@arhag wrote a [post](https://steemit.com/steem/@arhag/how-supercomputing-was-able-to-dominate-the-mining-queue-and-how-the-bug-was-fixed) described how @supercomputing was able to dominate the mining queue before hard fork 13.

Here is the old algorithm described in @arhag's post:
```
1) hash1     = SHA256(latest_block_id)

2) hash2     = hash1 except for the first 64-bits replaced by some nonce (basically some random number selected to try to make the final work value have a sufficient number of leading 0 bits)

3) input     = SHA256(hash2)

4) sig       = ECDSA signature (in 65-byte format) of input using d (the active private key) and k (which is just another nonce used for signing)

5) sig_hash  = SHA256(sig)

6) pubkey    = Recover public key (33-byte format) corresponding to the private key that would have signed sig_hash with signature sig

7) work      = SHA256(pubkey)

work must have sufficient number of leading 0 bits matching the current mining difficulty target
```

In the post @arhag described:
> ... quickly (within a millisecond) calculate the corresponding private key necessary to make the new PoW valid according to the mining algorithm ... With the appropriate active private key `d` computed, the attacker can then change their account's active public key to the one corresponding to the private key ...

But there is a hole in the description, because the private key of a given signature shouldn't be so quickly to be resolved -- it's the nature of ECC algo.

**Actually, with the old algorithm, to submit a PoW, an attacker doesn't need to know the private key.**

When an attacker got an `input` with latest `head_block_id` and whatever `nounce` in step 3), and if she already have a known will-work `sig` in step 4), she can simply **recover** the public key (which is needed to put into the PoW operation) with the same method used in step 6). In addition, because a transaction contains only a PoW operation requires no signature (which is another hole in the old algo which got fixed in new algo),  the PoW will be accepted by other nodes.