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Comment by vacri | Hacker News Reader

Out of curiosity, could a crypto-oriented person suggest the effective difference between a public/private key system, and a password system where the password is as long as a public key would be?

Given that most of the password-cracking articles focus on length of password being important regarding cracking time, it seems to this crypto-naif that a public-key-length password would do 99% of the job of moving to a public/private key system. I understand that you may as well use keys as a password of that length isn't human-memorable, but I'm curious as to what the effective difference would be.

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A public key system allows you to prove that you know a secret (the private key) without revealing the secret. To authenticate with a private key system you have to share the secret with the entity you're authenticating to, so you have to trust that entity to keep the secret. The fundamental problem with passwords is not that they're easy to guess, it's that using a password necessarily entails revealing the password.

> using a password necessarily entails revealing the password

Not always - the Secure Remote Password protocol doesn’t reveal the password to the server: http://en.wikipedia.org/wiki/Secure_Remote_Password_protocol

Yeah, but no browsers implement SRP (AFAICT) so this is a moot point. In today's world, using a password on the web means typing that password into a web form, at which point all bets are off: you have no control, or even knowledge, of how that password is processed from that point on. The only thing you can be even slightly confident of is that if you're typing the password into an HTTPS page then you're somewhat safe against MITM attacks. But there's no way to protect yourself against the incompetence (or maliciousness) of whoever you're doing business with.

Thanks, that makes more sense. I was expecting a more mathematical than philosophical answer, but in hindsight, I was wrong to do so.

That's actually a really good question that this post wasn't focused on. What's cool about the key pair is that the only information that is passed around is the signature, which is only valuable for a few seconds. The key itself is never transmitted and so it can never be intercepted.

That's a separate problem from the length of cracking, but an equally important one with regards to security.

Also, it would be pretty hard to remember even a single password that long...

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