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Assignment 1 Phuket Rajabhat University Assignment 1 Using Microsoft Word 2007 Wipawan Buathong 27/09/2014 Assignment 1 Using Microsoft Word 2007 Wipawan Buathong PUBLIC-KEY CRYPTOGRAPHY TABLE OF CONTENT HOW IT WORKS ................................................................................................................................................. 3 DESCRIPTION ..................................................................................................................................................... 3 PUBLIC KEY ENCRYPTION ............................................................................................................................... 3 DIGITAL SIGNATURES..................................................................................................................................... 3 TABLE OF FIGURES Figure 1 Public Key Cyptography ....................................................................................................................... 3 Figure 2 Public Key Encryption .......................................................................................................................... 4 Figure 3 Digital Signature .................................................................................................................................. 4 ublic-key cryptography1 refers to a cryptographic key cryptography". Some of these algorithms have the public system requiring two separate keys, one to lock or key / private key property, that is, neither key is derivable encrypt the plaintext, and one to unlock or decrypt from knowledge of the other; not all asymmetric key the cyphertext. Neither key will do both functions. algorithms do. Those with this property are particularly POne of these keys is published or public and the other is kept useful and have been widely deployed and are the source of private. If the lock/encryption key is the one published then the commonly used name. The public key is used to the system enables private communication from the public transform a message into an unreadable form, decryptable to the unlocking key's owner. If the unlock/decryption key is only by using the (different but matching) private key. the one published then the system serves as a signature Participants in such a system must create a mathematically verifier of documents locked by the owner of the private linked key pair (i.e., a public and a private key). By publishing key. This cryptographic approach uses asymmetric key the public key, the key producer empowers anyone who gets algorithms, hence the more general name of "asymmetric a copy of the public key to produce messages only he can read -- because only the key producer has a copy of the 1 From Wikipedia, the free encyclopedia, private key (required for decryption). When someone wants http://en.wikipedia.org/wiki/Public-key_cryptography to send a secure message to the creator of those keys, the 2 Assignment 1 Using Microsoft Word 2007 Wipawan Buathong sender encrypts it (i.e., transforms it into an unreadable In contrast, symmetric-key algorithms, variations of form) using the intended recipient's public key; to decrypt which have been used for thousands of years, use a the message, the recipient uses the private key. No one else, single secret key—which must be shared and kept including the sender can do so. private by both sender and receiver—for both encryption and decryption. To use a symmetric encryption scheme, the sender and receiver must securely share a key in advance. Because symmetric key algorithms are nearly always much less computationally intensive, it is common to exchange a key using a key-exchange algorithm and transmit data using that key and a symmetric key algorithm. PGP, and the SSL/TLS family of schemes do this, for instance, and are thus called hybrid cryptosystems. DESCRIPTION Figure 1 Public Key Cyptography The two main branches of public key cryptography are public key encryption and digital signatures. HOW IT WORKS PUBLIC KEY ENCRYPTION The distinguishing technique used in public key A message encrypted with a recipient's public key cryptography is the use of asymmetric key algorithms, cannot be decrypted by anyone except a possessor of where the key used to encrypt a message is not the the matching private key—presumably, this will be the same as the key used to decrypt it. Each user has a owner of that key and the person associated with the pair of cryptographic keys—a public encryption key public key used. This is used for confidentiality. and a private decryption key. The publicly available encrypting-key is widely distributed, while the private DIGITAL SIGNATURES decrypting-key is known only to the recipient. A message signed with a sender's private key can be Messages are encrypted with the recipient's public key verified by anyone who has access to the sender's and can only be decrypted with the corresponding public key, thereby proving that the sender had access private key. The keys are related mathematically, but to the private key (and therefore is likely to be the parameters are chosen so that determining the private person associated with the public key used), and the key from the public key is prohibitively expensive. The part of the message that has not been tampered with. discovery of algorithms that could produce On the question of authenticity, see also message public/private key pairs revolutionized the practice of digest. cryptography beginning in the middle 1970s. 3 Assignment 1 Using Microsoft Word 2007 Wipawan Buathong Figure 2 Public Key Encryption An analogy to public-key encryption is that of a locked mailbox with a mail slot. The mail slot is exposed and accessible to the public; its location (the street address) is in essence the public key. Anyone knowing the street address can go to the door and drop a written Figure 3 Digital Signature message through the slot; however, only the person who possesses the key can open the mailbox and read the message. HISTORY An analogy for digital signatures is the sealing of an envelope with a personal wax seal. The During the early history of cryptography, two parties message can be opened by anyone, but the would rely upon a key using a secure, but non- presence of the seal authenticates the cryptographic, method; for example, a face-to-face sender. meeting or an exchange via a trusted courier. This key, which both parties kept absolutely secret, could then A central problem for use of public-key cryptography is be used to exchange encrypted messages. A number confidence (ideally proof) that a public key is correct, of significant practical difficulties arise in this approach belongs to the person or entity claimed (i.e., is to distributing keys. Public-key cryptography 'authentic'), and has not been tampered with or addresses these drawbacks so that users can replaced by a malicious third party. The usual communicate securely over a public channel without approach to this problem is to use a public-key having to agree upon a shared key beforehand. infrastructure (PKI), in which one or more third parties, known as certificate authorities, certify In 1874, a book by William Stanley Jevons described ownership of key pairs. PGP, in addition to a certificate the relationship of one-way functions to cryptography authority structure, has used a scheme generally and went on to discuss specifically the factorization called the "web of trust", which decentralizes such problem used to create the trapdoor function in the authentication of public keys by a central mechanism, RSA system. In July 1996, one observer[2] commented substituting individual endorsements of the link on the Jevons book in this way: between user and public key. No fully satisfactory In his book The Principles of Science: A Treatise on solution to the public key authentication problem is Logic and Scientific Method, written and published in known. 4 Assignment 1 Using Microsoft Word 2007 Wipawan Buathong the 1890s, William S. Jevons observed that there are digital signature, and its security is connected to the many situations where the 'direct' operation is presumed difficulty of factoring large integers, a relatively easy, but the 'inverse' operation is problem for which there is no known efficient (i.e., significantly more difficult. One example mentioned practicably fast) general technique. In 1979 Michael O. briefly is that enciphering (encryption) is easy while Rabin published a related cryptosystem that is deciphering (decryption) is not. In the same section of probably secure as long as factorization of the public Chapter 7: Introduction titled 'Induction an Inverse key remains difficult; it remains an assumption that Operation', much more attention is devoted to the RSA also enjoys this security. principle that multiplication of integers is easy, but finding the (prime) factors of the product is much Since the 1970s, a large number and variety of harder. Thus, Jevons anticipated a key feature of the encryption, digital signature, key agreement, and RSA Algorithm for public key cryptography, though he other techniques have been developed in the field of certainly did not invent the concept of public key public-key cryptography. The ElGamal cryptosystem cryptography. (Ferguson N., 2003) (invented by Taher ElGamal) relies on the (similar, and related) difficulty of the discrete logarithm problem, as An asymmetric-key cryptosystem was published in does the closely related DSA developed at the US 1976 by Whitfield Diffie and Martin Hellman, who, National Security Agency
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