auto

notes/pbft.md

@@ -6,14 +6,17 @@
   - i.e., correct replicas will return identical results.
 
 ## Differences from fail-stop consensus
-- 3*f*+1 replicas instead of 2*f*+1 (non-byzantine consensus):
-  - must be possible to make progress w/ only *n - f* replicas (because *f* might be faulty and respond)
-  - however, the *f* not responding might be correct but slow (asynchrony), so there might be *f* bad responses in the *n - f* responses
-  - implies *(n - f - f) > f*, or *n >= 3f + 1* in order to guarantee majority
+- 3*f*+1 replicas instead of 2*f*+1 (non-byzantine consensus)
 - 3 phases instead of two
 - cryptographic signatures
 
-**Properties**
+## Proof Sketch
+- must be possible to make progress w/ only *n - f* replicas (because *f* might be faulty and respond)
+- however, the *f* not responding might be correct but slow (asynchrony), so there might be *f* bad responses in the *n - f* responses
+- implies *(n - f - f) > f*, or *n >= 3f + 1* in order to guarantee majority
+
+
+## Properties
 - safety, liveness (*n >= 3f+1*)
   - can't prove both in async environment
   - safety guaranteed through protocol