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# RSA encryption: Step 1

Video transcript

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. (lock clinking) As you may recall, encryption is a mapping from some message using a specific key, to a ciphertext message. To decrypt a ciphertex, 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 Diffy-Hellman key exchange. Plus, if Alice needs to
communicate with multiple people, perhaps she's a bank, then she's going to have
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. To see how inverse keys could work, let's do a simplified
exampled 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 complimentary 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 compliment 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.