Implication of rh and qc on information security sharad nalawade(author)
1.
Implication of Riemann Hypothesis
and Quantum Computers on
Information Security
Sharad B Nalawade
Author of The Speed of Time
2.
Is Public Key Encryption safe?
• RSA’s PKE uses One-way function/Primes to secure data.
• Prime numbers seem to occur randomly. As of Oct, 2013,
largest prime number is 257,885,161 − 1. It has 17,425,170
digits!
• E-commerce depends on primes to secure data.
• E.g. it is very easy to multiply two primes together, but very
difficult to factorise the product without knowing one of the
primes. (One-way or Trapdoor function)
• We don’t have a mathematical version of the chemical
spectrometer – given a molecule, it shows its atoms. So,
given a complex number, can a formula show its prime
number factors?
3.
Riemann Hypothesis
In 1859 Riemann gave a mathematical function,
called the Riemann zeta function, which calculates
number of primes below a given number.
4.
So, what’s the problem?
• The idea is that if RH is true, then there could be a
possibility of developing an algorithm to factorize a given
complex number into its primes in polynomial time.
• According to RSA paper, there is no method currently
available to do this in the polynomial time.
• Can a proof of the Riemann Hypothesis break our security
systems? A million dollar question!
• Riemann Hypothesis can be solved by using only a midsize Quantum Computer.
• This may spell disaster to RSA algorithm used for
encryption of internet data!
5.
Quantum Computers
• Based on Quantum Physics or Quantum Mechanics
Phenomena – Superposition and Entanglement.
• Quantum computers (QC) use Qubits unlike bits.
• A 30-Qubit QC runs 150 times faster than 2.5 GHx Intel i7
processor.
• A 250-Qubit QC can represent 1075 states simultaneously.
(more than the number of atoms on the visible universe!)
• RSA is no longer safe if QC is built!
• Integer factorization is computationally feasible on QC
using Shor’s algorithm in polynomial time.
8.
Avoiding disaster
• Quantum Key distribution (QKD) based on
Quantum Entanglement principle.
• Eavesdropping leads to quantum de-coherence.
• D-Wave, Microsoft, Google, NASA & many are
investing in QC research.
• The future of information security belongs to the
Quantum computers!
• QKD promises unconditional security to the internet
transactions.
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