Semicolon

Name: Jodi Junker
My age: 32
Country: Netherlands
Home town: Oudkarspel
Post code: 1724 Xg
Street: Waterlelie 22

my page - www.hostgator1centcoupon.info

In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1984. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The Digital Signature Algorithm is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption.

ElGamal encryption can be defined over any cyclic group $G$. Its security depends upon the difficulty of a certain problem in $G$ related to computing discrete logarithms (see below).

The algorithm

ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm.

Key generation

The key generator works as follows:

• Alice generates an efficient description of a multiplicative cyclic group $G$ of order $q$ with generator $g$. See below for a discussion on the required properties of this group.
• Alice chooses a random $x$ from $\{1,\dots ,q-1\}$.
• Alice computes $h=g^x$.
• Alice publishes $h$, along with the description of $G,q,g$, as her public key. Alice retains $x$ as her private key which must be kept secret.

Encryption

The encryption algorithm works as follows: to encrypt a message $m$ to Alice under her public key $(G,q,g,h)$,

• Bob chooses a random $y$ from $\{1,\dots ,q-1\}$, then calculates $c_1=g^y$.
• Bob calculates the shared secret $s=h^y$.

• Bob converts his secret message $m$ into an element $m^{\prime }$ of $G$.
• Bob calculates $c_2=m^{\prime }\cdot s$.
• Bob sends the ciphertext $(c_1,c_2)=(g^y,m^{\prime }\cdot h^y)=(g^y,m^{\prime }\cdot (g^x{)}^y)$ to Alice.

Note that one can easily find $h^y$ if one knows $m^{\prime }$. Therefore, a new $y$ is generated for every message to improve security. For this reason, $y$ is also called an ephemeral key.

Decryption

The decryption algorithm works as follows: to decrypt a ciphertext $(c_1,c_2)$ with her private key $x$,

• Alice calculates the shared secret $s=c_1^x$
• and then computes $m^{\prime }=c_2\cdot s^{-1}$ which she then converts back into the plaintext message $m$, where $s^{-1}$ is the inverse of $s$ in the group $G$. (E.g. modular multiplicative inverse if $G$ is a subgroup of a multiplicative group of integers modulo n).

The decryption algorithm produces the intended message, since

$c_2\cdot s^{-1}=m^{\prime }\cdot h^y\cdot (g^{xy}{)}^{-1}=m^{\prime }\cdot g^{xy}\cdot g^{-xy}=m^{\prime }.$

Practical use

The ElGamal cryptosystem is usually used in a hybrid cryptosystem. I.e., the message itself is encrypted using a symmetric cryptosystem and ElGamal is then used to encrypt the key used for the symmetric cryptosystem. This is because asymmetric cryptosystems like Elgamal are usually slower than symmetric ones, so it is faster to encrypt the symmetric key (which most of the time is quite small if compared to the size of the message) with Elgamal and the message (which can be arbitrarily large) with a symmetric cypher.

Security

The security of the ElGamal scheme depends on the properties of the underlying group $G$ as well as any padding scheme used on the messages.

If the computational Diffie–Hellman assumption (CDH) holds in the underlying cyclic group $G$, then the encryption function is one-way.

If the decisional Diffie–Hellman assumption (DDH) holds in $G$, then ElGamal achieves semantic security. Semantic security is not implied by the computational Diffie–Hellman assumption alone. See decisional Diffie–Hellman assumption for a discussion of groups where the assumption is believed to hold.

ElGamal encryption is unconditionally malleable, and therefore is not secure under chosen ciphertext attack. For example, given an encryption $(c_1,c_2)$ of some (possibly unknown) message $m$, one can easily construct a valid encryption $(c_1,2c_2)$ of the message $2m$.

To achieve chosen-ciphertext security, the scheme must be further modified, or an appropriate padding scheme must be used. Depending on the modification, the DDH assumption may or may not be necessary.

Other schemes related to ElGamal which achieve security against chosen ciphertext attacks have also been proposed. The Cramer–Shoup cryptosystem is secure under chosen ciphertext attack assuming DDH holds for $G$. Its proof does not use the random oracle model. Another proposed scheme is DHAES, whose proof requires an assumption that is weaker than the DDH assumption.

Efficiency

ElGamal encryption is probabilistic, meaning that a single plaintext can be encrypted to many possible ciphertexts, with the consequence that a general ElGamal encryption produces a 2:1 expansion in size from plaintext to ciphertext.

Encryption under ElGamal requires two exponentiations; however, these exponentiations are independent of the message and can be computed ahead of time if need be. Decryption only requires one exponentiation:

Decryption

The division by $s$ can be avoided by using an alternative method for decryption. To decrypt a ciphertext $(c_1,c_2)$ with Alice's private key $x$,

• Alice calculates $s^{\prime }=c_1^{q-1-x}=g^{y(q-1-x)}=g^{-xy}$.

$s^{\prime }$ is the inverse of $s$. This is a consequence of Lagrange's theorem, because

$s\cdot s^{\prime }=g^{xy}\cdot g^{y(q-1-x)}=g^{xy}\cdot g^{(-x)y}=1$. Note that operations

in the exponent are computed modulo $(q-1)$, rather than $q$.

• Alice then computes $m^{\prime }=c_2\cdot s^{\prime }$, which she then converts back into the plaintext message $m$.

The decryption algorithm produces the intended message, since

$c_2\cdot s^{\prime }=m^{\prime }\cdot s\cdot s^{\prime }=m^{\prime }\cdot 1=m^{\prime }$.

See also

• ElGamal signature scheme
• Homomorphic encryption

References

• 55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.
  
  You can view that web-site... ccleaner free download
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang