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The developers of this theme claim that it is a highly optimized theme for page loading speed. This quoted-overlap construction has better compatibility than the full-overlap construction of the previous section, but the compatibility comes at the expense of the compression ratio.

There, each added file cost only a central directory header; here, it costs a central directory header, a local file header, and another 5 bytes for the quoting header. Now that we have the basic zip bomb construction, we will try to make it as efficient as possible.

We want to answer two questions:. It pays to compress the kernel as densely as possible, because every decompressed byte gets magnified by a factor of N. All decent DEFLATE compressors will approach a compression ratio of when given an infinite stream of repeating bytes, but we care more about specific finite sizes than asymptotics.

For our purposes, filenames are mostly dead weight. While filenames do contribute something to the output size by virtue of being part of quoted local file headers, a byte in a filename does not contribute nearly as much as a byte in the kernel. We want filenames to be as short as possible, while keeping them all distinct, and subject to compatibility considerations. The first compatibility consideration is character encoding. TXT Appendix D.

But this is a major point of incompatibility across zip parsers, which may interpret filenames as being in some fixed or locale-specific encoding. We are further restricted by filesystem naming limitations. Some filesystems are case-insensitive, so "a" and "A" do not count as distinct names. As a safe but not necessarily optimal compromise, our zip bomb will use filenames consisting of characters drawn from a character alphabet that does not rely on case distinctions or use special characters:.

Filenames are generated in the obvious way, cycling each position through the possible characters and adding a position on overflow:. There are 36 filenames of length 1, 36 2 filenames of length 2, and so on.

Given that the N filenames in the zip file are generally not all of the same length, which way should we order them, shortest to longest or longest to shortest? A little reflection shows that it is better to put the longest names last, because those names are the most quoted. Ordering filenames longest last adds over MB of output to zblg. It is a minor optimization, though, as those MB comprise only 0.

The quoted-overlap construction allows us to place a compressed kernel of data, and then cheaply copy it many times. For a given zip file size X , how much space should we devote to storing the kernel, and how much to making copies?

To find the optimum balance, we only have to optimize the single variable N , the number of files in the zip file. Every value of N requires a certain amount of overhead for central directory headers, local file headers, quoting block headers, and filenames.

All the remaining space can be taken up by the kernel. Because N has to be an integer, and you can only fit so many files before the kernel size drops to zero, it suffices to test every possible value of N and select the one that yields the most output. It is not a coincidence.

Let's look at a simplified model of the quoted-overlap construction. In the simplified model, we ignore filenames, as well as the slight increase in output file size due to quoting local file headers. Analysis of the simplified model will show that the optimum split between kernel and file headers is approximately even, and that the output size grows quadratically when allocation is optimal.

Let H N be the amount of header overhead required by N files. Refer to the diagram to understand where this formula comes from. In this simplified model we ignore the minor additional expansion from quoted local file headers. Taking the derivative and finding the zero gives us N OPT , the optimal number of files. H N OPT gives the optimal amount of space to allocate for file headers. From this we see that the output size grows quadratically in the input size.

As we make the zip file larger, eventually we run into the limits of the zip format. It happens that the first limit we hit is the one on uncompressed file size. Accepting that we cannot increase N nor the size of the kernel without bound, we would like find the maximum compression ratio achievable while remaining within the limits of the zip format. The way to proceed is to make the kernel as large as possible, and have the maximum number of files.

Even though we can no longer maintain the roughly even split between kernel and file headers, each added file does increase the compression ratio—just not as fast as it would if we were able to keep growing the kernel, too. In fact, as we add files we will need to decrease the size of the kernel to make room for the maximum file size that gets slightly larger with each added file.

Any major improvements to the compression ratio can only come from reducing the input size, not increasing the output size. Among the metadata in the central directory header and local file header is a CRC checksum of the uncompressed file data. This poses a problem, because directly calculating the CRC of each file requires doing work proportional to the total unzipped size, which is large by design.

It's a zip bomb, after all. We would prefer to do work that in the worst case is proportional to the zipped size. SEO optimized. Compatible with SEO plugins. Optimized for Google PageSpeed. Microdata schema. Translation ready. Support for multi page articles. Custom Facebook Widget.

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We will provide professional technical support if you have any problems with installing, configuring or using the product. New products and latest versions. Direct Access will even download other parts of the Zip file in the background and prepare them when you select the files to unzip or view. Now you can toggle between creating Zip or Zipx files using a simple ribbon switch. WinZip Enterprise users will enjoy extended enterprise cloud services.

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