entropy and bits

[Gomar]

How is entropy and bits determined?

if my password has 10 characters, then using all printable characters:
95 ^ 10 - 59,873,693,923,837,894,000

Thus, even a 5 character pw is secure as the size of the pool of characters is very large.

62 ^ 10 - 839,299,365,868,340,200 [lower&upper case+numbers]
26 ^ 10 - 141,167,095,653,376 [lower or upper case]
10 ^ 10 - 10,000,000,000 [numbers]

How does 2^128(bits) relate to this? 2 of what? 2 bits, 1 or 0?

AMT pin has 4 digits. That is only 10^4 = 10000


<t3 Q%f#8E
Entropy: 48.3 bits
close to
G5riTf8A3s
Entropy: 45.7 bits

DRSVNBJXLR
Entropy: 41 bits


finally, to reach 128-bits:
y~g1 bTehQ xPr4j1>)p9Z%u}
Length: 25
Entropy: 130.4 bits
Charset Size: 95 characters

Online Password Calculator
pw length: 8
Speed: 10B/sec
Full ASCII
up to 20 years.
Cool. Thus proving an 8 character pw is more than secure against anyone not hooking up 1000 PCs.

[Taxmancometh]

Cool link. I figured that the NSA has around 500 computers and a speed of 2,000,000 passwords a second it would take them 160618186625454570000 years to crack my eBay and Paypal passwords.

I use this for Firefox. https://addons.mozilla.org/en-US/fir...rch/?q=pwdhash and a 17 character password for eBay and Paypal.

[Gomar]

The NSA has a single computer running 100,000,000,000 pws/sec.
It would take it 3 years to hack a 95^10 pw.

[Interrupt]

Hi,

I don't actually know much about entropy in detail but I do want to add I was recently at the NSA's Cryptologic Museum and was lucky enough to get a small tour of a few NSA facilities. I think their crypto analysis department is impressive, I'd like IBM to donate a Blue Gene over in their direction but from what I've gathered they have the very best tech and amazing mathematicians working there.

I would also love to learn more about entropy so ill gladly be watching the thread. Admittedly I'm no math geek but love crypto theory, lambda probability analysis via church code, etc. Cool stuff. Wish I was better at math.

[Gomar]

The NSA could have the best crackers, fastest PCs, PhDs or whatever they want but
it still takes millions of years to crack a 20 character pw using only lower case letters.

Not even 85-bit can be broken.