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When browsing websites with Chrome sometimes I can see a green lock and encryption info inside. It says the connection with this website is 128-bit or 256-bit encrypted with TLS1.2. So I'm wondering that is that possible to use 512-bit or higher encryption on websites?

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These 128-bit and 256-bit are symmetric key sizes. Against brute force attacks: assuming computing ability doubles each year, we gain 1 extra year of security per bit; that used to be about right in the last 20 years of the 20th century, and is now more like 2 years per bit, and growing; 80 bits was very safe in 1990, and remains hard to crack nowadays (there's no public claim that it was attempted, much less done); 128 bits seems very safe for two decades; we can expect 256 bits will never be cracked by humanity because progress will slow or/and humanity vanish; so why care for 512 bits? – fgrieu Apr 4 '14 at 7:09
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So I'm wondering that is that possible to use 512-bit or higher encryption on websites?

Not with the current TLS standard (v1.2), the strongest algorithm it appears to support is only Camellia or AES with 256 bit key lengths. The strength and type of the cipher actually used for a connection depends on the server's configuration and the client's browser. When browsing the internet it can be similar to a lottery regarding the quality and strength of the encryption you actually get on each site.

That does not stop anyone from writing their own website server code and a Javascript browser extension to use higher encryption than 256 bits. For example, you could use the Threefish block cipher which has key lengths of 512 bits and 1024 bits.

Remember, if you simply serve up the Javascript code from the web server using TLS and your custom code runs 512 bit encryption then your security is only as strong as the TLS connection itself. If an attacker breaks the TLS connection or performs a MITM attack, they can modify the Javascript in transit to remove the custom encryption completely. TLS is not so good, so this remains a real possibility. A signed Javascript extension is the way to go.

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TLS does not support any cipher suite combination with a symmetric key size larger than 256 bits. Asymmetric key sizes are available up to 15360 bits, which correspond to a 256-bit symmetric security level.

RFC5246 lists the available cipher suite combinations for TLS 1.2

It should be noted that the symmetric security of TLS is not the weak point, and 128-bits should be more than secure enough for the next 30 years.

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Ciphers can be added by means of TLS extensions. A complete list of cipher suites, including those added by extensions, can be found here – TruthSerum Apr 4 '14 at 9:31

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