Any message authentication or digital signature mechanism has two levels of functionality. At the lower level, there must be some sort of function that produces an authenticator: a value to be used to authenticate a message.

**MESSAGE
AUTHENTICATION FUNCTIONS**

Any message authentication or digital signature mechanism has two levels of functionality. At the lower level, there must be some sort of function that
produces an authenticator: a value to be used to authenticate a message. This
lower-level func- tion is then used as a primitive in a higher-level authentication protocol that enables
a receiver to verify the authenticity of a message.

This section is concerned with the types of functions
that may be used to pro-
duce an authenticator. These may be grouped
into three classes.

•
**Hash funct****i****on****: **A function that maps
a message of any length into a fixed- length hash value, which
serves as the authenticator

•
**Message encrypt****i****on****: **The ciphertext of the entire message
serves as its authen-
ticator

•
**Message authent****i****cat****i****on code (MAC)****:**** **A function of the message
and a secret key that produces
a fixed-length value that serves as the authenticator

Hash functions, and how they may serve for
message authentication, are dis-
cussed in Chapter 11. The remainder of this section
briefly examines the remaining
two topics. The remainder
of the chapter elaborates on the topic of MACs.

Message Encryption

Message encryption by itself can provide a measure of authentication. The analysis differs for symmetric and public-key encryption schemes.

*SYMMETRIC *** ENCRYPTION **Consider the straightforward use of symmetric encryption (Figure 12.1a). A message

In addition, B is assured
that the message
was generated by A. Why?
The mes- sage must have come from A, because
A is the only other party that possesses *K *and therefore the only other party
with the information necessary to construct cipher- text that can be decrypted
with *K*. Furthermore, if *M *is recovered, B knows that none of the bits of *M *have
been altered, because
an opponent that does not know *K *would not know how to alter
bits in the ciphertext to produce the desired changes
in the plaintext.

So we may say that symmetric encryption provides
authentication as well as confidentiality.
However, this flat statement needs
to be qualified. Consider exactly what
is happening at B. Given a
decryption function D and a secret key *K*, the destination will
accept *any *input *X *and produce output *Y *= *D*(*K*, *X*). If *X *is the ciphertext of a legitimate message *M *produced by the corresponding encryption function, then *Y *is some plaintext
message *M*. Otherwise, *Y *will
likely be a meaningless sequence of
bits. There may need to be some automated means of determining at B whether *Y
*is legitimate plaintext and therefore must have come from A.

The implications of the line of reasoning in the preceding paragraph are pro-
found from the point of view of authentication. Suppose
the message *M *can
be any arbitrary bit pattern. In that case, there is no way to determine
automatically, at the destination, whether an incoming
message is the ciphertext of a legitimate message. This conclusion is incontrovertible: If *M *can be any bit pattern, then
regardless of the value of *X*, the
value *Y *= D(*K*, *X*) is *some *bit pattern and therefore must be accepted as authentic plaintext.

Thus, in general, we require that only a small subset of all
possible bit pat- terns be considered legitimate plaintext. In that case, any spurious ciphertext is unlikely
to produce legitimate plaintext. For example,
suppose that only one bit pattern in
106 is legitimate
plaintext. Then the probability that any randomly cho- sen bit pattern, treated
as ciphertext, will produce a legitimate plaintext message is only 10 - 6.

For a number of applications and encryption schemes, the desired conditions prevail as a matter of course.
For example, suppose that we are transmitting English- language messages using a Caesar
cipher with a shift of one (*K *= 1). A sends the following legitimate ciphertext:

Nbsftfbupbutboeepftfbupbutboemjuumfmbnctfbujwz

B decrypts to produce the following
plaintext:

mareseatoatsanddoeseatoatsandlittlelambseativy

A simple frequency
analysis confirms that this message
has the profile of ordinary English.
On the other hand, if an opponent
generates the following random
sequence of letters:

zuvrsoevgqxlzwigamdvnmhpmccxiuureosfbcebtqxsxq

this decrypts to

ytuqrndufpwkyvhfzlcumlgolbbwhttqdnreabdaspwrwp

which does not fit the profile of ordinary English.

It may be difficult to determine *automatically *if incoming ciphertext decrypts to intelligible plaintext. If the plaintext is, say, a binary object
file or digitized X-rays, determination of properly formed and therefore
authentic plaintext may be diffi- cult. Thus, an opponent
could achieve a certain level of disruption simply by issuing messages with random content
purporting to come from a legitimate user.

One solution to this problem is to force the plaintext to
have some structure that is easily recognized but that cannot be replicated
without recourse to the encryption function. We could, for example, append an
error-detecting code, also known as a frame check sequence (FCS) or checksum,
to each message before encryption, as illustrated in Figure 12.2a. A prepares a
plaintext message *M *and then provides
this as input to a function F that produces an FCS. The FCS is appended to *M *and
the entire block is then encrypted. At the
destination, B

decrypts the incoming block and treats the
results as a message with an appended FCS. B applies the same function F to attempt to reproduce the FCS. If
the calcu- lated FCS is equal to the incoming FCS, then the message
is considered authentic. It is unlikely that any random
sequence of bits would exhibit
the desired relationship.

Note that the order in which the FCS and encryption functions
are performed is critical. The sequence illustrated in Figure 12.2a is referred
to in [DIFF79] as
**i****nternal**** ****error**** ****control**, which the authors contrast with **external
error control **(Figure
12.2b). With internal error control, authentication is provided because an
opponent would have difficulty generating ciphertext that, when decrypted, would have valid error control bits. If instead the FCS is the outer
code, an opponent can construct messages with valid error-control codes.
Although the opponent cannot know what the decrypted plaintext
will be, he or she can still hope to create confu-
sion and disrupt operations.

An error-control
code is just one example; in fact, any sort of structuring
added to the transmitted message
serves to strengthen the authentication capability. Such structure is provided
by the use of a communications architecture consisting of
layered protocols. As an example, consider the structure of messages
transmitted using the TCP/IP
protocol architecture. Figure
12.3 shows the format of a TCP seg-
ment, illustrating the TCP header. Now suppose that each pair of hosts shared a
unique secret key, so that all
exchanges between a pair of hosts used the same key, regardless of application. Then we could simply encrypt
all of the datagram except the IP header. Again, if an
opponent substituted some arbitrary bit pattern for the encrypted TCP segment, the
resulting plaintext would not include a meaningful
header. In this case, the header includes not only a checksum (which
covers the header) but also other
useful information, such as the sequence number. Because successive TCP segments on a given
connection are numbered
sequentially, encryp- tion assures
that an opponent does not delay, misorder, or delete any segments.

*P**UBLIC**-K**EY **E*** NCRYPTION **The
straightforward use of public-key
encryption (Figure 12.1b)
provides confidentiality but not authentication. The source
(A) uses the public key

corresponding private key *PRb*, only B can decrypt
the message. This scheme provides no authentication, because
any opponent could also use B’s public key to encrypt a message and claim to be A.

To provide authentication, A uses its private key to encrypt
the message, and B
uses A’s public key to decrypt
(Figure 12.1c). This provides authentication using the same type of reasoning as in the symmetric encryption case: The message must have
come from A because A is the only party that possesses
*PR**a *and therefore the only
party with the information necessary to construct ciphertext that can be
decrypted with *PU**a*. Again,
the same reasoning
as before applies:
There must be some internal structure to the plaintext so
that the receiver can distinguish between well-formed plaintext and random bits.

Assuming
there is such structure, then
the scheme of Figure 12.1c
does provide authentication.
It also provides what is known as digital signature.1 Only A could have constructed the ciphertext because only A possesses
*PR**a*.
Not even B, the recipient, could have constructed the ciphertext. Therefore, if B is in possession of the ciphertext, B has the means to prove that the message
must have come from A. In
effect, A has “signed” the message by using its private key to encrypt.
Note that this scheme
does not provide
confidentiality. Anyone in possession of A’s public key can decrypt the ciphertext.

To provide both confidentiality and authentication, A
can encrypt
*M *first using its private
key, which provides the digital signature, and then using
B’s public key, which provides confidentiality (Figure 12.1d).
The disadvantage of this approach is that the public-key algorithm, which is complex,
must be exercised four times rather than two in each communication.

Message Authentication Code

An alternative authentication technique involves the use of a secret key to generate
a small fixed-size block of data, known
as a **cryptograph****i****c checksum
**or MAC, that is
appended to the message. This
technique assumes that two communicating parties, say A and B, share
a common secret key *K*. When A has a
message to send to B, it calculates the MAC as a function of the message
and the key:

MAC = MAC(*K*, *M*)

where

*M *= input message

C = MAC function

*K *= shared secret key

MAC = message authentication code

The message plus MAC are transmitted to the intended
recipient. The recipient per- forms the same calculation on the
received message, using the same secret key, to

generate a new MAC. The received MAC is compared to the calculated MAC (Figure 12.4a).
If we assume that only the receiver
and the sender know the identity
of the secret key, and if the received
MAC matches the calculated MAC, then

**1.
**The receiver is assured that
the message has not been altered. If an attacker alters the message but does not alter the MAC, then the receiver’s calculation of the MAC will differ from the received
MAC. Because the attacker
is assumed not to know the secret key, the attacker
cannot alter the MAC to cor- respond to the alterations in the message.

**2.
**The receiver is assured that the message
is from the alleged sender. Because no one else knows the secret key, no one else could prepare
a message with a proper
MAC.

**3.
**If the message includes
a sequence number (such as is used with HDLC,
X.25, and TCP), then the receiver
can be assured of the proper sequence
because an attacker cannot
successfully alter the sequence number.

A MAC function
is similar to encryption. One difference is that the
MAC algorithm need not be reversible, as it must be for decryption. In general, the MAC function is a many-to-one function. The domain of the function
consists of messages of some arbitrary length,
whereas the range consists of all possible MACs
and all possible keys. If an *n*-bit MAC
is used, then there are 2*n *possible MACs, whereas
there are *N *possible messages with *N *77 2*n*. Furthermore, with a *k*-bit
key, there are 2*k *possible keys.

For example, suppose that we are using 100-bit messages and a 10-bit MAC. Then, there are a total of 2100 different messages
but only 210 different MACs. So, on average, each MAC value is generated by a total of 2100/210 = 290 different mes- sages. If a 5-bit key is used, then there are
25 = 32 different
mappings from the set of messages to the set of MAC values.

It turns out that, because
of the mathematical properties of the authentication function, it is less vulnerable to being broken than encryption.

The process depicted
in Figure 12.4a provides
authentication but not confiden-
tiality, because the message
as a whole is transmitted in the clear.
Confidentiality can be provided
by performing message
encryption either after
(Figure 12.4b) or before
(Figure 12.4c) the MAC algorithm. In both these
cases, two separate keys are needed, each of which is shared by the sender and the receiver. In the first case, the MAC is calculated with the message as input
and is then concatenated to the message. The
entire block is then encrypted. In the second case, the message is
encrypted first. Then the MAC is calculated using the resulting
ciphertext and is concatenated to the
ciphertext to form the transmitted block. Typically,
it is preferable to tie the authenti- cation directly to the plaintext, so the method
of Figure 12.4b is used.

Because symmetric encryption will provide
authentication and because it is widely used with
readily available products, why not simply
use this instead
of a sep- arate message authentication code? [DAVI89] suggests three situations in which
a message authentication code is used.

**1.
**There are a number of applications in which the same message
is broadcast to a number of destinations. Examples
are notification to users that the network is now unavailable or an alarm
signal in a military control
center. It is cheaper
and more reliable to have only one destination responsible for monitoring authenticity. Thus, the message must be broadcast in plaintext with an associ- ated message authentication code.
The responsible system has the
secret key and performs authentication. If a violation
occurs, the other destination
systems are alerted
by a general alarm.

**2.
**Another possible
scenario is an exchange in which one side has a heavy
load and cannot afford the time to decrypt all incoming messages.
Authentication is carried out
on a selective basis, messages being chosen at random for checking.

**3.
**Authentication
of a computer
program in plaintext is an attractive service. The computer
program can be executed without having to decrypt it every time, which
would be wasteful
of processor resources.
However, if a message authenti-
cation code were attached to the program,
it could be checked whenever assur- ance was required
of the integrity of the program.

Three other rationales may be added.

For some applications, it may not be of concern
to keep messages
secret, but it is important
to authenticate messages. An example is the Simple Network Management Protocol
Version 3 (SNMPv3), which
separates the functions of confidentiality and authentication. For this application, it is usually important for a managed system to authenticate incoming SNMP messages, particularly if the message contains a command
to change parameters at the managed system. On the other hand, it may not be necessary to conceal
the SNMP traffic.

**4.
**Separation of authentication and confidentiality
functions affords architectural flexibility. For example, it may be desired
to perform authentication at the appli-
cation level but to provide
confidentiality at a lower level, such as the transport
layer.

**5.
**A user may wish to prolong
the period of protection beyond
the time of recep-
tion and yet allow processing of message contents.
With message encryption, the protection is lost when
the message is decrypted, so the message is pro- tected against fraudulent modifications only in transit
but not within the target system.

**6.
**Finally, note that
the MAC does not provide a digital signature, because both sender and receiver
share the same key.

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Cryptography and Network Security Principles and Practice : Cryptographic Data Integrity Algorithms : Message Authentication Codes : Message Authentication Functions |

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