Introduction

This document defines message generation strategies that nodes can apply to increase communication resilience and privacy. Specifically, it guides node operators in selecting or designing methods for generating messages that increase the probability of successful data message delivery and reduce the likelihood of edge node censorship. The strategies presented here do not increase protocol complexity, as they define methods for generating and sending messages according to the existing Blend protocol rules. Nodes implement these strategies individually based on their requirements.

This document assumes that the reader is familiar with the [1.0.0] Blend Protocol and especially with the Leadership Quota.

Terminology

Independent Paths: A set of paths (for particular payload) that do not have common nodes.
Independent Private Header: A private header used to construct an independent path.
Independent Message: A message with an independent private header.

Notation Reference

Symbol	Description
$R_D$	Redundancy parameter (number of additional messages beyond the first)
$\bar{R}_D$	Initial redundancy in Hybrid strategy
$P$	Fraction of adversarial core nodes
$n$	Number of core nodes contacted
$L$	Number of blend nodes in a path
$\Delta$	Maximum delay at a blend node
$d$	Maximum broadcast latency
$\alpha$	Relative stake of a node
$\phi_f(\alpha)$	Lottery function (probability of winning leadership)

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In very small networks, constructing enough independent messages may be impossible due to insufficient nodes to maintain uniqueness across private headers. In such cases, node repetition is acceptable.

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Overview

In this design, we present two sets of basic strategies (detailed in the Constructions section below).

The first set of strategies increases the delivery rate of data messages. A node selected for message processing may fail to perform correctly due to connectivity issues or malicious behavior. In such cases, the message will not reach its destination and its payload will not be broadcast. These strategies increase the probability of successful delivery.

The simplest solution is to send more messages. However, this increases the probability of linking a node to its message, thereby reducing privacy.

Therefore, we present and discuss the following set of strategies:

Static strategy: A node sends the same data message by sending multiple independent messages simultaneously. This strategy improves the delivery rate at a higher cost of privacy but without a significant impact on latency.
Dynamic strategy: A node observes the processing of its data message, and if the processing is delayed beyond some time threshold, then it emits the same payload using an independent message. This strategy improves the delivery rate at the lowest cost of privacy but at the highest cost of latency. However, due to longer delay it will negatively impact consensus by increasing the frequency and depth of forks.
Hybrid strategy: A node sends the same data message using multiple independent messages and observes the processing of them. If it detects that all of the messages have been delayed beyond some time threshold, then it emits the same data message using an independent message. This strategy is a balance between the Static and Dynamic strategies.