This is followup of the “Security Analysis Roadmaps: From Cryptarchia v2, to v2-minus (draft)”. This report first provides a succinct summary of the “Security Analysis Roadmaps: From Cryptarchia v2, to v2-minus (draft)” and then provides a preliminary security analysis of the window referencing mechanism in both Cryptarchia v2 and v2-minus. Special attention is given to the interplay between the window size w, the block generation/network delay ratio p, and their implications for liveness and safety.
The “Security Analysis Roadmaps: From Cryptarchia v2, to v2-minus (draft)” report is organized around two main parts: an overview and analysis roadmap for Cryptarchia v2, and a tractable formal analysis of a simplified variant called v2-minus.
Cryptarchia v2 is a DAG-based proof-of-stake protocol designed to increase resilience against reorganizations, adapt to network delays, and allow for multiple concurrent proposers, enhancing censorship resistance. The protocol’s core is a sliding window referencing: each block references as many blocks as possible within a recent window (such as 30 slots), forming a maximal antichain. An optional "long-ref" can reference a block outside the window for connectivity, but this does not affect fork choice. Fork choice is based on the cumulative weight (number of windowed references) in the descendants of the closest common ancestor (CCA) between conflicting blocks. Slashing penalizes equivocation. Simulations suggest improved convergence and robustness, but the protocol introduces nuanced concerns, especially regarding window management and finalization of block eligibility.
To enable formal analysis, v2-minus removes the long-ref mechanism, assumes an idealized leader election (public-coin/Bernoulli process), ignores transaction dependencies, and assumes a fixed-delay, partially synchronous network. Block references are limited strictly to a maximal antichain within a fixed-size window. The report identifies attack vectors, especially the risk of honest blocks being stranded outside the window, and compares its security to PHANTOM, a DAG protocol with unlimited referencing. The result: v2-minus is more vulnerable to adversarial strategies that "strand" honest blocks outside the window, potentially undermining safety and liveness even under idealized conditions.
Let p be the number of blocks generated per network delay (that is, the block rate normalized by network delay). We analyze the security of v2 and v2-minus under varying p and window size w.
Both variants use a sliding reference window: every new block references as many as possible (maximal antichain) within the most recent w slots. Only in v2 does an optional "long-ref" connect to a block outside the window for liveness, but it has no effect on fork choice; v2-minus omits this mechanism.
p):
p: Blocks are generated much faster than network delay.p: Block generation and network delay are comparable.p: Blocks are generated much slower than network delay.w):
w slots.