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 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
  • 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

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?

  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

Pakistan, quantum computing and cryptography

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