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In the Yellow paper, appendix F "Signing Transactions", (BYZANTIUM VERSION f72032b - 2018-05-04 to be specific), it says:

The method of signing transactions is similar to the ‘Electrum style signatures’ as defined by Arnaud et al. [2017], heading “Managing styles with Radium” in the bullet point list.

The paper then goes on about how ECDSA is used in Ethereum, but never clarifies any furthur about what "Electrum style" means or how it's applied in this circumstance.

Here is the full quote of the mentioned section, retrieved at 27-07-2018:

Managing styles with Radium

We decided to use radium as the way to go to inject styles into components. By using the E instance provided by import Electrum from 'electrum'), components are automatically configured to use radium when wrapped like this:

import Electrum from 'electrum';
import _Button from './Button.component.js';
import _Button$styles from './Button.styles.js';
export const Button = Electrum.wrap ('Button', _Button, {styles: _Button$styles});

See electrum-theme for an explanation of how style functions should be defined. Style functions can have following signatures:

  • () => ... → a parameterless style function.
  • (theme) => ... → a style function, based on the theme.
  • (theme, props) => ... → a style function, based on the theme and on the component properties. The component should implement a getter named styleProps which returns a hash with the meaningful properties.

Multiple styles definitions can be exported as a hash of style functions.

Component with a single style function

A component linked with a style definition consisting of a single style function will expose following method and property:

  • styles → a styles object which can be set on DOM element style properties; the styles object is compatible with Radium. It exposes a with(s1, s2, ...) function which can be used to obtain an updated styles object into which additional styles have been merged.
  • mergeStyles(s1, s2, ...) → a hash containing the merged styles.

Component with a multiple style functions

A component linked with a style definition consisting of a multiple style functions will expose following methods:

  • getStyles(key) → a styles object for the specified style definiton, which can be set on DOM element style properties; the styles object is compatible with Radium. It exposes a with(s1, s2, ...) function which can be used to obtain an updated styles object into which additional styles have been merged.
  • mergeStyles(key, s1, s2, ...) → a hash containing the merged styles for the specified style definition.

Note that the signature of the methods are different from a component with a single style function.

I know that transaction signature Ethereum is a triplet of (v, r, s), but can't understand how any of the above description applies to it.

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This issue has also been brought up on the github.

It appears that the citation was added in this commit, and as you pointed out, it clearly has no relevance to the actual content. The "Electrum" referred to in the yellow paper is the Electrum light client for Bitcoin, while the citation points to some JS library.

I'm not exactly sure what is meant by "Electrum style signatures", but this phrase has been in the paper since the first draft so presumably it means something.

In my opinion, the whole line should just be deleted from the paper, and I will submit PR to do so.

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