Add "penalty-for-failure-to-defend" concept to book

[shielded-nate]

Our primary conceptual framework for quantitative comparison between Crosslink security properties versus pure PoW or Tendermint-like BFT protocols is called "penalty for failure to defend" (aka $PFD$).

Key Top-Level Details

• PFDs can be specific to compromising specific properties; example: $PFD_{liveness}$ and $PFD_{finality}$ are different (so there's no simple top-line number for a given protocol).
• $PFD$ is distinct from the confusing misnomer of "cost-to-attack" (because the penalty may accrue to non-attackers, and the nature of successful attacks is that they cost less than designers or security defense analyzers fail to anticipate).
• Neither $PFD$ or the ill-conceived "cost-to-attack" metrics are conclusive about financial feasibility, since they don't capture attacker revenue/profit.
• Some $PFD$ may be a "financial value gauge" such as in Tendermint protocols where a $PFD$ could slash a large bond at stake. Meanwhile others may be a "rate" such as in PoW where the penalty to miners is loss of a future revenue rate over time.
• The two different types of $PFD$ (gauge vs rate) cannot be directly compared for two reasons:
  • The obvious reason that rates and gauges are different unit types.
  • The less obvious reason that the trade-offs in compromise, response, and recovery dynamics are qualitatively incommensurate. (TODO: flesh out the nuance here.)

TODO

Incorporate other writing on this.

• From memory: there is a shared notes doc with important details.
• scoping.md: consider adding description of the cost-per-time vs cost-accumulated quality? #248 alludes to part of this issue.