Quantum Cryptography
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 computer science crazy Super Moderator Posts: 3,048 Joined: Dec 2008 22-09-2008, 09:56 AM Definition Quantum cryptography is an effort to allow two users of a common communication channel to create a body of shared and secret information. This information, which generally takes the form of a random string of bits, can then be used as a conventional secret key for secure communication. It is useful to assume that the communicating parties initially share a small amount of secret information, which is used up and then renewed in the exchange process, but even without this assumption exchanges are possible. The advantage of quantum cryptography over traditional key exchange methods is that the exchange of information can be shown to be secure in a very strong sense, without making assumptions about the intractability of certain mathematical problems. Even when assuming hypothetical eavesdroppers with unlimited computing power, the laws of physics guarantee (probabilistically) that the secret key exchange will be secure, given a few other assumptions. Cryptography is the art of devising codes and ciphers, and cryptoanalysis is the art of breaking them. Cryptology is the combination of the two. In the literature of cryptology, information to be encrypted is known as plaintext, and the parameters of the encryption function that transforms are collectively called a key. Existing cryptographic techniques are usually identified as ``traditional'' or ``modern.'' Traditional techniques date back for centuries, and are tied to the the operations of transposition (reordering of plaintext) and substitution (alteration of plaintext characters). Traditional techniques were designed to be simple, and if they were to be used with great secrecy extremely long keys would be needed. By contrast, modern techniques rely on convoluted algorithms or intractable problems to achieve assurances of security. There are two branches of modern cryptographic techniques: public-key encryption and secret-key encryption. In public-key cryptography, messages are exchanged using keys that depend on the assumed difficulty of certain mathematical problems -- typically the factoring of extremely large (100+ digits) prime numbers. Each participant has a ``public key'' and a ``private key''; the former is used by others to encrypt messages, and the latter by the participant to decrypt them. In secret-key encryption, a k-bit ``secret key'' is shared by two users, who use it to transform plaintext inputs to an encoded cipher. By carefully designing transformation algorithms, each bit of output can be made to depend on every bit of the input. With such an arrangement, a key of 128 bits used for encoding results in a key space of two to the 128th (or about ten to the 38th power). Assuming that brute force, along with some parallelism, is employed, the encrypted message should be safe: a billion computers doing a billion operations per second would require a trillion years to decrypt it. In practice, analysis of the encryption algorithm might make it more vulnerable, but increases in the size of the key can be used to offset this. The main practical problem with secret-key encryption is determining a secret key. In theory any two users who wished to communicate could agree on a key in advance, but in practice for many users this would require secure storage and organization of a awkwardly large database of agreed-on keys. Use Search at http://topicideas.net/search.php wisely To Get Information About Project Topic and Seminar ideas with report/source code along pdf and ppt presenaion
 seminar class Active In SP Posts: 5,361 Joined: Feb 2011 19-04-2011, 12:59 PM   Q2.docx (Size: 179.68 KB / Downloads: 69) ABSTRACT Quantum cryptography uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random bit string known only to them, which can be used as a key to encrypt and decrypt messages. An important and unique property of quantum cryptography is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental part of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold a key can be produced which is guaranteed as secure, otherwise no secure key is possible and communication is aborted. The security of quantum cryptography relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantee of key security. Quantum cryptography is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt and decrypt a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. KEY WORDS: qubit, uncertainty, entanglement, bit commitment, BB84 protocol, Ekert protocol, key distribution, one-time-pad INTRODUCTION Cryptography is the science of keeping private information from unauthorized access, of ensuring data integrity and authentication, and other tasks. In this survey, we will focus on quantum-cryptographic key distribution and bit commitment protocols and we in particular will discuss their security. Before turning to quantum cryptography, let me give a brief review of classical cryptography, its current challenges and its historical development. Two parties, Alice and Bob, wish to exchange messages via some insecure channel in a way that protects their messages from eavesdropping. An algorithm, which is called a cipher in this context, scrambles Alice’s message via some rule such that restoring the original message is hard—if not impossible—without knowledge of the secret key. This “scrambled” message is called the ciphertext. On the other hand, Bob (who possesses the secret key) can easily decipher Alice’s ciphertext and obtains her original plaintext. Figure 1 in this section presents this basic cryptographic scenario. CLASSICAL CRYPTOGRAPHY Overviews of classical cryptography can be found in various text books (see, e.g., Rothe [2005] and Stinson [2005]). Here, we present just the basic definition of a cryptosystem and give one example of a classical encryption method, the one-time pad. DEFENITION A (deterministic, symmetric) cryptosystem is a five-tuple (P, C, K, E, D) satisfying the following conditions: 1. P is a finite set of possible plaintexts. 2. C is a finite set of possible ciphertexts. 3. K is a finite set of possible keys. 4. For each k º K, there are an encryption rule ek º E and a corresponding decryption rule dk º D, where ek: P¨ C and dk : C¨ P are functions satisfying dk (ek (x)) = x for each plaintext element x º P. In the basic scenario in cryptography, we have two parties who wish to communicate over an insecure channel, such as a phone line or a computer network. Usually, these parties are referred to as Alice and Bob. Since the communication channel is insecure, an eavesdropper, called Eve, may intercept the messages that are sent over this channel. By agreeing on a secret key k via a secure communication method, Alice and Bob can make use of a cryptosystem to keep their information secret, even when sent over the insecure channel. This situation is illustrated in Figure 1. The method of encryption works as follows. For her secret message m, Alice uses the key k and the encryption rule ek to obtain the ciphertext c = ek (m). She sends Bob the ciphertext c over the insecure channel. Knowing the key k, Bob can easily decrypt the ciphertext by the decryption rule dk : dk © = dk (ek (m)) = m. Knowing the ciphertext c but missing the key k, there is no easy way for Eve to determine the original message m. There exist many cryptosystems in modern cryptography to transmit secret messages. An early well-known system is the one-time pad, which is also known as the Vernam cipher. The one-time pad is a substitution cipher. Despite its advantageous properties, which we will discuss later on, the one-time pad’s drawback is the costly effort needed to transmit and store the secret keys. ONE-TIME PAD For plaintext elements in P , we use capital letters and some punctuation marks, which we encode as numbers ranging from 0 to 29, see Figure2. As is the case with most cryptosystems, the ciphertext space equals the plaintext space. Furthermore, the key space K also equals P , and we have P =C= K={0, 1, . . . , 29}. Next, we describe how Alice and Bob use the one-time pad to transmit their messages. A concrete example is shown in Figure 3. Suppose Alice and Bob share a joint secret key k of length n = 12, where each key symbol kiº {0, 1, . . . , 29} is chosen uniformly at random. Let m = m1m2. . . mn be a given message of length n, which Alice wishes to encrypt. For each plaintext letter mi, where 1 ¡Ü i ¡Ü n, Alice adds the plaintext numbers to the key numbers. The result is taken modulo 30. For example, the last letter of the plaintext from Figure 3, “D,” is encoded by “m12=03.” The corresponding key is “m12= 28,” so we have c12= 3 + 28 = 31. Since 31 ß 1 mod 30, our plaintext letter “D” is encrypted as “B.” Decryption works similarly by subtracting, character by character, the key letters from the corresponding ciphertext letters. So the encryption and decryption can be written as respectively ci= (mi+ ki) mod 30 and mi=(ci- ki) mod 30, 1 ¡Ü i ¡Ü n. LIMITATIONS Cryptographic technology in use today relies on the hardness of certain mathematical problems. Classical cryptography faces the following two problems. First, the security of many classical cryptosystems is based on the hardness of problems such as integer factoring or the discrete logarithm problem. But since these problems typically are not provably hard, the corresponding cryptosystems are potentially insecure. For example, the famous and widely used RSA public-key cryptosystem [Rivest et al. 1978] could easily be broken if large integers were easy to factor. The hardness of integer factoring, however, is not a proven fact but rather a hypothesis.1.We mention in passing that computing the RSA secret key from the corresponding public key is polynomial-time equivalent to integer factoring [May 2004]. Second, the theory of quantum computation has yielded new methods to tackle these mathematical problems in a much more efficient way. Although there are still numerous challenges to overcome before a working quantum computer of sufficient power can be built, in theory many classical ciphers (in particular public-key cryptosystems such as RSA) might be broken by such a powerful machine. However, while quantum computation seems to be a severe challenge to classical cryptography in a possibly not so distant future, at the same time it offers new possibilities to build encryption methods that are safe even against attacks performed by means of a quantum computer. Quantum cryptography extends the power of classical cryptography by protecting the secrecy of messages using the physical laws of quantum mechanics.
 seminar class Active In SP Posts: 5,361 Joined: Feb 2011 21-04-2011, 03:43 PM   tomkha QC report.doc (Size: 278 KB / Downloads: 46) ABSTRACT Quantum cryptography uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random bit string known only to them, which can be used as a key to encrypt and decrypt messages. An important and unique property of quantum cryptography is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental part of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold a key can be produced which is guaranteed as secure, otherwise no secure key is possible and communication is aborted. The security of quantum cryptography relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantee of key security. Quantum cryptography is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt and decrypt a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. KEY WORDS: qubit, uncertainty, entanglement, bit commitment, BB84 protocol, Ekert protocol, key distribution, one-time-pad 1. INTRODUCTION Cryptography is the science of keeping private information from unauthorized access, of ensuring data integrity and authentication, and other tasks. In this survey, we will focus on quantum-cryptographic key distribution and bit commitment protocols and we in particular will discuss their security. Before turning to quantum cryptography, let me give a brief review of classical cryptography, its current challenges and its historical development. Two parties, Alice and Bob, wish to exchange messages via some insecure channel in a way that protects their messages from eavesdropping. An algorithm, which is called a cipher in this context, scrambles Aliceâ„¢s message via some rule such that restoring the original message is hardâ€if not impossibleâ€without knowledge of the secret key. This scrambled message is called the ciphertext. On the other hand, Bob (who possesses the secret key) can easily decipher Aliceâ„¢s ciphertext and obtains her original plaintext. Figure 1 in this section presents this basic cryptographic scenario. Fig. 1. Communication between Alice and Bob, with Eve listening. But unlike traditional cryptology methods -- encoding and decoding information or messages -- quantum cryptology depends on physics, not mathematics. In this report, we'll get to the bottom of how quantum encryption works, and how it differs from modern cryptology. But first, we'll look at the uses and the limitations of traditional cryptology methods. Traditional Cryptology Photo courtesy NSA A German Enigma machine Privacy is paramount when communicating sensitive information, and humans have invented some unusual ways to encode their conversations. In World War II, for example, the Nazis created a bulky machine called the Enigma that resembles a typewriter on steroids. This machine created one of the most difficult ciphers (encoded messages) of the pre-computer age. Even after Polish resistance fighters made knockoffs of the machines -- complete with instructions on how the Enigma worked -- decoding messages was still a constant struggle for the Allies [source: Cambridge University]. As the codes were deciphered, however, the secrets yielded by the Enigma machine were so helpful that many historians have credited the code breaking as a important factor in the Allies' victory in the war. What the Enigma machine was used for is called cryptology. This is the process of encoding (cryptography) and decoding (cryptoanalysis) information or messages (called plaintext). All of these processes combined are cryptology. Until the 1990s, cryptology was based on algorithms -- a mathematical process or procedure. These algorithms are used in conjunction with a key, a collection of bits (usually numbers). Without the proper key, it's virtually impossible to decipher an encoded message, even if you know what algorithm to use. There are limitless possibilities for keys used in cryptology. But there are only two widely used methods of employing keys: public-key cryptology and secret-key cryptology. In both of these methods (and in all cryptology), the sender (point A) is referred to as Alice. Point B is known as Bob. In the public-key cryptology (PKC) method, a user chooses two interrelated keys. He lets anyone who wants to send him a message know how to encode it using one key. He makes this key public. The other key he keeps to himself. In this manner, anyone can send the user an encoded message, but only the recipient of the encoded message knows how to decode it. Even the person sending the message doesn't know what code the user employs to decode it. PKC is often compared to a mailbox that uses two keys. One unlocks the front of the mailbox, allowing anyone with a key to deposit mail. But only the recipient holds the key that unlocks the back of the mailbox, allowing only him to retrieve the messages. The other usual method of traditional cryptology is secret-key cryptology (SKC). In this method, only one key is used by both Bob and Alice. The same key is used to both encode and decode the plaintext. Even the algorithm used in the encoding and decoding process can be announced over an unsecured channel. The code will remain uncracked as long as the key used remains secret. SKC is similar to feeding a message into a special mailbox that grinds it together with the key. Anyone can reach inside and grab the cipher, but without the key, he won't be able to decipher it. The same key used to encode the message is also the only one that can decode it, separating the key from the message. Traditional cryptology is certainly clever, but as with all encoding methods in code-breaking history, it's being phased out. Find out why on the next page. Traditional Cryptology Problems Both the secret-key and public-key methods of cryptology have unique flaws. Oddly enough, quantum physics can be used to either solve or expand these flaws.
 seminar flower Super Moderator Posts: 10,120 Joined: Apr 2012 19-06-2012, 02:33 PM Quantum Cryptography   Quantum Cryptography.ppt (Size: 405.5 KB / Downloads: 24) what is Quantum Mechanics? Quantum Mechanics is the study of mechanical systems whose dimensions are close to the atomic scale. Quantum effects, such as stable electron orbits, entaglement etc.. are not observable on a macroscopic scale, and exist only at the microscopic level. Applications of Quantum Mechanics range from explaining features of the subatomic world to computational chemistry. Current research is being done in the fields of Quantum Cryptography, Quantum Computing, and Quantum Teleportation. Finding Eve Problem If an eavesdropper were to gain information about the photons' polarization, the laws of quantum physics dictates that the quantum state of the photons would be altered, thus causing errors in Bob's measurements. Solution Alice and Bob compare a subset of remaining bit strings. If more than p bits differ, the key distribution process is aborted and repeated. Privacy Amplification As it is impossible to distinguish between eavesdropping and transmission imperfections, a threshhold p (currently 20%) is set for error margins. If differences occur above the threshhold, privacy amplification can occur. A new key is created by using Alice and Bob's key to produce a new, shorter key, in such a way that the eavesdropper's knowledge about the new key is negligible.