Welcome to section 4.
Section 4 is the first section of
our in-depth study of the famous public
key cryptography in this section. We'll
see the most common algorithms and
Protocols of public key cryptography.
In these first video, we will look
at the picture of public key cryptography and
start to understand. What is its
value compared to symmetric key cryptography.
Will revisit the Symmetry key methods we saw
in sections 2 and 3 and see their counterparts
in public key cryptography.
So let's get started.
The invention of public key cryptography is
related to a paper named new directions
in cryptography.
These people was published by the two cryptographers Whitefield
TV and Martin Hellman in
1976.
These people introduced the concept of public key
cryptography.
Defend Herman described how we can
use one-way functions to construct the
methods and algorithms of public key cryptography.
One Way functions are functions that are easy to
apply and hard to invert.
Unless you have the key bound to that one-way function.
No worries, if the concept of four way
function still seems abstract or clear.
We'll see it in more detail in this video and in the
coming videos.
Using this one-way functions different element
described how we can create encryption algorithms
that ensure data confidentiality.
And digital signatures that ensure data
integrity and origin Authentication.
Different element did not provide any concrete examples
of how we can create such encryption
or digital signature algorithms.
The only describe the high-level concept.
In the next years after this paper many cryptographers
will propose actual constructions
of public key encryption and digital
signature algorithms.
However, different element proposed both the
idea and actual contract construction for another
functionality.
key agreement
key agreement is a protocol that allows two
parties to construct a common key.
Let's start by seeing how we can have encryption using
public key cryptography.
first remember how symmetric key encryption
works
to parties I listen Bob have to
obtain a common secret key k
that is then used to encrypt plain texts and decrypt
cycle texts.
One of these parties yearbook generates this
key and transfer it to Alice using
some authenticated and confidential Channel.
Confidentiality requires that no other parties should
see the content of this communication.
And authentication means that Bob is sure
to transmit the key to Alice and not to an
adversary and similarly. Alice should be sure that this key
comes from Bob and not from adversary.
When it comes to public key encryption pubgenerates
a pair of keys.
the first key
called public key PK and the
second key called secret key
SK.
Bobs and PK to Alice and keeps Escape
when Alice wants to send a message to Bob using
unsecure Channel.
She uses PK to encrypt the message.
And send it ciphertext to Bob that
uses ski to decrypted back to the
plaintext.
The adversary that intercepts the ciphertext cannot retrieve the
original plaintext. That's exactly the same guarantee as
for symmetric key encryption.
There then two major differences with symmetric encryption.
First is the fact that there are two keys one used for
encryption and the other is for decryption.
And the second difference which is very important
here is related
to the key transfer.
Alison Bob needs only to
have an authenticated channel for the
key transfer, but the transfer of the PK.
So public cryptography allows a less
constraining setting for the key transfer compared
to symmetric key.
Cryptography where Alice and Bob has to
use an authenticated and confidential Channel.
So for symmetric key.
Alice and Bob has maybe to meet directly
and get the key while ensuring that
no one else is listening.
while for public key
Alice has only to be sure that the PK of Bob
comes really from
she doesn't need to meet him to get that she can
retrieve that key from his website or even
from another person that she
trusts that tells her about the key of
Pop.
so
For symmetric key. Alice has also to
store the key in a secure
location.
Because losing that key will break the confidentiality of
all the ciphertexts encrypted with
that key.
Well for public key. Alice does not even need to store it locally.
She just need to get it from where Bob
publish it.
Digital signatures are the counterpart of
message authentication codes Max in the
public key cryptography.
Let's review briefly Mac.
In Mac Alice and Bob have a common key.
Alice would like to prove to pop that her
message was not modified and comes from her.
So she computes using the key k a code
C that she appended to her message X.
Bob recomputes the code C on Alice's
message
using the key and checks if it matches
with the code that early set.
When it comes to digital signatures Alice has
a pair of public key and secret key.
She uses her secret key to compute a signature
as that. She opens it to her
message X.
And send them to Bob.
Bob uses Alice's public key
to verify that the pair of message and signature is
valid.
You might have noticed that for encryption at least
uses Bob's public key to
encrypt the message that only Bob can decrypt using his
secret key.
In signatures at least uses her own secret key
to sign a message and Bob uses Alice's
public key to verify that the message
was not modified and is authenticated.
Alice could not have used Bob's secret
key because only Bob has access to
that key.
Also, she could not do the
other way and use her own public key
because in that case anyone can force
signature because anyone can
do that because her public key is public.
There is also a last remark.
similar to encryption
For Mac.
The two parties need an authenticated and
confidential channel for the key transfer.
But for digital signatures only in
authenticated channel is needed to transfer
the public key.
Okay, let's now move to the
last functionality that was described in different
element paper.
Which is key agreement.
To understand key agreement. Let's start from the key
transfer that we used so far in the
symmetric key cryptography.
One party is responsible of generating the
key then transmitted to the second party
using an authenticated and confidential Channel.
Key agreement allows two users to construct together
a common key.
In order to construct this key the parties run
a protocol and exchange some data.
The channel to exchange this data has to only
be authenticated no confidentiality requirements
like in the symmetric key
cryptography.
At the end of the protocol I listened Bob obtained the
same TK.
And adversary that intercepted all their exchanges cannot
retrieve.
You might be wondering why are the two
parties constructed a key? We have seen in the
last two slides we can encrypt and sign messages using
the pair of public key and
secret key.
When key agreement is a very interesting
if we would like to combine public
key and symmetric key.
And this is very common in real world applications to
use public key cryptography to
agree on a key. And
then we use that key to switch to
symmetric key description.
The rationale behind this is that symmetric key
cryptography is much faster
than public key cryptography.
So we use this slow public key cryptography to agree
on the key and then we switch to more efficient
symmetry key scripture.
On this video. We introduced the high
level ideas public key cryptography.
We saw how we can have counterparts of symmetry
encryption and Max which are the
public encryption and digital signatures.
We saw that for this counterparts the key transfer
requires less constraining Channel.
That makes public key cryptography particularly powerful
to be used in many real
world applications. We are having confidential channels is
not possible.
In the next videos, we will see the actual constructions.
And you will start with the key agreement that different element
proposed in their publication.
So see you in the next video.