Modular exponentiation is a type of exponentiation performed over a modular arithmetic modulus . It is particularly useful in computer science , especially in the field of cryptography . Doing a modular exponentiation means calculating the remainder when dividing by a positive integer m called the modulus a positive integer b called the base raised to the e th power e is called the exponent . In other ... with the property 0 c < m . Modular exponentiation can be performed with a negative exponent e by finding ... m math Modular exponentiation problems similar to the one described above are considered easy to do ... exponentiation a good candidate for use in cryptographic algorithms. Straightforward method The most ... better security, the value b sup e sup becomes unwieldy. The time required to perform the exponentiation ... exponentiation requires more operations than the first method. Because the required memory is substantially ... required to perform modular exponentiation. It is a combination of the previous method and a more general principle called exponentiation by squaring also known as binary exponentiation . First, it is required ... exponentiation is an important operation in computer science, and there are efficient algorithms ... exponentiation Python programming language Python s built in tt pow tt exponentiation function http ... exponentiation Perl s tt Math BigInt tt module has a tt bmodpow tt method http perldoc.perl.org Math BigInt.html bmodpow 28 29 to perform modular exponentiation Go programming language Go s tt big.Int tt type contains an tt Exp tt exponentiation method http golang.org pkg big Int.Exp whose third ... http www.php.net manual en function.bcpowmod.php to perform modular exponentiation The GNU Multiple ... Integer Exponentiation.html to perform modular exponentiation See also Montgomery reduction , for calculating ... External links http www.math.umn.edu garrett crypto a01 FastPow.html Fast Modular Exponentiation Java ... de Diskrete Exponentialfunktion fr Exponentiation modulaire ja ... more details
for exponentiation do not provide defence against side channel attack s. Namely, an attacker observing ... The Euclidean method was first introduced in Efficient exponentiation using precomputation and vector ... exponentiation exponents modulo a number. Especially in cryptography , it is useful to compute powers ... http home.mnet online.de wzwz.de temp ebs en.htm Calculation of products of powers Exponentiation ... and generalizations main Addition chain exponentiationExponentiation by squaring can be viewed as a suboptimal addition chain exponentiation algorithm it computes the exponent via an addition chain ... those powers of x , one can sometimes perform the exponentiation using fewer multiplications ..., have fewer multiplications than exponentiation by squaring at the cost of additional bookkeeping ... O notation &Theta log n , so these algorithms only improve asymptotically upon exponentiation by squaring by a constant factor at best. See also Modular exponentiation Vectorial addition chain Montgomery ... precision algorithms Category Computer arithmetic ca Exponenciaci bin ria de Bin re Exponentiation es Exponenciaci n binaria fr Exponentiation rapide pl Algorytm szybkiego pot gowania ru simple Exponentiation by squaring sv Bin r exponentiering vi Thu t to n ... more details
In mathematics and computer science , optimal addition chain exponentiation is a method of exponentiation by positive integer powers that requires a minimal number of multiplications. It works by creating a shortest addition chain that generates the desired exponent. Each exponentiation in the chain can be evaluated by multiplying two of the earlier exponentiation results. More generally, addition chain exponentiation may also refer to exponentiation by non minimal addition chains constructed by a variety of algorithms since a shortest addition chain is very difficult to find . The shortest addition chain algorithm requires no more multiplications than binary exponentiation and usually less. The first example of where it does better is for math a 15 math , where the binary method needs six multiplies but a shortest addition chain requires only five math a 15 a times a times a times a 2 2 2 math binary, 6 multiplications math a 15 a 3 times a 3 2 2 math shortest addition chain, 5 multiplications . class wikitable Table demonstrating how to do Exponentiation using Addition Chains Number of br Multiplications Actual br Exponentiation Specific implementation of br Addition Chains to do Exponentiation 0 a sup 1 sup a 1 a sup 2 sup a a 2 a sup 3 sup a a a 2 a sup 4 sup a a b b 3 a sup 5 ... ref Even given a shortest chain, addition chain exponentiation requires more memory than the binary .... In practice, therefore, shortest addition chain exponentiation is primarily used for small fixed ... than binary exponentiation. Indeed, binary exponentiation itself is a suboptimal addition chain ... of fast exponentiation methods. J. Algorithms 27, 1 Apr. 1998 , 129 146. doi http dx.doi.org 10.1006 ... math , which also requires three multiplies . Addition subtraction chain exponentiation If both multiplication ... of division compared to multiplication makes this technique unattractive in general. For exponentiation ... division math a 31 a a 2 2 2 2 2 math addition subtraction chain, 5 mults 1 div . For exponentiation ... more details
Rcon may refer to A computer Remote administration remote control administration tool In Rijndael key schedule is the exponentiation of 2 to a user specified value R Con, in a Gasket seal, a type of joint disamb ... more details
The continuum function is math kappa mapsto 2 kappa math , i.e. raising 2 to the power of &kappa using cardinal exponentiation . Given a cardinal number , it is the cardinality of the power set of a set of the given cardinality. See also Continuum hypothesis Cardinality of the continuum Beth number Gimel function settheory stub Category Cardinal numbers ... more details
Wiktionary slog A slog is a type of shot in the game cricket. Slog may also be A super logarithm , the inverse function of tetration super exponentiation A creature of fictional Oddworld A blog run by Seattle alternative weekly newspaper The Stranger newspaper The Stranger disambig ... more details
Dunamis Ancient Greek is the scholarly term for the philosophical concept of potentiality and actuality. Dunamis may also refer to Dynamis Bosporan queen , a Roman Client Queen of the Bosporan Kingdom Dynamis beetle Dynamis beetle , a weevil genus of the tribe Rhynchophorini Dynamis Ensemble , an instrumental group from Italy See also Exponentiation disambig ... more details
This is a list of notable square roots Square root of two Square root of three Square root of 5 Square root of minus one , a number equaling 1 when being Exponentiation squared Square root of a matrix Category Mathematics related lists ... more details
The symbol , an upward pointing arrow can refer to Yn , a Romanian Cyrillic letter For the symbol, represented in Unicode, see Arrow symbol For the mathematical notation of undefined, see Defined and undefined For the mathematical notation of iterated exponentiation, see Knuth s up arrow notation For the mathematical game theory position Up , see Combinatorial game theory Up Up game theory It also resembles the medieval Roman numerals Roman numeral for 900. Up arrow key See also Arrow disambiguation disambig no ... more details
refimproveBLP date January 2011 Stephen Pohlig is an electrical engineer currently working at MIT Lincoln Laboratory . As a graduate student of Martin Hellman s at Stanford University in the mid 1970 s, he helped develop the Pohlig Hellman exponentiation cipher and the Pohlig Hellman algorithm for computing discrete logarithm s. Bibliography S. Pohlig and M. Hellman, An improved algorithm for computing logarithms over GF p and its cryptographic significance Corresp. , Information Theory, IEEE Transactions on 24, no. 1 1978 106 110. Martin E. Hellman and Stephen C. Pohlig, http patft.uspto.gov netacgi nph Parser?Sect2 PTO1&Sect2 HITOFF&p 1&u 2Fnetahtml 2FPTO 2Fsearch bool.html&r 1&f G&l 50&d PALL&RefSrch yes&Query PN 2F4424414 United States Patent 4424414 Exponentiation cryptographic apparatus and method , January 3, 1984. References http www.cbi.umn.edu oh display.phtml?id 353 Oral history interview with Martin Hellman , 2004, Palo Alto, California. Charles Babbage Institute , University of Minnesota, Minneapolis. Persondata Metadata see Wikipedia Persondata . NAME Pohlig, Stephen ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Pohlig, Stephen Category American electrical engineers Category Living people US engineer stub ... more details
In axiomatic set theory , the gimel function is the following function mapping cardinal number s to cardinal numbers math gimel colon kappa mapsto kappa mathrm cf kappa math where cf denotes the cofinality function the gimel function is used for studying the continuum function and the cardinal number Cardinal exponentiation cardinal exponentiation function. Values of the Gimel function The gimel function has the property math gimel kappa kappa math for all infinite cardinals &kappa by K nig s theorem set theory K nig s theorem . For regular cardinals math kappa math , math gimel kappa 2 kappa math , and Easton s theorem says we don t know much about the values of this function. For singular math kappa math , upper bounds for math gimel kappa math can be found from Saharon Shelah Shelah s PCF theory . Reducing the exponentiation function to the gimel function All cardinal exponentiation is determined recursively by the gimel function as follows. If &kappa is an infinite successor cardinal then math 2 kappa gimel kappa math If &kappa is a limit and the continuum function is eventually constant below &kappa then math 2 kappa 2 kappa times gimel kappa math If &kappa is a limit and the continuum function is not eventually constant below &kappa then math 2 kappa gimel 2 kappa math The remaining rules hold whenever &kappa and &lambda are both infinite If &alefsym sub 0 sub &le &kappa &le &lambda then &kappa sup &lambda sup 2 sup &lambda sup If &mu sup &lambda sup &ge &kappa for some &mu &kappa then &kappa sup &lambda sup &mu sup &lambda sup If &kappa &lambda and &mu sup &lambda sup &kappa for all &mu &kappa and cf &kappa &le &lambda then &kappa sup &lambda sup &kappa sup cf &kappa sup If &kappa &lambda and &mu sup &lambda sup &kappa for all &mu &kappa and cf &kappa &lambda then &kappa sup &lambda sup &kappa References Thomas Jech , Set Theory , 3rd millennium ed., 2003, Springer Monographs in Mathematics, Springer, ISBN 3 540 44085 2. Category Cardinal numbers cs Funkce gi ... more details
Unreferenced stub auto yes date December 2009 Decimalization process refers to the conversion of measurements to a decimal system, i.e. one where the all ratios between the different measuring units are Exponentiation power s of ten. Practical examples of decimalization include metrication , which started with the introduction of the metric system in France after the French Revolution , but is still incomplete in a few English speaking countries, and Decimalisation decimalization of currency , which is essentially completed worldwide. Informally, decimalization of time of day decimalization of time periods within the day sees occasional use. Decimalization is generally advocated for reducing effort of calculations involving quantities of different scale. DEFAULTSORT Decimalization Process Category Measurement Measurement stub ... more details
Wiktionary exponent According to the Oxford English Dictionary , to expone is to set forth , and an exponent is a person or a statement that sets something forth. The word has assumed a plethora of other meanings Mathematics List of exponential topics Exponentiation Exponential function Matrix exponential Periodic group Exponent group theory Statistics Exponential distribution Exponential family Exponential function Exponential growth Exponential decay Linguistics Exponent linguistics Music The Exponents Publications Purdue Exponent Woman s Exponent Companies Exponent consulting firm See also Exponential disambiguation List of exponential topics Mathematics related exponents disambig cs Exponent de Exponent ... more details
O log m sup 2 sup , assuming a m , and is generally more efficient than exponentiation. Using ... exponentiation is already available. Some disadvantages of this method include the required knowledge ... such as when m is known to be prime or a power of a prime. exponentiation. Though it can be implemented more efficiently using modular exponentiation , when large values of m are involved this is most ... method, we re left with standard binary exponentiation which requires division mod m at every step, a slow operation when m is large. Furthermore, any kind of modular exponentiation is a taxing operation ... more details
Other uses Kilo disambiguation Wiktionary kilo Kilo symbol k, lowercase is a SI prefix unit prefix in the metric system denoting multiplication of the unit by one thousand. For example one kilogram is 1000 gram s one kilometre is 1000 metre s one kilojoule is 1000 joule s one kilobaud is a rate of transfer used primarily in telecommunications one kilobyte is formally equal to 1000 byte s. However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of information as 1024 2 sup 10 sup this is due to the Mathematical coincidence Concerning base 2 mathematical coincidence that math 2 10 approx 10 3. math Thus, in these fields 1 kilobyte is equal to 1 kibibyte , a new unit standardized as part of the binary prefix es to resolve the ambiguity. ref http physics.nist.gov cuu Units binary.html Definition of binary prefixes at NIST ref The kilo prefix is derived from the Greek language Greek word chilioi , meaning thousand . It was originally adopted by Antoine Lavoisier s group in 1795, and introduced into the metric system in France with its establishment in 1799. Exponentiation When units occur in exponentiation , such as in square and cubic forms, any multiplier prefix is considered part of the unit, and thus included in the exponentiation. 1 km sup 2 sup means one square kilometre or the area of a Square geometry square of 1000 m by 1000 m or 10 sup 6 sup m sup 2 sup . 1 km sup 3 sup means one cubic kilometre or the volume of a cube of 1000 m by 1000 m by 1000 m or 10 sup 9 sup m sup 3 sup . See also International System of Units References reflist SI prefixes Category SI prefixes ar br Kilo bg ca Kilo cs Kilo da Kilo et Kilo es Kilo prefijo eu Kilo fa fr Kilo gl Quilo ko hy hi id Kilo it Chilo prefisso he ka ... ... more details
In mathematics , Cutler s bar notation is a notation system for large number s, introduced by Mark Cutler in 2004. The idea is based on iterated exponentiation in much the same way that exponentiation is iteration iterated multiplication . Introduction A regular exponentiation exponential can be expressed as such math begin matrix a b & & underbrace a times a times dots times a & & b mbox copies of a end matrix math However, these expressions become arbitrarily large when dealing with systems such as Knuth s up arrow notation . Take the following math begin matrix & underbrace a a . , . , . , a & & b mbox copies of a end matrix math Cutler s bar notation shifts these exponentials counterclockwise, forming math b bar a math . A bar is placed above the variable to denote this change. As such math begin matrix b bar a & underbrace a a . , . , . , a & & b mbox copies of a end matrix math This system becomes effective with multiple exponent, when regular denotation becomes too cumbersome. math begin matrix b b bar a & underbrace a a . , . , . , a & & b bar a mbox copies of a end matrix math At any time, this can be further shortened by rotating the exponential counter clockwise once more. math begin matrix underbrace b b . , . , . , b bar a c bar a c mbox copies of b end matrix math The same pattern could be iterated a fourth time, becoming math bar a d math . For this reason, it is sometimes referred to as Cutler s circular notation . Advantages and drawbacks The Cutler Bar Notation can be used to easily express other notation systems in exponent form. It also allows for a flexible summarisation of multiple copies of the same exponents, where any number of stacked exponents can be shfted counter clockwise and shortened to a single variable. The Bar Notation also allows for farily rapid composure of very large numbers. For instance, the number math bar 10 10 math would contain more than a googolplex digits, whilst remaining fairly simple to write with and remember. Howev ... more details
In mathematics, for positive integers k and s , a vectorial addition chain is a sequence V of k dimensional vectors of nonnegative integers v sub i sub for &minus k 1 i s together with a sequence w , such that v sub k 1 sub 1,0,0,,...0,0 v sub k 2 sub 0,1,0,,...0,0 . . v sub 0 sub 0,0,0,,...0,1 v sub i sub v sub j sub v sub r sub for all 1 i s with k 1 j,r i 1 v sub s sub n sub 0 sub ,..., n sub k 1 sub w w sub 1 sub ,... w sub s sub , w sub i sub j,r . For example, a vectorial addition chain for 22,18,3 is V 1,0,0 , 0,1,0 , 0,0,1 , 1,1,0 , 2,2,0 , 4,4,0 , 5,4,0 , 10,8,0 , 11,9,0 , 11,9,1 , 22,18,2 , 22,18,3 w 2, 1 , 1,1 , 2,2 , 2,3 , 4,4 , 1,5 , 0,6 , 7,7 , 0,8 Vectorial addition chains are well suited to perform multi exponentiation . Input Elements x sub 0 sub ,..., x sub k 1 sub of an abelian group G and a vectorial addition chain of dimension k computing n sub 0 sub ,..., n sub k 1 sub Output The element x sub 0 sub sup n sub 0 sub sup ... x sub k 1 sub sup n sub r 1 sub sup for i k 1 to 0 do y sub i sub math leftarrow math x sub i k 1 sub for i 1 to s do y sub i sub math leftarrow math y sub j sub y sub r sub return y sub s sub Addition sequence An addition sequence for the set of integer S n sub 0 sub , ...,n sub r 1 sub is an addition chain v that contains every element of S . For example, an addition sequence computing 47,117,343,499 is 1,2,4,8,10,11,18,36, 47 ,55,91,109, 117 ,226, 343 ,434,489, 499 . It s possible to find addition sequence from vectorial addition chains and vice versa, so they are in a sense dual. ref Cohen, H., Frey, G. editors Handbook of elliptic and hyperelliptic curve cryptography. Discrete Math. Appl., Chapman & Hall CRC 2006 ref See also Addition chain Addition chain exponentiation Exponentiation by squaring Non adjacent form References reflist Category Sequences and series ... more details
In mathematics , an algebraic expression is an Expression mathematics expression that contains only algebraic number s, Variable mathematics variables and algebraic Operation mathematics operations . Algebraic operations are addition , subtraction , multiplication , division and exponentiation with integral or fractional exponents. A rational algebraic expression or rational expression is an algebraic expression that can be written as a quotient of polynomial s, such as math x 2 2x 4 math . An irrational algebraic expression is one that is not rational, such as math sqrt x 4 math . Reference cite book last1 James first1 Robert Clarke last2 James first2 Glenn title Mathematics dictionary page 8 year 1992 External links MathWorld title Algebraic Expression id AlgebraicExpression Category Elementary algebra ... more details
This article is about the mathematical lambda function math lambda x,b math . For information about the computer science lambda function, see Lambda calculus . For the Dirichlet lambda function ref MathWorld DirichletLambdaFunction Dirichlet lambda Function ref , a Dirichlet L Series, see there. In mathematics , the Lambda Function is a type of exponential function, where a number, x, is raised to itself, raised to b&minus 1 math lambda x,b x x b 1 math Sending b to infinity causes the function to approach 1 for x 1, and infinity for x 1. It can be thought of as an iterated exponential function math lambda x,b x x x dots math , where there are b levels of exponentiation, associated from the bottom up. See also Tetration References references MathWorld LambdaFunction Lambda Function math stub Category Exponentials ru ... more details
The Itoh Tsujii inversion algorithm is used to invert elements in a finite field . It was introduced in 1988 and first used over GF 2 sup m sup using the normal basis representation of elements, however the algorithm is generic and can be used for other bases, such as the polynomial basis . It can also be used in any finite field, GF p sup m sup . The algorithm is as follows Input A GF p sup m Output A sup &minus 1 sup r p sup m sup &minus 1 p &minus 1 compute A sup r &minus 1 sup in GF p sup m sup compute A sup r sup A sup r &minus 1 sup A compute A sup r sup sup &minus 1 sup in GF p compute A sup &minus 1 sup A sup r sup sup &minus 1 sup A sup r &minus 1 sup return A sup &minus 1 sup This algorithm is fast because steps 3 and 5 both involve operations in the subfield GF p . Similarly, if a small value of p is used a lookup table can be used for inversion in step 4. The majority of time spent in this algorithm is in step 2, the first exponentiation. This is one reason why this algorithm is well suited for the normal basis, since squaring and exponentiation are relatively easy in that basis. References T. Itoh and S. Tsujii. A Fast Algorithm for Computing Multiplicative Inverses in GF 2 sup m sup Using Normal Bases. Information and Computation , 78 171 177, 1988. External links http www.win.tue.nl henkvt ItohTsujiiEnciclopediaOfInfoSec Submitted.pdf A thorough discussion of the Itoh Tsujii algorithm by Guajardo Category Finite fields Category Computational number theory ... more details
The Schmidt&ndash Samoa cryptosystem is an asymmetric cryptographic technique, whose security, like Rabin cryptosystem Rabin depends on the difficulty of integer factorization . Unlike Rabin this algorithm does not produce an ambiguity in the decryption at a cost of encryption speed. Key generation Choose two large distinct primes p and q and compute math N p 2q math Compute math d N 1 mod text lcm p 1,q 1 math Now N is the public key and d is the private key. Encryption To encrypt a message m we compute the ciphertext as math c m N mod N. math Decryption To decrypt a ciphertext c we compute the plaintext as math m c d mod pq, math which like for Rabin and RSA algorithm RSA can be computed with the Chinese remainder theorem . Example math p 7, q 11, N p 2q 539, d N 1 mod text lcm p 1,q 1 29 math math m 32, c m N mod N 373 math Now to verify math m c d mod pq 373 29 mod pq 373 29 mod 77 32 math Security The algorithm, like Rabin, is based on the difficulty of factoring the modulus N , which is a distinct advantage over RSA. That is, it can be shown that if there exists an algorithm that can decrypt arbitrary messages, then this algorithm can be used to factor N . Efficiency The algorithm processes decryption as fast as Rabin and RSA, however it has much slower encryption since the sender must compute a full exponentiation. Since encryption uses a fixed known exponent an addition chain exponentiation addition chain may be used to optimize the encryption process. The cost of producing an optimal addition chain can be amortized over the life of the public key, that is, it need only be computed once and cached. References http eprint.iacr.org 2005 278.pdf A New Rabin type Trapdoor Permutation Equivalent to Factoring and Its Applications crypto navbox public key Category Asymmetric key cryptosystems ... more details
radix is negative . In exponentiation split section Base exponentiation Discussion date October 2011 In exponentiation , the base refers to the number var b var in an expression of the form var b sup n var sup . The number var n var is called the exponent and the expression is known formally as exponentiation ... used to refer to the exponent. The inverse function to exponentiation with base var b var when it is well ... more details
of the nth grade , ref name bennett z fold iterated exponentiation of x with y , ref name black Knuth ... operation s of addition , multiplication and exponentiation , after which the sequence proceeds with further binary operations extending beyond exponentiation. For the operations beyond exponentiation ... The axioms successor which is a unary operation , addition , multiplication , and exponentiation ... , , math math H 3 a, b a b , , math and for n 4 it extends these basic operations beyond exponentiation ... s next in the sequence Peano postulates The axioms successor , addition , multiplication , exponentiation ... are sometimes referred to by their analogous exponentiation term ref name romerioTerms cite web .... The concepts of successor, addition, multiplication and exponentiation are all hyperoperations the successor ... of times a number is to be added to itself, and exponentiation refers to the number of times a number ... a cdot a cdot a cdot ldots cdot a atop b math hyper3, exponentiation a 0, b real, or a non zero ..., etc., for the extended operations beyond exponentiation because they correspond to the indices ... , multiplication , exponentiation , and to make a more seamless extension of these beyond exponentiation ... than the successor function , then multiplication n 1 , exponentiation n 2 , etc. Secondly, the initial ... differing from the hyperoperations beyond exponentiation. ref name black ref cite web author Robert ... , and math F k a, b a b math exponentiation . Also, if the last condition is relaxed i.e. there is no exponentiation ... may produce different hyperoperations above exponentiation, while still corresponding ... to math n 0 math , multiplication to math n 1 math and exponentiation to math n 2 math , so the initial ... exponentiation , and so does not form a hyperoperation hierarchy. class wikitable n Operation Comment ... a, b e ln a ln b math A Commutativity commutative form of exponentiation . 4 math F 4 a, b e e ln ln ... a b a 2 log 2 b math This is exponentiation . 4 math F 4 a, b x to x x log 2 b a math Not to be confused ... more details
modular exponentiation. Classically, math a b pmod n math is calculated by repeatedly multiplying a by itself ... becomes apparent when dealing with a sequence of multiplications, as required for modular exponentiation e.g. exponentiation by squaring . Examples The Montgomery step Working with n digit numbers to base ... be preferable. Modular exponentiation Raising a number to a k bit exponent involves between k and 2 k multiplications. In most applications of modular exponentiation the exponent is at least several hundred bits long. To fix our ideas, suppose that a particular modular exponentiation requires 800 ... exponentiated, 800 to do the exponentiation, and one to de Montgomeryize the result. If a Montgomery ... will produce a faster result than conventional modular exponentiation. Side channel Attacks When ... more details
Other uses Mega disambiguation Mega symbol M is an SI prefix prefix in the metric system denoting a factor of million 10 sup 6 sup or 1000000 number gaps 1 000 000 . Confirmed in 1960, it comes from the Greek language Greek , meaning great . ref OED http dictionary.oed.com cgi entry 00304790 mega ref Other common examples of usage megapixel 1 million pixel s in a digital camera one TNT equivalent megatonne of TNT a unit often used in measuring the explosive power of nuclear weapon s is the approximate energy released on igniting one million tonnes of TNT. megahertz frequency of electromagnetic radiation for radio and television broadcasting, GSM , etc. 1 MHz 1,000,000 Hertz Hz . Exponentiation When units occur in exponentiation , such as in square and cubic forms, any size prefix is considered part of the unit, and thus included in the exponentiation. 1 Mm sup 2 sup means one square megametre or the size of a Square geometry square of 1,000,000 m by 1,000,000 m or 10 sup 12 sup m sup 2 sup , and not 1,000,000 square metre s 10 sup 6 sup m sup 2 sup . 1 Mm sup 3 sup means one cubic megametre or the size of a cube of 1,000,000 m by 1,000,000 m by 1,000,000 m or 10 sup 18 sup m sup 3 sup , and not 1,000,000 cubic metre s 10 sup 6 sup m sup 3 sup Computing In computing , mega can sometimes denote 1,048,576 2 sup 20 sup of information units example a megabyte , a megaword , but can denote 1,000,000 10 sup 6 sup of other quantities, for example, transfer rates 1 megabit s 1,000,000 bit s . The prefix mebi has been suggested as a prefix for 2 sup 20 sup to avoid ambiguity. SI prefixes See also SI prefix Binary prefix Mebibyte Orders of magnitude References references External links wiktionary mega http www.bipm.org BIPM website Category SI prefixes bg br Mega ca Mega cs Mega da Mega et Mega es Mega eo Mega eu Mega fa fr M ga gl Mega ko hy hi id Mega it Mega he ... more details
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