How Digital Signature Technology Works
　　Digital signatures are created and verified by cryptography, the branch of applied mathematics that concerns itself with transforming messages into seemingly unintelligible forms and back again. Digital signatures use what is known as "public key cryptography," which employs an algorithm using two different but mathematically related "keys;" one for creating a digital signature or transforming data into a seemingly unintelligible form, and another key for verifying a digital signature or returning the message to its original form. <19> Computer equipment and software utilizing two such keys are often collectively termed an "asymmetric cryptosystem."

　　The complementary keys of an asymmetric cryptosystem for digital signatures are arbitrarily termed the private key, which is known only to the signer <20> and used to create the digital signature, and the public key, which is ordinarily more widely known and is used by a relying party to verify the digital signature. If many people need to verify the signer's digital signatures, the public key must be available or distributed to all of them, perhaps by publication in an on-line repository or directory where it is easily accessible. Although the keys <21> of the pair are mathematically related, if the asymmetric cryptosystem has been designed and implemented securely <22> it is "computationally infeasible <23> to derive the private key from knowledge of the public key. Thus, although many people may know the public key of a given signer and use it to verify that signer's signatures, they cannot discover that signer's private key and use it to forge digital signatures. This is sometimes referred to as the principle of "irreversibility."

　　Another fundamental process, termed a "hash function," is used in both creating and verifying a digital signature. A hash function is an algorithm which creates a digital representation or "fingerprint" in the form of a "hash value" or "hash result" of a standard length which is usually much smaller than the message but nevertheless substantially unique to it. <24> Any change to the message invariably produces a different hash result when the same hash function is used. In the case of a secure hash function, sometimes termed a "one-way hash function," it is computationally infeasible <25> to derive the original message from knowledge of its hash value. Hash functions therefore enable the software for creating digital signatures to operate on smaller and predictable amounts of data, while still providing robust evidentiary correlation to the original message content, thereby efficiently providing assurance that there has been no modification of the message since it was digitally signed.

　　Thus, use of digital signatures usually involves two processes, one performed by the signer and the other by the receiver of the digital signature:

　　Digital signature creation uses a hash result derived from and unique to both the signed message and a given private key. For the hash result to be secure, there must be only a negligible possibility that the same digital signature could be created by the combination of any other message or private key.
　　Digital signature verification is the process of checking the digital signature by reference to the original message and a given public key, thereby determining whether the digital signa ture was created for that same message using the private key that corresponds to the referenced public key.
　　To sign a document or any other item of information, the signer first delimits precisely the borders of what is to be signed. The delimited information to be signed is termed the "message" in these Guidelines. Then a hash function in the signer's software computes a hash result unique (for all practical purposes) to the message. The signer's software then transforms the hash result into a digital signature using the signer's private key. <26> The resulting digital signature is thus unique to both the message and the private key used to create it.

　　Typically, a digital signature (a digitally signed hash result of the message) is attached to its message and stored or transmitted with its message. However, it may also be sent or stored as a separate data element, so long as it maintains a reliable association with its message. Since a digital signature is unique to its message, it is useless if wholly disassociated from its message.

　　Verification of a digital signature is accomplished by computing a new hash result of the original message by means of the same hash function used to create the digital signature. Then, using the public key and the new hash result, the verifier checks: (1) whether the digital signature was created using the corresponding private key; and (2) whether the newly computed hash result matches the original hash result which was transformed into the digital signature during the signing process. The verification software will confirm the digital signature as "verified" if: (1) the signer's private key was used to digitally sign the message, which is known to be the case if the signer's public key was used to verify the signature because the signer's public key will verify only a digital signature created with the signer's private key; <27> and (2) the message was unaltered, which is known to be the case if the hash result computed by the verifier is identical to the hash result extracted from the digital signature during the verification process.

　　Various asymmetric cryptosystems create and verify digital signatures using different algorithms and procedures, but share this overall operational pattern.

　　The processes of creating a digital signature and verifying it accomplish the essential effects desired of a signature for many legal purposes:

　　Signer authentication: If a public and private key pair is associated with an identified signer, the digital signature attributes the message to the signer. The digital signature cannot be forged, unless the signer loses control of the private key (a "compromise" of the private key), such as by divulging it or losing the media or device in which it is contained.
　　Message authentication: The digital signature also identifies the signed message, typically with far greater certainty and precision than paper signatures. Verification reveals any tampering, since the comparison of the hash results (one made at signing and the other made at verifying) shows whether the message is the same as when signed.
　　Affirmative act: Creating a digital signature requires the signer to use the signer's private key. This act can perform the "ceremonial" function of alerting the signer to the fact that the signer is consummating a transaction with legal consequences. <28>
　　Efficiency: The processes of creating and verifying a digital signature provide a high level of assurance that the digital signature is genuinely the signer's. As with the case of modern electronic data interchange ("EDI") the creation and verification processes are capable of complete automation (sometimes referred to as "machinable"), with human interaction required on an exception basis only. Compared to paper methods such as checking specimen signature cards -- methods so tedious and labor-intensive that they are rarely actually used in practice -- digital signatures yield a high degree of assurance without adding greatly to the resources required for processing.
　　The processes used for digital signatures have undergone thorough technological peer review for over a decade. Digital signatures have been accepted in several national and international standards developed in cooperation with and accepted by many corporations, banks, and government agencies. <29> The likelihood of malfunction or a security problem in a digital signature cryptosystem designed and implemented as prescribed in the industry standards is extremely remote, <30> and is far less than the risk of undetected forgery or alteration on paper or of using other less secure electronic signature techniques.

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