Let's now examine public key asymmetric algorithms.
Let's start with their operation scheme.
There's the plain text that will be encrypted using a key.
This time the key used for encryption will be called the public key.
The output of this operation is the ciphertext But unlike with symmetric key algorithms the reverse
encryption and to read the ciphertext a different key will be needed.
The private key asymmetric cryptography makes use of two different keys although they're related to
each other you can extract either from the other if you have a public key you will not be able to generate
a corresponding private key.
What are the benefits of replacing a shared key scheme with a pair of keys.
First of all exchange is not the problem anymore.
The user needs only two keys regardless of the number of other users they want to exchange data with
a private key and a public key.
The public doesn't have or even shouldn't be protected.
The name is self-explanatory.
The key is public and should be shared with all users in the system.
A private key on the other hand is a user's exclusive property if it's shared the entire system is compromised
secure data exchange in public key cryptography systems with 50 users requires 100 keys to keys per
user symmetric key systems required as many as 1225.
What's more asymmetric algorithms allow users to establish a trust relationship.
They have one strength that symmetric algorithms lacked the so-called non repudiation.
You can use this feature to establish the authenticity of the ciphertext.
We'll show you how in a moment and also to prove to a message sender that the message truly comes from
them and that its integrity has not been breached.
This solution has some shortcomings as well.
Public key cryptography is extremely slow as you've seen the basic operation used in symmetric ciphers
was the exclusive disjunction ex-SO are this operation is quick and equivalent of the X-O are an asymmetric
cryptography is a Madugalle operation.
The result of modular exponentiation can be a large prime this operation has a high computational cost
and other weaknesses the asymmetric ciphers have not been designed for encrypting long messages.
This flows naturally out of the first problem.
Several well documented attacks on metric ciphers have been developed that rely on excessive key use
the situation involves using a key to encrypt messages that are longer than necessary.
As a rule asymmetric encryption should be applied to data that is of similar length to the used key
kids should be a bit longer than the plaintext.
The strength of a 512 bit asymmetric key is more or less equivalent to the strength of a 60 bit symmetric
key as you know 60 bits does not provide adequate security.
512 bits is likewise insufficient.
Today even a 1024 bit strength can proved not enough people do but the.
We'll talk about this at greater length later in the module.
There are also problems that don't stream from any cryptographic solutions if asymmetric algorithms
allow you to establish trust relationships.
You need to keep in mind that ciphers and keys are used by software not by users themselves.
You shouldn't transpose this trust freely.
The starting point for asymmetric encryption depends on finding some one way functions one way functions
or isn't sufficient to compute one direction but computationally hard to invert it's difficult to establish
the exact computational complexity of these functions.
Whether it's an MP a complete problem or the complexity is simply over exponential is determined by
the development of mathematics.
A good example of this is the controversy surrounding the RSA algorithm which we'll talk about soon.
The RSA algorithm security is based on the fact that multiplying is relatively easy it's fast.
While the decomposition of the object into factors factorization has high computational complexity just
how complex is it.
Factoring problems were analyzed by Turing one of the greatest mathematicians of the 20th century Turing's
paper on factorization remains classified confidential.
The UK has been keeping and handling this document as an exclusive possession.
What is the reason for this.
It could be that in fact efficient factoring methods exist after all.
I can risk saying this because there is a peculiar correlation mathematicians that examined this problem
and published works on factorization and did disappear from the scientific limelight in scientific life
altogether.
They are probably working now for agencies that pay better and beginning from that point.
It is
this is relevant since practically all facets of our security depend on the assumed high computational
complexity of factorization many critically important systems have been based on the RSA algorithm.
If a simple laptop would be enough to crack the algorithm we'd be in a tight spot.
RSA is not the only asymmetric algorithm El-Gamal is just as popular and perhaps even more secure.
The two algorithms are designed for encryption and decryption while the TSA algorithm is used for digital
signatures El-Gamal NTSA are based on a discrete logarithms problem.
The logarithm is the inverse operation of exponentiation.
The exponentiation can be modular Ahmadullah is counting to 20 on ten fingers.
The characteristic trait of the Modelo operation is that while something is lost not all information
is lost.
The same was true for the axle or operation.
Since you can perform exponentiation over a MONDOUBLEAU you can calculate Ahmadullah logarithm.
As we mentioned El-Gamal and DSA are based on the computational simplicity of modular exponentiation.
This is the logarithmic complexity class inverting this operation seems to require a brute force search
of all possible exponent values.