RSA encryption: Step 1 - Electronics & Communication Engineering Video Lecture - Electronics and Communication Engineering (ECE) | Best Video for Electronics and Communication Engineering (ECE)

Up until the 1970s,
cryptography had
been based on symmetric keys.
That is, the sender
encrypts their message
using a specific
key, and the receiver
decrypts using an identical key.
As you may recall,
encryption is a mapping
from some message using a
specific key to a cipher text
message.
To decrypt a cipher text,
you use the same key
to reverse the mapping.
So for Alice and Bob to
communicate securely,
they must first
share identical keys.
However, establishing
a shared key
is often impossible if Alice
and Bob can't physically
meet, or requires extra
communications overhead
when using the
Diffie-Hellman key exchange.
Plus, if Alice
needs to communicate
with multiple people,
perhaps she's a bank,
then she's going
to have to exchange
distinct keys with each person.
Now she'll have to
manage all of these keys
and send thousands of messages
just to establish them.
Could there be a simpler way?
In 1970, James Ellis, a British
engineer and mathematician,
was working on an idea
for non-secret encryption.
It's based on a simple
yet clever concept.
Lock and unlock are
inverse operations.
Alice could buy a
lock, keep the key,
and send the open lock to Bob.
Bob then locks his message
and sends it back to Alice.
No keys are exchanged.
This means she could publish
the lock widely and let
anyone in the world use
it to send her a message.
And she now only needs to
keep track of a single key.
Ellis never arrived at
a mathematical solution,
though he had an intuitive
sense of how it should work.
The idea is based
on splitting a key
into two parts, an encryption
key and a decryption key.
The decryption key performs the
inverse, or undo, operation,
which was applied by
the encryption key.
Too see how inverse
keys could work,
let's do a simplified
example with colors.
How could Bob send
Alice a specific color
without Eve, who is always
listening, intercepting it?
The inverse of some
color is called
a complementary color,
which when added to it
produces white, undoing the
effect of the first color.
In this example, we
assume that mixing colors
is a one-way function because
it's fast to mix colors
and output a third, and
it's much slower to undo.
Alice first generates
her private key
by randomly selecting
a color, say, red.
Next, assume Alice uses
a secret color machine
to find the exact
complement of her red.
And nobody else
has access to this.
This results in cyan, which she
sends to Bob as her public key.
Let's say Bob wants to send
a secret yellow to Alice.
He mixes this with
her public color
and sends the resulting
mixture back to Alice.
Now Alice adds her private
color to Bob's mixture.
This undoes the effect
of her public color,
leaving her with
Bob's secret color.
Notice Eve has no easy
way to find Bob's yellow,
since she needs Alice's
private red to do so.
This is how it should work.
However, a mathematical
solution was
needed to make this
work in practice.