A number of proposals have been made for hash functions based on using a cipher block chaining technique, but without using the secret key.

**HASH FUNCTIONS BASED ON CIPHER
BLOCK CHAINING**

A number of proposals have been made for hash functions based
on using a cipher
block chaining technique, but without using the secret key. One of the first such proposals was that of Rabin [RABI78]. Divide a message *M *into fixed-size blocks *M*1, *M*2, Á , *M**N *and use a symmetric encryption system such as DES to
compute the hash code *G *as

* *

This is similar to the CBC technique,
but in this case, there is no secret key. As with any hash
code, this scheme is subject
to the birthday attack, and if the encryption algorithm is DES and only a 64-bit
hash code is produced,
then the system
is vulnerable.

Furthermore, another version of the birthday
attack can be used even if the opponent has access to only one message and its
valid signature and cannot obtain multiple signings. Here is the scenario: We
assume that the opponent intercepts a message with a signature in the form of
an encrypted hash code and that the unencrypted hash code is *m *bits long.

**1.
**Use the algorithm
defined at the beginning of this subsection to calculate the unencrypted hash code *G*.

**2.
**Construct any desired
message in the form *Q*1, *Q*2, ………, *Q**N *- 2.

**3.
**Compute *H**i *= E(*Q**i*,
*H**i *- 1) for 1 …
*i *…
(*N *- 2).

**4.
**Generate 2*m*/2 random blocks; for each block *X*, compute
E(*X*, *H**N *- 2). Generate an additional 2*m*/2 random blocks; for each block *Y*, compute
D(*Y*, *G*), where D is the
decryption function corresponding to E.

** 5.
**Based on the birthday paradox, with high probability there
will be an

such that E(*X*, *H**N *- 2) = D(*Y*, *G*).

** 6.
**Form the message

and therefore can be used with the
intercepted encrypted signature.

This form of attack
is known as a **meet-****i****n-the-m****i****ddle-attack**. A
number of researchers have proposed
refinements intended to strengthen the basic block chaining approach. For example, Davies and Price [DAVI89] describe
the variation:

However,
both of these
schemes have been shown to be vulnerable to a variety of attacks [MIYA90]. More generally, it can be shown
that some form of birthday attack will succeed
against any hash scheme involving the use of cipher block
chain- ing without a secret key, provided that either the resulting hash code is small enough (e.g., 64 bits or less) or that a larger hash code can be decomposed into independent subcodes [JUEN87].

Thus, attention
has been directed at finding other
approaches to hashing.

Many of these have also been shown to have
weaknesses [MITC92].

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Cryptography and Network Security Principles and Practice : Cryptographic Data Integrity Algorithms : Cryptographic Hash Functions : Hash Functions Based on Cipher Block Chaining |

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