BB84

The BB84 protocol (Bennett & Brassard, 1984) is a method for Quantum Key Exchange. It allows two parties (Alice and Bob) to generate a shared, secret random key.

Its security relies on the fundamental principles of quantum mechanics: observation disturbs the system.

It is impossible for an eavesdropper (Eve) to measure the photons transmitting the key without altering their state (and introducing detectable errors), ensuring that any interception is noticed.

Protocol

1. Alice generates a random bit (0 or 1) and selects a random basis:
   • Rectilinear ($+$):
     • 0 → $|$ (vertical)
     • 1→ $-$ (horizontal)
   • Diagonal ($\times$)
     • 0→ $\backslash$ (135°)
     • 1→ $/$ (45°)
2. Alice transmits the polarized photon to Bob via a quantum channel (e.g., fiber optics).
3. Bob chooses a random basis ($+$ or $\times$) to measure the incoming photon.
   • Match: If Bob’s basis matches Alice’s, he measures the bit correctly (100% correlation).
   • Mismatch: If Bob uses the wrong basis (e.g., measuring a $|$ photon with a $\times$ filter), the result is random (50% probability of 0 or 1).
4. Bob and Alice communicate over an authenticated classical channel.
5. They announce which bases they used for each photon (but not the measurement results).
6. They keep only the bits where their bases matched (the “sifted key”) and discard the rest (approx. 50% data loss).
7. Error Check: They compare a subset of the sifted key. If the error rate (Quantum Bit Error Rate - QBER) is above a threshold, they assume Eve is listening and abort the protocol.

Examples

Normal Operation (No Interference)

Step	1	2	3	4	5
Alice bit	1	1	0	0	0
Alice base	$+$	$\times$	$+$	$+$	$\times$
Alice sends	$|$ (=1)	$/$ (=1)	$-$ (=0)	$-$ (=0)	$\setminus$ (=0)
Bob’s filter	$+$	$+$	$\times$	$+$	$\times$
Bob’s result	$|$ (=1)	$|$ or $-$	$/$ or $\setminus$	$-$ (=0)	$\setminus$ (=0)

Alice and Bob only keep data when bases match (Steps 1, 4 & 5).

Eavesdropping (Eve Intercepts)

Eve tries to measure the photon before resending it to Bob. If she guesses the wrong basis, she changes the photon’s state.

Focus on Step 1: Eve measures a $|$ photon with a $\times$ filter.

Step	1	2	3	4	5
Alice sends	$|$	$/$	$-$	$-$	$\setminus$
Eve’s filter	$\times$	any	any	$+$	$+$
Eve gets/sends	$/$ or $\setminus$			$-$	$-$ or $+$
Bob’s filter	$+$	$+$	$\times$	$+$	$\times$
Bob’s result	$|$ or $-$	$|$ or $-$	$/$ or $\setminus$	$-$	$/$ or $\setminus$

Result: Even though Alice and Bob used the correct matching bases ($\times$), Bob might measure a $-$ (Bit 0) instead of $|$ (Bit 1) because Eve disturbed the state. This error reveals Eve’s presence.

Limitations & Requirements

• Authenticated Channel: The classical channel must be authenticated to prevent a Man-in-the-Middle (MitM) attack. If Eve can impersonate Bob, she can just perform the protocol with Alice herself.
  • Paradox: Requires pre-shared keys (AES) or Post-Quantum Public Key Cryptography to establish the QKD session.
• Physical Constraints: Requires a direct line of sight or uninterrupted fiber optic cable. Signal attenuation limits distance (requires trusted repeaters or quantum repeaters).

---

Relevant Note(s):