# Pakistan, quantum computing and cryptography

Abdullah Khalid

Quantum Information Scientist

The Second Floor

3rd October 2019

1788

1700s

1950s

1940s

## Electronic Computers

Total world computing capacity

2 x 1020 – 1.5 x 1021 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
• Rational sieve
• General number field sieve
• Shanks's square forms factorization

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

Key: 10101011101...

Security ∝ number of digits

Recommended key size: 4096 bits

(for security till 2030)

# Quantum Computers

1600 onwards

## Quantum Physics

1900 onwards

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

## 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 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

# 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

\$5000-50,000

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

1. Invest in quantum computing and cryptography research.

2. Build quantum cryptography infrastructure.

3. Invest in policy research.

4. Participate in international encryption standards committees.

#### Pakistan, quantum computing and cryptography

By abdullahkhalids

• 1,471