Welcome to a course on the working principles inapplicability of symmetric and asymmetric ciphers the
module will focus on examining diverse components of cryptographic systems.
Let's begin with a short introduction before we can move on.
We must understand what information theory means.
This field was developed by Claude Shannon who you can see in the picture.
Shannon is the author of two of the most seminal works on information theory a mathematical theory of
cryptography and a mathematical theory of communication which was published soon after the first book
Shannon first coined the word bit a bit is defined as the smallest information unit required to encode
one of the two values zero or one will come back to this later Jether term Shannon and used as entropy.
Entropy is the smallest amount of information needed on the average to encode and invent.
There's a set of probable events for which you need to determine information entropy.
The more improbable or unlikely an event the bigger the entropy is.
If you roll fair dice the entropy of the probability that you will get a 1 is quite small the number
of total outcomes is only 6.
On the other hand in lotto games with the draw results of 5 15:23 and so on the information entropy
is very high because the probability of winning is extremely low.
There was a huge number of possibilities.
Our task in cryptography is to maximize entropy.
Let's start with this simple example.
Let's take a look at a short script that will launch in a moment this short script is designed to calculate
the password entropy in bits.
We'll have to calculate a logarithm from multiplying two values.
The first variable range specifies the range of possibilities determined in the definition.
If a password can for example only be expressed in upper case the range of this will be one to 26.
The second variable number specifies still length of our password since the desired result should be
in bits well divided by the logarithm from two.
Next we'll call the previously mentioned simple function for some of the passwords.
The first password uses 8 uppercase characters.
The range is 1 to 26.
The second case allows passwords to use lower case letters
the third password is again limited to uppercase only password length is doubled
the fourth password uses both upper case and lower case letters and a relatively secure number of characters
16.
Let's now find out the true entropy strength of the individual passwords.
The first password is only 38 bits Strong see entropy as indicative of the secrecy of something the
bigger the entropy the more secret or improbable something is.
Your password should be as secretive as possible for everyone except yourself.
38 bits is not a good strength.
In the second case there are 46 bits.
It's more but the difference is not likely to matter.
8 character letter only passwords are not secure.
16 character uppercase passwords provide security level for modern computer systems that amount to 77
bits of entropy.
The last password is 93 bit strong.
This means that even if you have a 16 bit password that contains both upper case and lower case letters
you still won't get over 100 bits of entropy when we'll be talking about algorithms.
We'll show you that algorithms that make use of a key with a length similar to the result we've got.
Provide no security.
The passwords are not really secure.
There should be more complicated before we move on to discuss algorithms symmetric algorithms in particular
will need to explain two terms.
The first concept is confusion confusion measures a non-linear relationship between the plaintext ciphertext
and the key.
It describes the dissimilarity of the ciphertext in the plaintext and the difficulty of extracting information
about the key from the ciphertext.
This is a vital concept.
The bigger the confusion the more immune to the linear approximation cryptanalysis your cipher will
be.
The second crucial term is diffusion diffusion specifies the distribution or spreading of the plaintext
information in the ciphertext Caesar cipher diffusion was one to one.
The letter A always represented the letter D.
The diffusion was practically non-existent in that case read like the plaintext information not to be
distributed to one fixed position in the cipher text.
Rather it should be spread all over the ciphertext diffusion as measured by the probability of the successful
differential approximation.