Key Distribution

Goal: agree on a uniformly random secret key

. . .

Key Distribution

Once Alice and Bob have agreed on a secret key:

s = 01011

s = 01011

m = 11100

=

Key Distribution

s = 01011

s = 01011

m = 11100

= 1

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

= 10

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

= 101

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

= 1011

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

= 10111

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

c = 10111

c = 10111

= 11100

= 10111

For all m, this ciphertext is uniformly distributed from the point of view of an eavesdropper who doesn’t know s.

(i.e. when s is uniformly random)

So, IF there were a way for Alice and Bob to perform “key distribution” (i.e. agree on a uniformly random secret key only known by the two of them), then they would be able to communicate with “unconditional” security!

Once Alice and Bob have agreed on a secret key:

Key Distribution

s = 01011

s = 01011

m = 11100

c = 10111

c = 10111

= 11100

= 10111

For all m, this ciphertext is uniformly distributed from the point of view of an eavesdropper who doesn’t know s.

(i.e. when s is uniformly random)

So, IF there were a way for Alice and Bob to perform “key distribution” (i.e. agree on a uniformly random secret key only known by the two of them), then they would be able to communicate with “unconditional” security!

Means that security holds no matter how much computational power an eavesdropper has

Once Alice and Bob have agreed on a secret key:

Key Distribution

Goal: agree on a uniformly random secret key

Key distribution with unconditional security is impossible classically.

. . .