.
- public_key is $K^{n}_i$,
a public key from the set $\mathbf K^n_h$
- public_key is $K^{n}_{i}$,
a public key from the set $\mathbf{K}^{n}_{h}$
as defined in the Message Encapsulation spec.
- proof_of_quota is $\pi^{K^{n}i}{Q}$,
a corresponding proof of quota for the key $K^{n}_i$ from the $\mathbf K^n_h$
- proof_of_quota is $\pi^{K^{n}_{i}}_{Q}$,
a corresponding proof of quota for the key $K^{n}_{i}$ from the $\mathbf{K}^{n}_{h}$;
it also contains the key nullifier.
- signature is $\sigma_{K^{n}_{i}}(\mathbf {h|P}i)$,
- signature is $\sigma_{K^{n}_{i}}(\mathbf{h|P}_{i})$,
a signature of the concatenation of the $i$-th encapsulation
of the payload $\mathbf P$ and the private header $\mathbf h$,
that can be verified by the public key $K^{n}{i}$.
of the payload $\mathbf{P}$ and the private header $\mathbf{h}$,
that can be verified by the public key $K^{n}_{i}$.
#### Private Header
@@ -107,7 +107,7 @@ The private_header must be generated as the outcome of
the Message Encapsulation Mechanism.
The private header contains a set of encrypted blending headers
$\mathbf h = (\mathbf b_1,...,\mathbf b_{h_{max}})$.
$\mathbf{h} = (\mathbf{b}_{1},...,\mathbf{b}_{h_{max}})$.
```python
private_header: list[BlendingHeader]
@@ -118,7 +118,7 @@ as defined in the Global Parameters.
**Blending Header:**
The BlendingHeader ($\mathbf b_l$) is defined as follows:
The BlendingHeader ($\mathbf{b}_{l}$) is defined as follows:
```python
class BlendingHeader:
@@ -132,17 +132,17 @@ class BlendingHeader:
**Fields:**
- public_key is $K^{n}_{l}$,
a public key from the set $\mathbf K^n_h$.
- proof_of_quota is $\pi^{K^{n}l}{Q}$,
a corresponding proof of quota for the key $K^{n}_l$ from the $\mathbf K^n_h$
a public key from the set $\mathbf{K}^{n}_{h}$.
- proof_of_quota is $\pi^{K^{n}_{l}}_{Q}$,
a corresponding proof of quota for the key $K^{n}_{l}$ from the $\mathbf{K}^{n}_{h}$;
it also contains the key nullifier.
- signature is $\sigma_{K^{n}_{l}}(\mathbf {h|P}l)$,
- signature is $\sigma_{K^{n}_{l}}(\mathbf{h|P}_{l})$,
a signature of the concatenation of $l$-th encapsulation
of the payload $\mathbf P$ and the private header $\mathbf h$,
that can be verified by public key $K^{n}{l}$.
- proof_of_selection is $\pi^{K^{n}{l+1},m{l+1}}{S}$,
a proof of selection of the node index $m{l+1}$
assuming valid proof of quota $\pi^{K^{n}{l}}{Q}$.
of the payload $\mathbf{P}$ and the private header $\mathbf{h}$,
that can be verified by public key $K^{n}_{l}$.
- proof_of_selection is $\pi^{K^{n}_{l+1},m_{l+1}}_{S}$,
a proof of selection of the node index $m_{l+1}$
assuming valid proof of quota $\pi^{K^{n}_{l}}_{Q}$.
- is_last is $\Omega$,
a flag that indicates that this is the last encapsulation.