Quantum Mechanics; a Blessing and a Curse By Elias Marcopoulos
Quantum Computers • Quantum Computers are just like regular computers, they crunch numbers
Quantum Computers • Quantum Computers are just like regular computers, they crunch numbers • The difference lies in the fact that Quantum Computers can crunch multiple numbers at the same time
Quantum Computers • Quantum Computers are just like regular computers, they crunch numbers • The difference lies in the fact that Quantum Computers can crunch multiple numbers at the same time
Superposition • They do this through a phenomena known as superposition
Superposition • They do this through a phenomena known as superposition • Superposition is when two waves occupy the same physical space, so that their waves are additively combined • This allows a wave to be both a 0 and a 1 at the same time, for instance.
Superposition • You may remember a picture that looks like this, if you ever took a high school physics course
Superposition • You may remember a picture that looks like this, if you ever took a high school physics course This might represent a 1
Superposition • You may remember a picture that looks like this, if you ever took a high school physics course This might represent a 1 And This might represent a 0
Superposition • You may remember a picture that looks like this, if you ever took a high school physics course This might represent a 1 And this would be the resultant superposition And This might represent a 0 (In quantum computers, waves do not look like This, but the concept is the same)
What a Quantum Computer Looks Like
What a Quantum Computer Looks Like Each of these gold things are called a qubit, or quantum bit
What a Quantum Computer Looks Like Each of these gold things are called a qubit, or quantum bit Each qubit contains a particle, like an atom
What a Quantum Computer Looks Like Each of these gold things are called a qubit, or quantum bit Each qubit contains a particle, like an atom Every atom describes a wave, which can Interfere with all the waves described by the Other atoms from the other qubits
Wait, If they all superposition together… • Then for each qubit which is in a superposition between a 1 and a 0, each other qubit is also in a 1 and a 0
Wait, If they all superposition together… • Then for each qubit which is in a superposition between a 1 and a 0, each other qubit is also in a 1 and a 0 • So in total, 2 n states exist simultaneously, where n is the number of qubits
What’s So Great About Being in Exponential States?
What’s So Great About Being in Exponential States? • Image you are guessing someone’s password
What’s So Great About Being in Exponential States? • Image you are guessing someone’s password • Lets imagine their password is 150 bits long
What’s So Great About Being in Exponential States? • Image you are guessing someone’s password • Lets imagine their password is 150 bits long • With one computer, there are 1.4272477 x 10 45 passwords that would have to be tried iteratively, which would take forever
What’s So Great About Being in Exponential States? • Image you are guessing someone’s password • Lets imagine their password is 150 bits long • With one computer, there are 1.4272477 x 10 45 passwords that would have to be tried iteratively, which would take forever • A Quantum Computer with 150 qubits could represent each possible password at once
What’s So Great About Being in Exponential States? • Image you are guessing someone’s password • Lets imagine their password is 150 bits long • With one computer, there are 1.4272477 x 10 45 passwords that would have to be tried iteratively, which would take forever • A Quantum Computer with 150 qubits could represent each possible password at once • If the place to enter the password was a physical device compatible with the quantum computer, it would be opened immediately
So it can try a lot of things at once?
So it can try a lot of things at once? • Basically
So it can try a lot of things at once? • Basically • In fact, with 2 n computers, you can simulate a quantum computer
What do you think is less expensive, more efficient and more reliable?
What do you think is less expensive, more efficient and more reliable? 2 n computers?
What do you think is less expensive, more efficient and more reliable? 2 n computers? Or n qubits?
What do you think is less expensive, more efficient and more reliable? 2 n computers? Or n qubits?
What do you think is less expensive, more efficient and more reliable? 2 n computers? Or n qubits? That’s why so many big companies are investing in quantum technology
I don’t know any places to enter a password that are “quantum enabled”
I don’t know any places to enter a password that are “quantum enabled” • There aren’t any, as far as I know! So thankfully quantum computers can’t be used as the ultimate hacking devices.
I don’t know any places to enter a password that are “quantum enabled” • There aren’t any, as far as I know! So thankfully quantum computers can’t be used as the ultimate hacking devices. • Think of it this way: Even with 2 n computers, they all can’t try their password at once, they have to take turns entering it into the server.
I don’t know any places to enter a password that are “quantum enabled” • There aren’t any, as far as I know! So thankfully quantum computers can’t be used as the ultimate hacking devices. • Think of it this way: Even with 2 n computers, they all can’t try their password at once, they have to take turns entering it into the server. • The area that quantum computers can actually break things is in hard mathematical functions
Breaking RSA • RSA is a popular public encryption model.
Breaking RSA • RSA is a popular public encryption model. • There is a secret key and a public key, the public key is used to encrypt data and send it to the server, where it can be decrypted with the secret key
Breaking RSA • RSA is a popular public encryption model. • There is a secret key and a public key, the public key is used to encrypt data and send it to the server, where it can be decrypted with the secret key • The public and private keys must be correlated, and they are with math!
Prime Number Factorization • The math RSA is based on is multiplying very large prime numbers together Much bigger than this!!!!
Prime Number Factorization • The math RSA is based on is multiplying very large prime numbers together • Factoring the resultant number is difficult to do without brute force (currently no polynomial time algorithm exists for a classical computer)
Prime Number Factorization • The math RSA is based on is multiplying very large prime numbers together • Factoring the resultant number is difficult to do without brute force (currently no polynomial time algorithm exists for a classical computer) • But this is no problem for a quantum computer! Peter Shor came up with a polynomial time algorithm that has already been used to factor small prime numbers
(Incomplete) List of Public Key Systems Vulnerable to Quantum Computing • RSA • DSA • ECHD • ECDSA • BLISS • NTRU
(Incomplete) List of Public Key Systems Vulnerable to Quantum Computing • RSA • DSA • ECHD • ECDSA • BLISS • NTRU
(Incomplete) List of Public Key Systems Vulnerable to Quantum Computing • RSA • DSA • ECHD • ECDSA • BLISS • NTRU Most Public Key Systems are compromised, so we need another type of system to remain secure
The One Time Pad • Symmetric key systems are quantum resistant!
The One Time Pad • Symmetric key systems are quantum resistant! • The One Time Pad is the most unbreakable symmetric key system
The One Time Pad • Symmetric key systems are quantum resistant! • The One Time Pad is the most unbreakable symmetric key system Each character in the message is given its own random key, Which is added to the original message
Problems with the One Time Pad • A new key needs to be transmitted between the two users each time
Problems with the One Time Pad • A new key needs to be transmitted between the two users each time • Anyone can eavesdrop on network traffic and just steal the key, then read the secret message
Problems with the One Time Pad • A new key needs to be transmitted between the two users each time • Anyone can eavesdrop on network traffic and just steal the key, then read the secret message • The key needs to be truly random, or an attacker can find a pattern
Problems with the One Time Pad • A new key needs to be transmitted between the two users each time • Anyone can eavesdrop on network traffic and just steal the key, then read the secret message • The key needs to be truly random, or an attacker can find a pattern • Currently, random numbers generators are all pseudo-random • That means they are deterministic and can be predicted by an attacker
The Quantum One Time Pad • Both of these problems can be fixed using quantum mechanics!
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