# Pakistan, quantum computing and cryptography

Abdullah Khalid

Quantum Information Scientist

The Second Floor

3rd October 2019

## (Human) Computer

1788

1700s

1950s

## Mechanical Computer

1940s

## Electronic Computers

Total world computing capacity

2 x 10^{20} – 1.5 x 10^{21} FLOPS

## Computational Problems

### Multiplication

Input: integers P and Q

Output: integer R = P x Q

Algorithms

## Computational Problems

### Factorization

Input: integer R

Ouput: prime numbers P and Q

such that R = P x Q

Algorithms

R = 21

digits = 2

R = 498556150811

digits = 12

- Dixon's algorithm
- Continued fraction factorization
- Quadratic sieve
- Rational sieve
- General number field sieve
- Shanks's square forms factorization

## Computational Problems

Multiplication

Factorization

# Cryptography

"Top secret info"

"Top secret info"

"hf72h18v82ja9"

You

You

Military

Bank

Email provider

Military

# RSA encryption protocol

Encryption/Decryption = Multiplication

Cracking = Factorization

Rivest–Shamir–Adleman

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

## Cracking RSA

# Quantum Computers

## Classical Physics

1600 onwards

## Quantum Physics

1900 onwards

Newton Faraday

Einstein

Heisenberg

Born

Schrodinger

"The underlying **physical laws ... of physics and the whole of chemistry** are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much **too complicated to be soluble**." 1929

# Computational Problem

Simulating atoms, molecules and materials

Paul Dirac

# Birth of Quantum Computers

Simulating atoms, molecules and materials

### "Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy." Richard Feynman, 1982

## Quantum Computers: The transport analogy

Human computer

Super computer

Quantitative

Qualitative

Quantum computer

Computational problem: Go from A to B

# Visions of Quantum Computing

Simulating atoms, molecules and materials

Simulate this

By controlled experiments on this

# Quantum Computing Today

### Quantum computers CANNOT

~~do industrial optimization~~

predict the stock market

optimize airline schedules

predict the stock market

optimize airline schedules

~~NP-Complete problems~~

### exponentially faster than classical computers.

### Quantum computers can

## simulate atoms, molecules and materials,

### exponentially faster than classical computers.

### Quantum computers can

## maybe do machine learning and optimization

### exponentially faster than classical computers.

### Quantum computers can

## break all currently used asymmetric encryption protocols

### exponentially faster than classical computers.

## Quantum Computer

Breaking encryption on Quantum Computer

Text

NP-Complete Problems on Classical Computer

NP-Complete Problems on Quantum Computer

Breaking encryption on Classical Computer

arXiv:1909.07353

## Cryptographic Algorithms in Use

# How do we prepare for the a world where Quantum Computers exist?

## First Option: Post-Quantum Crypto Algorithms

arXiv:1909.07353

No proofs of security, but hope!

## Second Option: Quantum Key Distribution

Secret key: 1011101111010...

## Second Option: Quantum Key Distribution

Provably secure against quantum computers

## Second Option: Quantum Key Distribution

$5000-50,000

## What should Pakistan do to prepare for the quantum computing future?

- Invest in quantum computing and cryptography research.

- Build quantum cryptography infrastructure.

- Invest in policy research.

- Participate in international encryption standards committees.

#### Pakistan, quantum computing and cryptography

By abdullahkhalids