Policy-Discussion

[<Lambert.Hofstra AT ins.com>]

Did some research: asymmetric 1024 is comparable with 72-80 bit symmetric, 
asymmetric 2048bit is comparable with 96-128bit symmetric.( 
http://www.keylength.com/en/4/ ;) So actually you need to find 2^80 or 2^128 
keys.
 
However, your point still stands: it requires a huge amount of storage ( 
~10^20 Exabyte) so still not feasable
 
Lambert 
________________________________

Van: 
cacert-policy-bounces AT lists.cacert.org
 namens Philipp Gühring
Verzonden: wo 5/30/2007 13:06
Aan: Policy-Discussion
Onderwerp: Re: [CAcert-Policy] How to deal with "cooperation" ?



Hi,

> You all  know that password attacks are not done brute force (brute force
> attacks on a long password can take years) , but by lookups in a table with
> precalculated hashes (rainbow table lookup, crack a password in
> milliseconds). What would stop a dedicated foreign agency to start
> generating rainbow tables for public/private key pairs? If well funded,
> they can build dedicated hardware for it, and once such a table is created
> they can simply do a lookup to find any private key based on the public key
> in milliseconds... I'm not a crypto specialist, so could someone give an
> indication of the number of valid public/private key pair with 1024bit key
> size?

Given proper entropy was used properly to generate the keys (which both isn´t
given in practice, but let´s assume it anyway), you get something like 2^1024
possible keys, which is

17976931348623159077293051907890247336179769789423065727343008115773
26758055009631327084773224075360211201138798713933576587897688144166
22492847430639474124377767893424865485276302219601246094119453082952
08500576883815068234246288147391311054082723716335051068458629823994
7245938479716304835356329624224137216 possible keys. Let´s assume that a key
usually costs a Kilobyte, and you succeed to need only 10 Bytes for each
entry in your rainbow table, then you need

17976931348623159077293051907890247336179769789423065727343008115773
26758055009631327084773224075360211201138798713933576587897688144166
22492847430639474124377767893424865485276302219601246094119453082952
08500576883815068234246288147391311054082723716335051068458629823994
72459384797163048353563296242241372160 Bytes, which is about

17976931348623159077293051907890247336179769789423065727343008115773
26758055009631327084773224075360211201138798713933576587897688144166
22492847430639474124377767893424865485276302219601246094119453082952
08500576883815068234246288147391311054082723716335051068458629823994
72459384797163048353563296242241 Megabyte, which is about

17976931348623159077293051907890247336179769789423065727343008115773
26758055009631327084773224075360211201138798713933576587897688144166
22492847430639474124377767893424865485276302219601246094119453082952
08500576883815068234246288147391311054082723716335051068458629823994
72459384797163048353563296 Terabyte

> Am I missing something?

If you have a cheap source for that amount of storage, please let me know!

Best regards,
Philipp Gühring

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