## Entropy[Back] Encrypted content tends not to a have a magic number (apart from detecting it in a disk partition. If we analyse both compressed and encrypted fragments of files we see high degrees of randomness. An important detection method for detecting compressed and encrypted files is the randomness of the bytes in the file. This measure is known as entropy, as defined by Claude E. Shannon in his 1948 paper. The maximum entropy occurs when there is an equal distribution of all bytes across the file, and where it is not possible to compress the file any more, as it is truly random. Enter hex values to calculate the entropy. A value of 8 bits per byte is the maximum compression, and is random data: |

## Calculations

We determine frequences and then use:

\(En = -\sum_{n=1}^{255} f_n . log_2(f_n)\)

For example "00 01 02 03" gives f1=0.25, f2=0.25, f3=0.25 and f4=0.25, which gives:

\(En =- 4 x (0.25xlog(0.25)/log(2)) = 8\)

for freq in freqList ent = ent + freq * math.log(freq, 2)

## Examples

The following are some examples:

**00 FF 00 FF 00 FF 00 FF 00 FF 00**. Try**00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F**. Try**00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F**. Try**First 256 bytes of TrueCrypt volume**. Try**First 256 bytes of PKZip file (notice major number: 50 4b 03 04)**. Try

## Background

If we measure the Shannon entropy of a TrueCrypt volume we get the results of:

C:\Python27>python en.py "c:\1.tc" File size in bytes: 3145728 Shannon entropy (min bits per byte-character): 7.99994457357 Min possible file size assuming max theoretical compression efficien-cy: 25165649.6435 in bits 3145706.20544 in bytes

We can see that the file size is 3,145,728 bytes and the minimum bytes for each character is 7.99994457357, which is extremely close to an almost perfect rating of 8 bits per byte. The efficiency is thus 99.999307 (3145706.20544/3145728 x 100%).

If we now try a compressed file (DOCX, which derives from the PKZip file for-mat), we get:

File size in bytes: 318724 Shannon entropy (min bits per byte-character): 7.98787618412 Min possible file size assuming max theoretical compression efficien-cy: 2545927.84891 in bits 318240.981113 in bytes

And we now get an efficiency of 99.84% with an entropy of 7.98787618412. A measure of entropy on a DOC file (a non-compressed or encrypted file format) gives:

File size in bytes: 62464 Shannon entropy (min bits per byte-character): 4.64286159485 Min possible file size assuming max theoretical compression efficien-cy: 290011.706661 in bits 36251.4633326 in bytes

Which gives an efficiency of 58.03577%. Thus a typical characteristics is that encrypted content results in the highest levels of Shannon entropy, followed closely by compressed file formats. An entropy value of over 98% is likely to identify com-pressed or encrypted content.