NTRU (Number Theory Research Unit)
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28082009, 02:16 AM
NTRU (Number Theory Research Unit) Abstract CRYPTOGRAPHY: Cryptography is an algorithmic process of converting a plain text message to a cipher text message based on an algorithm that both the sender and receiver know, so that the cipher text message can be returned to its original, plain text form. In its cipher form, a message cannot be read by anyone other than the intended receiver. The act of converting a plain text message to its cipher text is called enciphering. Reversing that act is deciphering. Enciphering and deciphering are more commonly referred to as Encryption and decryption, respectively. Cryptography concerns itself with four 1) Confidentiality (the information cannot be understood by anyone for whom 2) Integrity (the information cannot be altered in storage or transit between sender and intended receiver without the alteration being detected) 3) Nonrepudiation (the creator/sender of the information cannot deny at a later stage his or her intentions in the creation or transmission of the 4) Authentication (the sender and receiver can confirm each otherâ„¢s identity and the origin/destination of the information) Procedures and protocols that meet some or all of the above criteria are known as crypto systems. There are a number of algorithms for performing encryption and decryption, but comparatively few such algorithms have stood the test of time. The most successful algorithms use a key. A key is simply a parameter to the algorithm that allows the encryption and decryption process to occur. There are many modern keybased cryptographic techniques. These are divided into two classes: symmetric and asymmetric (also called public/private) key cryptography. In symmetric Key cryptography, the same key is used for both encryption and decryption. In asymmetric key cryptography, one key is used for encryption and another, mathematically related key, is used for decryption. Cryptographic algorithms are of two types: 1.1.1 Secret key or Symmetric key algorithms 1.1.2 Public key cryptographic algorithms 1.1.1 SYMMETRIC KEY CRYPTOGRAPHY: Symmetrickey systems are simpler and faster, but their main drawback is that the two parties must somehow exchange the key in a secure way. Public key encryption avoids this problem because the public key can be distributed in a nonsecure way, and the private key is never transmitted. Symmetrickey cryptography is sometimes called secretKey cryptography. The most popular symmetrickey system is the Data Encryption Standard (DES). 1.1.2 PUBLIC KEY CRYPTOGRAPHY: The study and application of asymmetric encryption systems Classical Symmetric cryptographic algorithms provide a secure communication channelto each pair of users. In order to establish such a channel, the symmetric key algorithms employ a classical encryption scheme in which both the algorithm depends on the same secret key k. This key is used for both encryption and decryption. After establishing a secure communication channel, the secrecy of a message can be guaranteed. Symmetric cryptography also includes methods to detect modification s of messages and methods to verify the origin of a message. Thus, confidentiality and integrity can be accomplished using secret key techniques. In secret key algorithms we have D (k, E (k, m)) = m for each plain text m. There are many algorithms in this process .The famous ones among them are DES, IDEA etc. An encryption system in which the sender and receiver of a message share a single, common key that is used to encrypt and decrypt the message. Contrast this with publickey cryptology, which utilizes two keys  a public key to encrypt messages and a private key to decrypt them. Which use one key For encryption and another for decryption. A corresponding pair of such keys constitutes a key pair. Also called asymmetric cryptography. It is a coding System in which encryption and decryption are done with public and private Keys, allowing users who donâ„¢t know each other to send secure or verifiable Messages. Suppose Fred wants to send a message. He would encrypt it with His private key, which no one else knows; then, the recipient would decrypt it Using Fredâ„¢s publicly available key, thus verifying that the message came from Fred. Alternately, suppose Fred wants to receive an encrypted message. The Sender would encrypt the message with Fredâ„¢s public key, and only Fred Would be able to decrypt it, using his private key. This method, also known as Dualkey cryptography contrasts with the older secretkey or symmetric Cryptography, in which the sender and recipient must agree on and use the same private key for encryption and decryption. Type of cryptography in which the encryption process is publicly available and unprotected, but in which a Part of the decryption key is protected so that only a party with knowledge of both parts of the decryption process can decrypt the cipher text. In public key cryptography, keys are created in matched pairs. Encrypt with one half of a pair and only the matching other half can decrypt it. This contrasts with symmetric or secret key cryptography in which a single key known to both parties is used for both encryption and decryption. One half of each pair, called the public key, is made public. The other half, called the private key, is kept secret. Messages can then be sent by anyone who knows the public key to the holder of the private key. Encrypt with the public key and you know only someone with the matching private key can decrypt. Public key techniques can be used to create digital signatures and to deal with key management issues, perhaps the hardest part of effective deployment of symmetric ciphers. The resulting hybrid cryptosystems use public key methods to manage keys for symmetric ciphers. Many organizations are currently creating PKCs, public key infrastructures to make these benefits widely available. Example: A widely used public/private key algorithm is RSA, named after the initials of its inventors, Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman .RSA depends on the difficulty of factoring the product of two very large prime numbers. Although used for encrypting whole messages, RSA is much less efficient than symmetric key algorithms such as DES. ElGamal is another public/private key algorithm. It uses a different arithmetic algorithm than RSA, called the discrete logarithm problem. The most recently evolved public key cryptography is the NTRU pkcs. The NTRU Encrypt cryptosystem is much faster than exponentiation systems such as RSA, El Gamal, and ECC. One reason is that the basic operations used by NTRUEncrypt involve manipulation of small numbers, generally numbers less than 255. Exponentiation systems, on the other hand, require numbers with hundreds of digits. A careful mathematical analysis shows that for keys consisting of around N bits, the RSA, El Gamal, and ECC systems require on the order of N3 operations to encrypt or decrypt a message, while NTRU Encrypt requires only on the order of N2 operations to encrypt or decrypt a message. 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