Confirmation means reducing the likelihood that a transaction can be double spent down to an acceptably unlikely level.
There is a lot of math in the Satoshi whitepaper about how the likelihood that a transaction can be double spent reduces with each block the transaction is buried under. All of this math is based on average 10 minute blocks and the parameters with which Bitcoin was implemented.
If you change all those parameters, like the timing of the blocks, you will also be changing the difficulty of rewriting the block chain and thus changing the likelihood that a transaction can be double spent.
You cannot merely make blocks faster and claim that your blockchain has "faster confirmations." You have to do the math!
From Meni Rosenfield's
Analysis of hashrate-based double-spending (
link):
The probability of success depends on the number of confirmations and not on the amount of time waited. An alternative network with a different time constant T0 can thus obtain more security with a given amount of wait time.
Consider the math done. (I'm not being lazy, I'm just way more confident in his math than my own.)
"The time constant might be relevant, if we assume that the attacker cannot sustain his hashrate for a prolonged period of time."
6 confirmations with 10 minute block times would mean you'd have to maintain enough of a hashrate for over an hour. 6 confirmations with 1 minute block times means you only have to maintain it for just over 6 minutes or so. Course if you're actually relying on the shorter time frame to be successful, you probably don't have the hashrate to succeed anyway. lol