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In Cryptography , a digital signature or '''digital signature scheme''' is a type of Asymmetric Cryptography used to simulate the security properties of a Signature in digital, rather than written, form. Digital signature schemes normally give two algorithms, one for signing which involves the user's secret or Private Key , and one for verifying signatures which involves the user's Public Key . The output of the signature process is called the "digital signature." Digital signatures, like written signatures, are used to provide Authentication of the associated input, usually called a "message." Messages may be anything, from Electronic Mail to a Contract , or even a message sent in a more complicated Cryptographic Protocol . Digital signatures are used to create Public Key Infrastructure (PKI) schemes in which a user's public key (whether for Public-key Encryption , digital signatures, or any other purpose) is tied to a user by a Digital Identity Certificate issued by a Certificate Authority . PKI schemes attempt to unbreakably bind user information (name, address, phone number, etc.) to a public key, so that public keys can be used as a form of Identification . Digital signatures are often used to implement , and in the European Union , electronic signatures have legal significance. However, laws concerning electronic signatures do not always make clear their applicability towards cryptographic digital signatures, leaving their legal importance somewhat unspecified. DEFINITION See Also: Public-key cryptography A digital signature scheme typically consists of three algorithms:
Two main properties are required. First, signatures computed honestly should always verify. That is, ''V'' should accept (''m'', ''PK'', ''S'' (''m'', ''SK'')) whenever ''SK'' is the secret key related to ''PK'', for any message ''m''. Secondly, it should be hard for any adversary, knowing only ''PK'', to create valid signature(s) HISTORY In the famous paper "New Directions in Cryptography", , 2002. Soon afterwards, Ronald Rivest , Adi Shamir , and Len Adleman invented the RSA algorithm, the first scheme for digital signatures"A Method For Obtaining Digital Signatures and Public-Key Cryptosystems," Communications of the ACM, 21(2): 120-126, Feb. 1978.. The first widely marketed software package to offer digital signature was Lotus Notes 1.0, released in 1989, which used the RSA algorithm. The History of Lotus Notes , accessed April 27 , 2007 . RSA signatures are performed using the algorithms of the RSA cryptosystem. To generate RSA signature keys, one simply generates an RSA key pair. To sign a message ''m'', the signer computes σ=''E''(''SK'',''m''): that is, the signer ''encrypts'' the message ''m'' to obtain σ. To verify a signature, we check that ''D''(''PK'',σ) = ''m'', that is, that ''decrypting'' σ gives the message ''m.'' (See trapdoor permutation for terminology clarification below). In this procedure, any ''m'' up to a certain maximum size can be used as input. In order to sign messages of arbitrary size, we typically first apply a Cryptographic Hash Function to the message ''m'' to get a uniquely identifying summary of the message (called the digest or hash) that is of a fixed or maximum length, which is then signed to obtain σ. However, other digital signature schemes were soon developed after RSA, the earliest being Lamport Signature s"Constructing digital signatures from a one-way function.", Leslie Lamport , Technical Report CSL-98, SRI International, Oct. 1979., Merkle Signatures (also known as "Merkle trees" or simply "Hash trees")"A certified digital signature", Ralph Merkle, In Gilles Brassard, ed., Advances in Cryptology -- CRYPTO '89, vol. 435 of Lecture Notes in Computer Science, pp. 218-238, Spring Verlag, 1990., and Rabin Signature s"Digitalized signatures as intractable as factorization." Michael O. Rabin , Technical Report MIT/LCS/TR-212, MIT Laboratory for Computer Science, Jan. 1979, which required simpler Computational Hardness Assumption s. In 1988, Shafi Goldwasser , Silvio Micali , and Ronald Rivest became the first to rigorously define the security requirements of digital signature schemes. They described a hierarchy of attack models: # In a ''key-only'' attack, the attacker is only given the public verification key. # In a ''known message'' attack, the attacker is given valid signatures for a variety of messages known by the attacker but not chosen by the attacker. # In a ''chosen message'' attack, the attacker first learns signatures on arbitrary messages of the attacker's choice. They also describe a hierarchy of attack results: # A ''total break'' results in the recovery of the signing key. # A ''universal forgery'' attack results in the ability to forge signatures for any message. # A ''selective forgery'' attack results in a signature on a message of the adversary's choice. # An ''existential forgery'' merely results in some valid message/signature pair not already known to the adversary. They also present The GMR Signature Scheme , the first that can be proven to prevent even an existential forgeries against even a chosen message attack."A digital signature scheme secure against adaptive chosen-message attacks.", Shafi Goldwasser, Silvio Micali, and Ronald Rivest. SIAM Journal on Computing, 17(2):281-308, Apr. 1988. Most early signature schemes were of a similar type: they involve the use of a Trapdoor Permutation , such as the RSA function, or in the case of the Rabin Signature scheme, computing square modulo composite ''n.'' A trapdoor permutation family is a family of Permutation s, specified by a parameter, that is easy to compute in the forward direction, but is difficult to compute in the reverse direction. However, for every parameter there is a "trapdoor" that enables easy computation of the reverse direction. Trapdoor permutations can be viewed as public-key encryption systems, where the parameter is the public key and the trapdoor is the secret key, and where encrypting corresponds to computing the forward direction of the permutation, while decrypting corresponds to the reverse direction. Trapdoor permutations can also be viewed as digital signature schemes, where computing the reverse direction with the secret key is thought of as signing, and computing the forward direction is done to verify signatures. Because of this correspondence, digital signatures are often described as based on public-key cryptosystems, where signing is equivalent to decryption and verification is equivalent to encryption, but this is not the only way digital signatures are computed. Used directly, this type of signature scheme is vulnerable to a key-only existential forgery attack. To create a forgery, the attacker picks a random signature σ and uses the verification procedure to determine the message ''m'' corresponding to that signature."Modern Cryptography: Theory & Practice", Wenbo Mao, Prentice Hall Professional Technical Reference, New Jersey, 2004, pg. 308. ISBN 0-13-066943-1 In practice, however, this type of signature is not used directly, but rather, the message to be signed is first Hashed to produce a short digest that is then signed. This forgery attack, then, only produces the hash function output that corresponds to σ, but not a message that leads to that value, which does not lead to an attack. In the Random Oracle Model , this Hash-and-decrypt form of signature is existentially unforgeable, even against a chosen-message attack. There are several reasons to sign such a hash (or message digest) instead of the whole document.
BENEFITS OF DIGITAL SIGNATURES These are common reasons for applying a digital signature to communications: Authentication Although messages may often include information about the entity sending a message, that information may not be accurate. Digital signatures can be used to authenticate the source of messages. When ownership of a digital signature secret key is bound to a specific user, a valid signature shows that the message was sent by that user. The importance of high confidence in sender authenticity is especially obvious in a financial context. For example, suppose a bank's branch office sends instructions to the central office requesting a change in the balance of an account. If the central office is not convinced that such a message is truly sent from an authorized source, acting on such a request could be a grave mistake. Integrity In many scenarios, the sender and receiver of a message may have a need for confidence that the message has not been altered during transmission. Although encryption hides the contents of a message, it may be possible to ''change'' an encrypted message without understanding it. (Some encryption algorithms, known as Nonmalleable ones, prevent this, but others do not.) However, if a message is digitally signed, any change in the message will invalidate the signature. Furthermore, there is no efficient way to modify a message and its signature to produce a new message with a valid signature, because this is still considered to be computationally infeasible by most Cryptographic Hash Functions (see Collision Resistance ). DRAWBACKS OF DIGITAL SIGNATURES Despite their usefulness, digital signatures do not alone solve all the problems we might wish them to. Association of digital signatures and trusted time stamping Digital signature algorithms and protocols do not inherently provide certainty about the date and time at which the underlying document was signed. The signer might, or might not, have included a time stamp with the signature, or the document itself might have a date mentioned on it, but a later reader cannot be certain the signer did not, for instance, backdate the date or time of the signature. Such misuse can be made impracticable by using Trusted Time Stamping in addition to digital signatures. Non-repudiation See Also: Non-repudiation In a cryptographic context, the word ''repudiation'' refers to any act of disclaiming responsibility for a message. A message's recipient may insist the sender attach a signature in order to make later repudiation more difficult, since the recipient can show the signed message to a third party (eg, a court) to reinforce a claim as to its signatories and integrity. However, loss of control over a user's private key will mean that all digital signatures using that key, and so ostensibly 'from' that user, are suspect. Nonetheless, a user cannot repudiate a signed message without repudiating their signature key. It is aggravated by the fact there is no trusted time stamp, so new documents (after the key compromise) cannot be separated from old ones, further complicating signature key invalidation. Certificate Authorities usually maintain a public repository of public-key so the association user-key is certified and signatures cannot be repudiated. Expired certificates are normally removed from the directory. It is a matter for the security policy and the responsibility of the authority to keep old certificates for a period of time if a non-repudiation of data service is provided. ADDITIONAL SECURITY PRECAUTIONS =Putting the private key on a smart card All public key / private key cryptosystems depend entirely on keeping the private key secret. A private key can be stored on a user's computer, and protected by, for instance, a local password, but this has two disadvantages:
A more secure alternative is to store the private key on a Smart Card . Many smart cards are deliberately designed to be tamper resistant (however, quite a few designs have been broken, notably by Ross Anderson and his students). In a typical implementation, the hash calculated from the document is sent to the smart card, whose CPU encrypts the hash using the stored private key of the user and returns it. Typically, a user must activate his smart card by entering a Personal Identification Number or PIN code (thus providing a Two-factor Authentication ). Note that it can be sensibly arranged (but is not always done) that the private key never leaves the smart card. If the smart card is stolen, the thief will still need the PIN code to generate a digital signature. This reduces the security of the scheme to that of the PIN system, but is nevertheless more secure than are many PCs. =Using smart card readers with a separate keyboard Entering a PIN code to activate the smart card, commonly requires a numeric keypad. Some card readers have their own numeric keypad. This is safer than using a card reader integrated into a PC, and then entering the PIN using that computer's keyboard. The computer might be running a Keystroke Logger (by its owner/operators intention or otherwise -- due to a virus, for instance) so that the PIN code becomes compromised. Specialized card readers are less vulnerable, though not invulnerable, against tampering with their software or hardware. And, of course, eavesdropping attacks against all such equipment are possible. =Other smart card designs Smart card design is an active field, and there are smart card schemes which are intended to avoid these particular problems, though so far with little security proofs. =Using digital signatures only with trusted applications One of the main differences between a digital signature and a written signature is that the user does not "see" what he signs. It's the application that presents a hash code to be encrypted with the private key, but in the case of a malicious application a hash code of another document might be presented so that the users thinks he is signing the document he sees on the screen but is actually unwillingly signing another (probably less favorable). SOME DIGITAL SIGNATURE ALGORITHMS
THE CURRENT STATE OF USE — LEGAL AND PRACTICAL Digital signature schemes all have several prior requirements without which no such signature can mean anything, whatever the cryptographic theory or legal provision.
Only if all of these conditions are met will a digital signature actually be any evidence of who sent the message, and therefore of their assent to its contents. Legal enactment cannot change this reality of the existing engineering possibilities, though some such have not reflected this actuality. Legislatures, being importuned by businesses expecting to profit from operating a PKI, or by the technological avant-garde advocating new solutions to old problems, have enacted statutes and/or regulations in many jurisdictions authorizing, endorsing, encouraging, or permitting digital signatures and providing for (or limiting) their legal effect. The first appears to have been in Utah in the United States, followed closely by the states Massachusetts and California . Other countries have also passed statutes or issued regulations in this area as well and the UN has had an active model law project for some time. These enactments (or proposed enactments) vary from place to place, have typically embodied expectations at variance (optimistically or pessimistically) with the state of the underlying Cryptographic Engineering , and have had the net effect of confusing potential users and specifiers, nearly all of whom are not cryptographically knowledgeable. Adoption of technical standards for digital signatures have lagged behind much of the legislation, delaying a more or less unified engineering position on Interoperability , Algorithm choice, Key Length s, and so on what the engineering is attempting to provide. See also =Using separate key pairs for signing and encryption In several countries, a digital signature has a status somewhat like that of a traditional pen and paper signature. Generally, these provisions mean that what is digitally signed legally binds the signer of the document to the terms therein. For that reason, it is often thought best to use separate key pairs for encrypting and signing. Using the encryption key pair a person can engage in an encrypted conversation (eg, about buying a house), but does not legally sign every message he sends. Only when both parties come to an agreement do they sign a contract with their signing keys, and only then are they legally bound by the terms of a specific document. After signing, the document can be sent over the encrypted link. SEE ALSO REFERENCES EXTERNAL LINKS
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