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I am studying Triple DES.

I have got two basic questions. One, why are we following a sequence like encrypt(decrypt(encrypt)); what is the problem using a sequence encrypt(encrypt(encrypt))?

Second, why are we not using a single long key (say 168 independent key bits) in lieu of three individual 56 bits keys?

Thanks.

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The first question is already answered here.

For the second question, a single key $k \in \left\{0,1\right\}^{168}$ can be trivially converted back and forth from three keys $k_1, k_2, k_3 \in \left\{0,1\right\}^{56}$ – there is no semantic difference between the two. DES itself operates only on 56-bit keys, and triple-DES requires three independent DES operations. Software that implements triple-DES can trivially be written to either accept a single 168-bit key or three 56-bit keys.

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So, in case of security perception either single key or 3 keys playing the same role? Only the number of bits matters? –  Sharmin Mar 22 at 0:39
    
I'm not sure what you mean by "security perception". One long key and three short keys (whose sum of lengths are the same as the length of the long key) are completely interchangeable. –  Stephen Touset Mar 22 at 0:40
    
I mean if someone tries to break. –  Sharmin Mar 22 at 0:40
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@user2966119: actually, if we look at how 3DES is used in standard protocols (TLS, IPsec), we see that it is treated as if it were a block cipher that takes a single 192 bit key (192, not 168, because standard DES keys are 64 bits, and it doesn't matter to the protocol that some of those key bits are ignored). –  poncho Mar 22 at 4:03
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