A quick tour of new functions in BARK that support Azure Key Vault tradecraft research, including a walk-through of how an adversary may chain these functions together as part of an attack path: posts.specterops.io/azure-ke…
For this graph of 5 strongly connected nodes there are 120 paths.
Do you see the pattern yet?
We can find the number of paths to each node in the strongly connected graph by finding the factorial of n, where n is the number of nodes in the graph:
5*4*3*2*1 = 120
Again we must start from each node and find all paths to all other nodes. Doing so when starting from one node (at the center) looks like this:
But remember we must start from EACH node. Starting from node 1 gives us 6 paths. 6 paths * 4 starting nodes = 24 paths.
What if the graph has 5 nodes?
Again we must start from each node and find all paths to all other nodes from each node:
1:
1, 2, 3, 4 and 1, 2, 4, 3 and 1, 3, 2, 4 and 1, 3, 4, 2 and 1, 4, 2, 3 and 1, 4, 3, 2
Just visualizing this ONE starting point we get this:
This simple graph of 3 strongly connected nodes produces a total of 6 paths.
What if we increase the number of nodes to 4?
To find ALL paths, we start from EACH node and find EVERY path to all OTHER nodes.
Starting from 1 we have:
1, 2, 3 and 1, 3, 2
Starting from 2 we have:
2, 1, 3 and 2, 3, 1
Starting from 3 we have:
3, 1, 2 and 3, 2, 1
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