10.6
09
by admin ·
A MAC algorithm, sometimes called a keyed (cryptographic) hash function, accepts as input a secret key and an arbitrary-length message to be authenticated, and outputs a MAC (sometimes known as a tag). The MAC value protects both a message’s data integrity as well as its authenticity, by allowing verifiers (who also possess the secret key) to detect any changes to the message content.
The term message integrity code (MIC) is frequently substituted for the term MAC, especially in communications, where the acronym MAC traditionally stands for Media Access Control. However, some authors use MIC as a distinctly different term from a MAC; in their usage of the term the MIC operation does not use secret keys. This lack of security means that any MIC intended for use gauging message integrity should be encrypted or otherwise be protected agaist tampering. MIC algorithms are created such that a given message will always produce the same MIC assuming the same algorithm is used to generate both. Conversely, MAC algorithms are designed to produce matching MACs only if the same message, secret key and initialization vector are input to the same algorithm. MICs do not use secret keys and, when taken on their own, are therefore a much less reliable gauge of message integrity than MACs. Because MACs use secret keys, they do not necessarily need to be encrypted to provide the same level of assurance.
While MAC functions are similar to cryptographic hash functions, they possess different security requirements. To be considered secure, a MAC function must resist existential forgery under chosen-plaintext attacks. This means that even if an attacker has access to an oracle which possesses the secret key and generates MACs for messages of the attacker’s choosing, the attacker cannot guess the MAC for other messages without performing unfeasible amounts of computation.
MACs differ from digital signatures as MAC values are both generated and verified using the same secret key. This implies that the sender and receiver of a message must agree on the same key before initiating communications, as is the case with symmetric encryption. For the same reason, MACs do not provide the property of non-repudiation offered by signatures: any user who can verify a MAC is also capable of generating MACs for other messages. In contrast, a digital signature is generated using the private key of a key pair, which is asymmetric encryption. Since this private key is only accessible to its holder, a digital signature proves that a document was signed by none other than that holder. Thus, digital signatures do offer non-repudiation.
MAC algorithms can be constructed from other cryptographic primitives, such as cryptographic hash functions (as in the case of HMAC) or from block cipher algorithms (OMAC, CBC-MAC and PMAC). However many of the fastest MAC algorithms are constructed based on universal hashing.
10.6
09
by admin ·
In cryptography, RSA (which stands for Rivest, Shamir and Adleman who first publicly described it; see below) is an algorithm for public-key cryptography. It is the first algorithm known to be suitable for signing as well as encryption, and one of the first great advances in public key cryptography. RSA is widely used in electronic commerce protocols, and is believed to be secure given sufficiently long keys and the use of up-to-date implementations.
Operation
The RSA algorithm involves three steps: key generation, encryption and decryption.
Key generation
RSA involves a public key and a private key. The public key can be known to everyone and is used for encrypting messages. Messages encrypted with the public key can only be decrypted using the private key. The keys for the RSA algorithm are generated the following way:
1. Choose two distinct prime numbers p and q.
* For security purposes, the integers p and q should be chosen uniformly at random and should be of similar bit-length. Prime integers can be efficiently found using a Primality test.
2. Compute n = pq.
* n is used as the modulus for both the public and private keys
3. Compute the totient: \varphi(n) = (p-1)(q-1)\,.
4. Choose an integer e such that 1 < e < \varphi(n), and e and \varphi(n) share no divisors other than 1 (i.e. e and \varphi(n) are coprime).
* e is released as the public key exponent.
* Choosing e having a short addition chain results in more efficient encryption. Small public exponents (such as e=3) could potentially lead to greater security risks.
5. Determine d (using modular arithmetic) which satisfies the congruence relation d e \equiv 1\pmod{\varphi(n)}.
* Stated differently, ed − 1 can be evenly divided by the totient (p − 1)(q − 1).
* This is often computed using the Extended Euclidean Algorithm.
* d is kept as the private key exponent.
The public key consists of the modulus n and the public (or encryption) exponent e. The private key consists of the modulus n and the private (or decryption) exponent d which must be kept secret.
Notes on some variants:
* PKCS#1 v2.0 and PKCS#1 v2.1 specifies using \lambda(n) = {\rm lcm}(p-1, q-1) \,, where lcm is the least common multiple instead of \varphi(n) = (p-1)(q-1) \,.
* For efficiency the following values may be precomputed and stored as part of the private key:
o p and q: the primes from the key generation,
o d\mod (p – 1) and d\mod(q – 1),
o q^{-1} \mod(p).
Encryption
Alice transmits her public key (n,e) to Bob and keeps the private key secret. Bob then wishes to send message M to Alice.
He first turns M into an integer 0 < m < n by using an agreed-upon reversible protocol known as a padding scheme. He then computes the ciphertext c corresponding to:
c \equiv m^e \pmod{n}.
This can be done quickly using the method of exponentiation by squaring. Bob then transmits c to Alice.
Decryption
Alice can recover m from c by using her private key exponent d by the following computation:
m \equiv c^d \pmod{n}.
Given m, she can recover the original message M by reversing the padding scheme.
The above decryption procedure works because:
c^d \equiv (m^e)^d \equiv m^{ed}\pmod{n}.
Now, since ed = 1 + k\varphi(n),
m^{ed} \equiv m^{1 + k\varphi(n)} \equiv m (m^{\varphi(n)})^{k} \equiv m \pmod{n}.
The last congruence directly follows from Euler’s theorem when m is relatively prime to n. Using the Chinese remainder theorem, it can be shown that the equations holds for all m.
This shows that we get the original message back:
c^d \equiv m \pmod{n}.
08.23
09
by admin ·
Neptune is the eighth and outermost-known planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third-largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 Earth masses and not as dense. On average, Neptune orbits the Sun at a distance of 30.1 AU, approximately 30 times the Earth-Sun distance. Its astronomical symbol is Astronomical symbol for Neptune., a stylized version of the god Neptune’s trident.
Discovered on September 23, 1846, Neptune was the first planet found by mathematical prediction rather than by empirical observation. Unexpected changes in the orbit of Uranus led astronomers to deduce that its orbit was subject to gravitational perturbation by an unknown planet. Neptune was subsequently found within a degree of its predicted position, and its largest moon, Triton, was discovered shortly thereafter, though none of the planet’s remaining 12 moons was located telescopically until the 20th century. Neptune has been visited by only one spacecraft, Voyager 2, which flew by the planet on August 25, 1989.
Neptune is similar in composition to Uranus, and both have compositions which differ from those of the larger gas giants Jupiter and Saturn. Neptune’s atmosphere, while similar to Jupiter’s and Saturn’s in that it is composed primarily of hydrogen and helium, along with traces of hydrocarbons and possibly nitrogen, contains a higher proportion of “ices” such as water, ammonia and methane. Astronomers sometimes categorize Uranus and Neptune as “ice giants” in order to emphasize these distinctions. The interior of Neptune, like that of Uranus, is primarily composed of ices and rock. Traces of methane in the outermost regions in part account for the planet’s blue appearance.
In contrast to the relatively featureless atmosphere of Uranus, Neptune’s atmosphere is notable for its active and visible weather patterns. At the time of the 1989 Voyager 2 flyby, for example, the planet’s southern hemisphere possessed a Great Dark Spot comparable to the Great Red Spot on Jupiter. These weather patterns are driven by the strongest sustained winds of any planet in the Solar System, with recorded wind speeds as high as 2100 km/h. Because of its great distance from the Sun, Neptune’s outer atmosphere is one of the coldest places in the Solar System, with temperatures at its cloud tops approaching −218 °C (55 K). Temperatures at the planet’s centre, however, are approximately 5,400 K (5,000 °C).Neptune has a faint and fragmented ring system, which may have been detected during the 1960s but was only indisputably confirmed in 1989 by Voyager 2.
08.23
09
by admin ·
Uranus is the seventh planet from the Sun, and the third-largest and fourth most massive planet in the Solar System. It is named after the ancient Greek deity of the sky Uranus (Ancient Greek: Οὐρανός) the father of Kronos (Saturn) and grandfather of Zeus (Jupiter). Though it is visible to the naked eye like the five classical planets, it was never recognized as a planet by ancient observers because of its dimness and slow orbit.Sir William Herschel announced its discovery on March 13, 1781, expanding the known boundaries of the Solar System for the first time in modern history. Uranus was also the first planet discovered with a telescope.
Uranus is similar in composition to Neptune, and both have different compositions from those of the larger gas giants Jupiter and Saturn. As such, astronomers sometimes place them in a separate category, the “ice giants”. Uranus’s atmosphere, while similar to Jupiter’s and Saturn’s in being composed primarily of hydrogen and helium, contains a higher proportion of “ices” such as water, ammonia and methane, along with traces of hydrocarbons.[11] It is the coldest planetary atmosphere in the Solar System, with a minimum temperature of 49 K (−224 °C). It has a complex, layered cloud structure, with water thought to make up the lowest clouds, and methane thought to make up the uppermost layer of clouds. In contrast the interior of Uranus is mainly composed of ices and rock.
Like the other giant planets, Uranus has a ring system, a magnetosphere, and numerous moons. The Uranian system has a unique configuration among the planets because its axis of rotation is tilted sideways, nearly into the plane of its revolution about the Sun. As such, its north and south poles lie where most other planets have their equators. Seen from Earth, Uranus’s rings can sometimes appear to circle the planet like an archery target and its moons revolve around it like the hands of a clock, though in 2007 and 2008 the rings appeared edge-on. In 1986, images from Voyager 2 showed Uranus as a virtually featureless planet in visible light without the cloud bands or storms associated with the other giants. However, terrestrial observers have seen signs of seasonal change and increased weather activity in recent years as Uranus approached its equinox. The wind speeds on Uranus can reach 250 meters per second (900 km/h, 560 mph).
08.23
09
by admin ·
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn, along with Jupiter, Uranus and Neptune, is classified as a gas giant. Together, these four planets are sometimes referred to as the Jovian, meaning “Jupiter-like”, planets.
Saturn is named after the Roman god Saturn (that became the namesake of Saturday), equated to the Greek Kronos (the Titan father of Zeus) the Babylonian Ninurta and to the Hindu Shani. Saturn’s symbol represents the god’s sickle (Unicode: ♄).
The planet Saturn is composed of hydrogen, with small proportions of helium and trace elements. The interior consists of a small core of rock and ice, surrounded by a thick layer of metallic hydrogen and a gaseous outer layer. The outer atmosphere is generally bland in appearance, although long-lived features can appear. Wind speeds on Saturn can reach 1,800 km/h, significantly faster than those on Jupiter. Saturn has a planetary magnetic field intermediate in strength between that of Earth and the more powerful field around Jupiter.
Saturn has a prominent system of rings, consisting mostly of ice particles with a smaller amount of rocky debris and dust. Sixty-one known moons orbit the planet, not counting hundreds of “moonlets” within the rings. Titan, Saturn’s largest and the Solar System’s second largest moon (after Jupiter’s Ganymede), is larger than the planet Mercury and is the only moon in the Solar System to possess a significant atmosphere.
PLANETARY RINGS
Saturn is probably best known for its system of planetary rings, which makes it the most visually remarkable object in the solar system. They extend from 6 630 km to 120 700 km above Saturn’s equator, average approximately 20 meters in thickness, and are composed of 93 percent water ice with a smattering of tholin impurities, and 7 percent amorphous carbon. The particles that make up the rings range in size from specks of dust to the size of a small automobile. There are two main theories regarding the origin of Saturn’s rings. One theory is that the rings are remnants of a destroyed moon of Saturn. The second theory is that the rings are left over from the original nebular material from which Saturn formed.
08.23
09
by admin ·
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with a mass slightly less than one-thousandth that of the Sun but is two and a half times the mass of all of the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn, Uranus and Neptune. Together, these four planets are sometimes referred to as the Jovian planets.
The planet was known by astronomers of ancient times and was associated with the mythology and religious beliefs of many cultures. The Romans named the planet after the Roman god Jupiter. When viewed from Earth, Jupiter can reach an apparent magnitude of −2.8, making it on average the third-brightest object in the night sky after the Moon and Venus. (Mars can briefly exceed Jupiter’s brightness at certain points in its orbit.)
Jupiter is primarily composed of hydrogen with a quarter of its mass being helium; it may also have a rocky core of heavier elements. Because of its rapid rotation, Jupiter’s shape is that of an oblate spheroid (it possesses a slight but noticeable bulge around the equator). The outer atmosphere is visibly segregated into several bands at different latitudes, resulting in turbulence and storms along their interacting boundaries. A prominent result is the Great Red Spot, a giant storm that is known to have existed since at least the 17th century when it was first seen by telescope. Surrounding the planet is a faint planetary ring system and a powerful magnetosphere. There are also at least 63 moons, including the four large moons called the Galilean moons that were first discovered by Galileo Galilei in 1610. Ganymede, the largest of these moons, has a diameter greater than that of the planet Mercury.
Jupiter has been explored on several occasions by robotic spacecraft, most notably during the early Pioneer and Voyager flyby missions and later by the Galileo orbiter. The most recent probe to visit Jupiter was the Pluto-bound New Horizons spacecraft in late February 2007. The probe used the gravity from Jupiter to increase its speed and adjust its trajectory toward Pluto, thereby saving years of travel. Future targets for exploration in the Jovian system include the possible ice-covered liquid ocean on the moon Europa.
08.23
09
by admin ·
Mars is the fourth planet from the Sun in the Solar System. The planet is named after Mars, the Roman god of war. It is also referred to as the “Red Planet” because of its reddish appearance, due to iron oxide prevalent on its surface.
Mars is a terrestrial planet with a thin atmosphere, having surface features reminiscent both of the impact craters of the Moon and the volcanoes, valleys, deserts and polar ice caps of Earth. It is the site of Olympus Mons, the highest known mountain in the Solar System, and of Valles Marineris, the largest canyon. Furthermore, in June 2008 three articles published in Nature presented evidence of an enormous impact crater in Mars’ northern hemisphere, 10,600 km long by 8,500 km wide, or roughly four times larger than the largest impact crater yet discovered, the South Pole-Aitken basin. In addition to its geographical features, Mars’ rotational period and seasonal cycles are likewise similar to those of Earth.
Until the first flyby of Mars by Mariner 4 in 1965, many speculated that there might be liquid water on the planet’s surface. This was based on observations of periodic variations in light and dark patches, particularly in the polar latitudes, which looked like seas and continents, while long, dark striations were interpreted by some observers as irrigation channels for liquid water. These straight line features were later proven not to exist and were instead explained as optical illusions. Still, of all the planets in the Solar System other than Earth, Mars is the most likely to harbor liquid water, and perhaps life. Radar data from Mars Express and the Mars Reconnaissance Orbiter have revealed the presence of large quantities of water ice both at the poles (July 2005) and at mid-latitudes (November 2008). The Phoenix Mars Lander directly sampled water ice in shallow martian soil on July 31, 2008.
Mars is currently host to three functional orbiting spacecraft: Mars Odyssey, Mars Express, and the Mars Reconnaissance Orbiter. With the exception of Earth, this is more than any planet in the Solar System. The surface is also home to the two Mars Exploration Rovers (Spirit and Opportunity) and several inert landers and rovers, both successful and unsuccessful. The Phoenix lander recently completed its mission on the surface. Geological evidence gathered by these and preceding missions suggests that Mars previously had large-scale water coverage, while observations also indicate that small geyser-like water flows have occurred during the past decade. Observations by NASA’s Mars Global Surveyor show evidence that parts of the southern polar ice cap have been receding.
Mars has two moons, Phobos and Deimos, which are small and irregularly shaped. These may be captured asteroids, similar to 5261 Eureka, a Martian Trojan asteroid. Mars can be seen from Earth with the naked eye. Its apparent magnitude reaches −2.9, a brightness surpassed only by Venus, the Moon, and the Sun, although most of the time Jupiter will appear brighter to the naked eye than Mars. Mars has an average opposition distance of 78 million km but can come as close as 55.7 million km during a close approach, such as occurred in 2003.
08.23
09
by admin ·
Earth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets (non-gas planets) in the Solar System in terms of diameter, mass and density. It is also referred to as the World, the Blue Planet,and Terra.
Home to millions of species,including humans, Earth is the only place in the universe where life is known to exist. The planet formed 4.54 billion years ago,and life appeared on its surface within a billion years. Since then, Earth’s biosphere has significantly altered the atmosphere and other abiotic conditions on the planet, enabling the proliferation of aerobic organisms as well as the formation of the ozone layer which, together with Earth’s magnetic field, blocks harmful radiation, permitting life on land. The physical properties of the Earth, as well as its geological history and orbit, allowed life to persist during this period. The world is expected to continue supporting life for another 1.5 billion years, after which the rising luminosity of the Sun will eliminate the biosphere.
Earth’s outer surface is divided into several rigid segments, or tectonic plates, that gradually migrate across the surface over periods of many millions of years. About 71% of the surface is covered with salt-water oceans, the remainder consisting of continents and islands; liquid water, necessary for all known life, is not known to exist on any other planet’s surface. Earth’s interior remains active, with a thick layer of relatively solid mantle, a liquid outer core that generates a magnetic field, and a solid iron inner core.
Earth interacts with other objects in outer space, including the Sun and the Moon. At present, Earth orbits the Sun once for every roughly 366.26 times it rotates about its axis. This length of time is a sidereal year, which is equal to 365.26 solar days. The Earth’s axis of rotation is tilted 23.4° away from the perpendicular to its orbital plane,producing seasonal variations on the planet’s surface with a period of one tropical year (365.24 solar days). Earth’s only known natural satellite, the Moon, which began orbiting it about 4.53 billion years ago, provides ocean tides, stabilizes the axial tilt and gradually slows the planet’s rotation. Between approximately 4.1 and 3.8 billion years ago, asteroid impacts during the Late Heavy Bombardment caused significant changes to the surface environment.
Both the mineral resources of the planet, as well as the products of the biosphere, contribute resources that are used to support a global human population. The inhabitants are grouped into about 200 independent sovereign states, which interact through diplomacy, travel, trade and military action. Human cultures have developed many views of the planet, including personification as a deity, a belief in a flat Earth or in Earth being the center of the universe, and a modern perspective of the world as an integrated environment that requires stewardship.
08.22
09
by admin ·
Venus is the second-closest planet to the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6. Because Venus is an inferior planet from Earth, it never appears to venture far from the Sun: its elongation reaches a maximum of 47.8°. Venus reaches its maximum brightness shortly before sunrise or shortly after sunset, for which reason it is often called the Morning Star or the Evening Star.
Classified as a terrestrial planet, it is sometimes called Earth’s “sister planet” because they are similar in size, gravity, and bulk composition. Venus is covered with an opaque layer of highly reflective clouds of sulfuric acid, preventing its surface from being seen from space in visible light. Venus has the densest atmosphere of all the terrestrial planets, consisting mostly of carbon dioxide, as it has no carbon cycle to lock carbon back into rocks and surface features, nor organic life to absorb it in biomass. A younger Venus is believed to have possessed Earth-like oceans, but these totally evaporated as the temperature rose, leaving a dusty dry desertscape with many slab-like rocks. The water has most likely dissociated, and, because of the lack of a planetary magnetic field, the hydrogen has been swept into interplanetary space by the solar wind. The atmospheric pressure at the planet’s surface is 92 times that of the Earth.
Venus’s surface was a subject of speculation until some of its secrets were revealed by planetary science in the twentieth century. It was finally mapped in detail by Project Magellan in 1990–91. The ground shows evidence of extensive volcanism, and the sulfur in the atmosphere may indicate that there have been some recent eruptions. However, it is an enigma why no evidence of lava flow accompanies any of the visible caldera. There are a low number of impact craters, demonstrating that the surface is relatively young, approximately half a billion years old. There is no evidence for plate tectonics, possibly because its crust is too strong to subduct without water to make it less viscous. Instead, Venus may lose its internal heat in periodic massive resurfacing events.
08.22
09
by admin ·
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about the axis for every two orbits. The perihelion of Mercury’s orbit precesses around the Sun at an excess of 43 arcseconds per century; a phenomenon that was explained in the 20th century by Albert Einstein’s General Theory of Relativity.Mercury is bright when viewed from Earth, ranging from −2.0 to 5.5 in apparent magnitude, but is not easily seen as its greatest angular separation from the Sun is only 28.3°. Since Mercury is normally lost in the glare of the Sun, unless there is a solar eclipse, Mercury can only be viewed in morning or evening twilight.
Comparatively little is known about Mercury; ground-based telescopes reveal only an illuminated crescent with limited detail. The first of two spacecraft to visit the planet was Mariner 10, which mapped only about 45% of the planet’s surface from 1974 to 1975. The second is the MESSENGER spacecraft, which mapped another 30% during its flyby of January 14, 2008. MESSENGER will make one more pass by Mercury in 2009, followed by orbital insertion in 2011, and will then survey and map the entire planet.
Mercury is similar in appearance to the Moon: it is heavily cratered with regions of smooth plains, has no natural satellites and no substantial atmosphere. However, unlike the moon, it has a large iron core, which generates a magnetic field about 1% as strong as that of the Earth. It is an exceptionally dense planet due to the large relative size of its core. Surface temperatures range from about 90 to 700 K (−183 °C to 427 °C, −297 °F to 801 °F), with the subsolar point being the hottest and the bottoms of craters near the poles being the coldest.
Recorded observations of Mercury date back to at least the first millennium BC. Before the 4th century BC, Greek astronomers believed the planet to be two separate objects: one visible only at sunrise, which they called Apollo; the other visible only at sunset, which they called Hermes. The English name for the planet comes from the Romans, who named it after the Roman god Mercury, which they equated with the Greek Hermes. The astronomical symbol for Mercury is a stylized version of Hermes’ caduceus.
