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what are the applications of multiple encryptions? where the multiple encryption like double DES and triple DES algorithms are use?

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Double DES is vulnerable to meet-in-the-middle, don't use it: en.wikipedia.org/wiki/Meet-in-the-middle_attack –  buherator Sep 10 '13 at 16:45

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3DES tries to cope with the biggest weakness of DES, which is its short key. A DES key contains only 56 useful bits, which makes it amenable to exhaustive search. This has been demonstrated as early as 1998.

Cascading two or three instances of the algorithms, with distinct keys, is a fix which was easy to apply on hardware which already included some DES circuitry. Moreover, 3DES has been especially designed so that it can be "DES-compatible": since 3DES is "encrypt-decrypt-encrypt", it suffices to make all three DES keys identical to obtain the same result as plain DES.

3DES remains in active use in a lot of legacy systems, and also in many smart cards because it is inexpensive in hardware (DES is slow in software, and 3DES thrice so, because DES is full of permutations of bits which are hard for code, but in hardware this is "just" plugging the right wires to the right transistors, with almost zero cost).

Security of 3DES is, in an academic way, about 2112 operations, which translates as "you cannot break that". The main trouble with 3DES is that it operates on 64-bit blocks, so some issues begin to happen when you encrypt more than 232 blocks with the same key (that's thirty gigabytes or so, which is large but not huge nowadays). The AES is meant to replace 3DES, but such migrations are always slow so not everybody has switched to AES yet.

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3DES was created to work with legacy financial systems that had previously been working with DES. During the cutover, replacing a DES module with a 3DES using the legacy DES key repeated 3 times (keying option 3) was a transparent operation. Once all the systems were ready, the full 3DES keys (keying option 1) could be deployed.

3DES remains in use in those industries because the cost of change is so high.

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