# Is a 4DES or 5DES system possible?

We know that 3DES is created with $E_{K_3}(D_{K_2}(E_{K_1}(m)))$ to extend DES's key length. Is it possible to extend it further by repeating this pattern? Perhaps using $E_{K_5}(D_{K_4}(E_{K_3}(D_{K_2}(E_{K_1}(m)))))$ for a 280 bit key.

• of course, but why would you want to considering how slow DES is, and that its block size is only 64-bits? – Richie Frame Feb 16 '16 at 7:22
• @RichieFrame This is more theoretical than practical. However, I can imagine a scenario where technology has moved on and 128-bit keys are considered too small, but legacy systems still only support DES. – Daffy Feb 16 '16 at 7:24

There is a very interesting paper that relates to this exact question (but you wouldn't guess it from the title). The paper is titled Efficient Dissection of Composite Problems, with Applications to Cryptanalysis, Knapsacks, and Combinatorial Search Problems. In Section 3, the paper considers the multiple encryption problem and gives novel attacks that are better than what you would expect (for a general multiple encryption $r$ times). For example, for 2DES there is an attack taking about $2^{56}$ time and $2^{56}$ space. You would therefore expect that 4DES would give you $2^{112}$ time and $2^{112}$ space. However, they show an attack that takes time $2^{112}$ and only space $2^{56}$.