C191: Quantum Cryptography

Umesh V. Vazirani

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How to agree on a secret key?

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Quantum Crypto Setup

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RSA: Public-key Cryptography

Alice Bob

• Alice publishes public key = (N, e).

• N = PQ, with P, Q primes known only to Alice.Her private key is d: de = 1 mod (P-1)(Q-1)

• Ed = mde = m (mod N)

• Eavesdropper Eve doesn’t know d, and cannot decrypt.

message mE= me mod N

Decrypts: m = Ed

• Unconditional security

• Quantum factoring breaks RSA!

• Has been implemented using today’s technology

• Measurement disturbs the system

- detect eavesdropper

Why Quantum Cryptography?

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Photon Polarization

• The polarization of a photon is a direction in the plane normal to the direction of propagation.

• The polarization of a photon is a qubit.

• A polarizing filter blocks photons whose polarization is perpendicular to the orientation of the filter and transmits photons whose polarization is aligned with the orientation of the filter.

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