Section 13.1. Digital Signatures | Cryptography and Network Security (4th Edition)

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13.1. Digital Signatures

Requirements

Message authentication protects two parties who exchange messages from any third party. However, it does not protect the two parties against each other. Several forms of dispute between the two are possible.

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For example, suppose that John sends an authenticated message to Mary, using one of the schemes of Figure 11.4. Consider the following disputes that could arise:

Mary may forge a different message and claim that it came from John. Mary would simply have to create a message and append an authentication code using the key that John and Mary share.
John can deny sending the message. Because it is possible for Mary to forge a message, there is no way to prove that John did in fact send the message.

Both scenarios are of legitimate concern. Here is an example of the first scenario: An electronic funds transfer takes place, and the receiver increases the amount of funds transferred and claims that the larger amount had arrived from the sender. An example of the second scenario is that an electronic mail message contains instructions to a stockbroker for a transaction that subsequently turns out badly. The sender pretends that the message was never sent.

In situations where there is not complete trust between sender and receiver, something more than authentication is needed. The most attractive solution to this problem is the digital signature. The digital signature is analogous to the handwritten signature. It must have the following properties:

It must verify the author and the date and time of the signature.
It must to authenticate the contents at the time of the signature.
It must be verifiable by third parties, to resolve disputes.

Thus, the digital signature function includes the authentication function.

On the basis of these properties, we can formulate the following requirements for a digital signature:

The signature must be a bit pattern that depends on the message being signed.
The signature must use some information unique to the sender, to prevent both forgery and denial.
It must be relatively easy to produce the digital signature.
It must be relatively easy to recognize and verify the digital signature.
It must be computationally infeasible to forge a digital signature, either by constructing a new message for an existing digital signature or by constructing a fraudulent digital signature for a given message.
It must be practical to retain a copy of the digital signature in storage.

A secure hash function, embedded in a scheme such as that of Figure 11.5c or d, satisfies these requirements.

A variety of approaches has been proposed for the digital signature function. These approaches fall into two categories: direct and arbitrated.

Direct Digital Signature

The direct digital signature involves only the communicating parties (source, destination). It is assumed that the destination knows the public key of the source. A digital signature may be formed by encrypting the entire message with the sender's private key (Figure 11.1c) or by encrypting a hash code of the message with the sender's private key (Figure 11.5c).

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Confidentiality can be provided by further encrypting the entire message plus signature with either the receiver's public key (public-key encryption) or a shared secret key (symmetric encryption); for example, see Figures 11.1d and 11.5d. Note that it is important to perform the signature function first and then an outer confidentiality function. In case of dispute, some third party must view the message and its signature. If the signature is calculated on an encrypted message, then the third party also needs access to the decryption key to read the original message. However, if the signature is the inner operation, then the recipient can store the plaintext message and its signature for later use in dispute resolution.

All direct schemes described so far share a common weakness. The validity of the scheme depends on the security of the sender's private key. If a sender later wishes to deny sending a particular message, the sender can claim that the private key was lost or stolen and that someone else forged his or her signature. Administrative controls relating to the security of private keys can be employed to thwart or at least weaken this ploy, but the threat is still there, at least to some degree. One example is to require every signed message to include a timestamp (date and time) and to require prompt reporting of compromised keys to a central authority.

Another threat is that some private key might actually be stolen from X at time T. The opponent can then send a message signed with X's signature and stamped with a time before or equal to T.

Arbitrated Digital Signature

The problems associated with direct digital signatures can be addressed by using an arbiter.

As with direct signature schemes, there is a variety of arbitrated signature schemes. In general terms, they all operate as follows. Every signed message from a sender X to a receiver Y goes first to an arbiter A, who subjects the message and its signature to a number of tests to check its origin and content. The message is then dated and sent to Y with an indication that it has been verified to the satisfaction of the arbiter. The presence of A solves the problem faced by direct signature schemes: that X might disown the message.

The arbiter plays a sensitive and crucial role in this sort of scheme, and all parties must have a great deal of trust that the arbitration mechanism is working properly. The use of a trusted system, described in Chapter 20, might satisfy this requirement.

Table 13.1, based on scenarios described in [AKL83] and [MITC92], gives several examples of arbitrated digital signatures.^[1] In the first, symmetric encryption is used. It is assumed that the sender X and the arbiter A share a secret key K_xa and that A and Y share secret key K_ay. X constructs a message M and computes its hash value H(M). Then X transmits the message plus a signature to A. The signature consists of an identifier ID_X of X plus the hash value, all encrypted using K_xa. A decrypts the signature and checks the hash value to validate the message. Then A transmits a message to Y, encrypted with K_ay. The message includes ID_X, the original message from X, the signature, and a timestamp. Y can decrypt this to recover the message and the signature. The timestamp informs Y that this message is timely and not a replay. Y can store M and the signature. In case of dispute, Y, who claims to have received M from X, sends the following message to A:

^[1] The following format is used. A communication step in which P sends a message M to Q is represented as P Q:
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E(K_ay, [ID_X||M||E(K_xa, [ID_X||H(M)])])

Table 13.1. Arbitrated Digital Signature Techniques
(1) X A: K_xa, [ID_X||H(M)])
(2) A Y: E(ID_X||M||E(K_xa, [ID_X||H(M)])||T])
(a) Conventional Encryption, Arbiter Sees Message
(1) X A: K_xy, M)||E(K_xa, [ID_X||H(E(K_xy, M))])
(2) A Y: E(ID_X||E(K_xy, M)])||E(K_xa, [ID_X||H(E(K_xy, M))||T])
(b) Conventional Encryption, Arbiter Does Not See Message
(1) X A: PR_x, [ID_X||E(PU_y, E(PR_x, M))])
(2) A Y: E(ID_X||E(PU_y, E(PR_x, M))||T])
(c) Public-Key Encryption, Arbiter Does Not See Message
Notation:

X
= sender
Y
= recipient
A
= Arbiter
M
= message
T
= timestamp

The arbiter uses K_ay to recover ID_X, M, and the signature, and then uses K_xa to decrypt the signature and verify the hash code. In this scheme, Y cannot directly check X's signature; the signature is there solely to settle disputes. Y considers the message from X authentic because it comes through A. In this scenario, both sides must have a high degree of trust in A:

X must trust A not to reveal K_xa and not to generate false signatures of the form E(K_xa, [ID_X||H(M)]).
Y must trust A to send E(K_ay, [ID_X||M||E(K_xa, [ID_X||H(M)])||T]) only if the hash value is correct and the signature was generated by X.
Both sides must trust A to resolve disputes fairly.

If the arbiter does live up to this trust, then X is assured that no one can forge his signature and Y is assured that X cannot disavow his signature.

The preceding scenario also implies that A is able to read messages from X to Y and, indeed, that any eavesdropper is able to do so. Table 13.1b shows a scenario that provides the arbitration as before but also assures confidentiality. In this case it is assumed that X and Y share the secret key K_xy. Now, X transmits an identifier, a copy of the message encrypted with K_xy, and a signature to A. The signature consists of the identifier plus the hash value of the encrypted message, all encrypted using K_xa. As before, A decrypts the signature and checks the hash value to validate the message. In this case, A is working only with the encrypted version of the message and is prevented from reading it. A then transmits everything that it received from X, plus a timestamp, all encrypted with K_ay, to Y.
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Although unable to read the message, the arbiter is still in a position to prevent fraud on the part of either X or Y. A remaining problem, one shared with the first scenario, is that the arbiter could form an alliance with the sender to deny a signed message, or with the receiver to forge the sender's signature.

All the problems just discussed can be resolved by going to a public-key scheme, one version of which is shown in Table 13.1c. In this case, X double encrypts a message M first with X's private key, PR_x and then with Y's public key, PU_y. This is a signed, secret version of the message. This signed message, together with X's identifier, is encrypted again with PR_x and, together with ID_X, is sent to A. The inner, double-encrypted message is secure from the arbiter (and everyone else except Y). However, A can decrypt the outer encryption to assure that the message must have come from X (because only X has PR_x). A checks to make sure that X's private/public key pair is still valid and, if so, verifies the message. Then A transmits a message to Y, encrypted with PR_a. The message includes ID_X, the double-encrypted message, and a timestamp.

This scheme has a number of advantages over the preceding two schemes. First, no information is shared among the parties before communication, preventing alliances to defraud. Second, no incorrectly dated message can be sent, even if PR_x is compromised, assuming that PR_a is not compromised. Finally, the content of the message from X to Y is secret from A and anyone else. However, this final scheme involves encryption of the message twice with a public-key algorithm. We discuss more practical approaches subsequently.