Cryptographic Applications - Introduction to Cryptography with Java Applets - page 337

641194989852455577634720396702065575387017714394831539504200403961645096
728072726095322023421112943523393879161424144304336692169642791406419470
91918468321515459948865 (mod p )

and

w g d ( P )

438908365050492172112141159266916014689430122622767850409990603339138565
278995621692689044958914233869339458908488816024934068379856100514306151
641194989852455577634720396702065575387017714394831539504200403961645096
728072726095322023421112943523393879161424144304336692169642791406419470
91918468321515459948865.

B takes note of the fact that v and w are equal, and accepts the signature.

Storing Passwords or Passphrases as Digests A system administrator has a
peculiar problem. She must store the passwords or passphrases of all her users, so that she
can compare these entries to the entered passwords when a user attempts a login. However,
she must be able to protect these passwords, so unauthorized users cannot obtain them. Ide-
ally, it would be best if the system administrator herself could not obtain the passwords.
Cryptographically secure digest functions provide a solution. A user's password is not
stored, but rather, a digest of the password is stored. When a user attempts a login, a digest
of the password is taken, then compared against this user's entry in a table. If an adversary
somehow obtains the hashed password list, it does him little good if the digest function is
a good one; that is, it will be nearly impossible for him to obtain any particular password
from its digest. Even the system administrator does not know any particular password; only
the user who created it knows (assuming he or she didn't forget it). Various operating sys-
tems grant access based on such an idea; Figure 16.11 illustrates this process:

16.8

ATTACKS ON DIGEST FUNCTIONS
There are various approaches to defeating a digest function. To defeat a digest function,
one must be able to produce a bogus message, say P , which hashes to the same value as

Figure 16.11

hashed password user

User 5 login:

h(P(1)) 1 - Billy

Tutti:
Enter password:

h(P(2)) 2 - Kenton

X

h(P(3)) 3 - Mandy

***********

h

h(P(4)) 4 - Seth

h(X)

h(P(5)) 5 -Tutti

Allow login iff h(X) = h(P(5))