QUANTUM COMPUTER IN CRYPTOGRAPHY

AKSHAY MAHADEO SHELAKE(T.Y.B.SC–COMP. SCI.)

Introduction • What is Quantum Computer?• The History of Quantum Computing • What is Cryptography ?• What are used todays Cryptography technology?• Computer Security Organizations and Quantum Computing

What is Quantum Computer ?• A quantum computer is a machine that performs

calculations based on the laws of quantum mechanics, which is the behavior of particles at the sub-atomic level.

The History of Quantum Computing

The idea of a quantum computer began in the early 1980s and was conceived by • Paul Benioff • Charles Bennett• David Deutsch• Richard Feynman • Yuri Manin

classical computers VS quantum computersThe essence of the difference between

classical computers and quantum computersis in the way information is stored and processed.

In classical computers, information is represented on macroscopic level by bits, which can take one of the two values

0 or 1

In quantum computers, information is represented on microscopic level using qubits, (quantum bits) which can take on any from the following uncountable many values

a | 0 ń + b | 1 ńwhere a, b are arbitrary complex numbers such that

| a | 2 + | b | 2 = 1.

Figure 3: Two-slit experiment

Figure 4: Two-slit experiment with an observation

Figure 1: Experiment with bullets

Figure 2: Experiments with waves

Classical Experiments VS Quantum Experiments

a,b G , ak = b , find k

Discrete logarithms (basis of DH crypto, including ECC):

Integer Factorization (basis of RSA cryptography):

Given N=pq, find p and q.

Quantum Algorithms

Computational Complexity Comparison

(in terms of number of group multiplications for n-bit inputs)

Scaling of number field sieve (NFS) on classical computers and Shor’s algorithm for factoring on a quantum computer, using Beckman-Chari-Devabhaktuni-Preskill modular exponentiation with various clock rates. Both horizontal and vertical axes are log scale. The horizontal axis is the size of the number being factored (Van Meter, Itoh, & Ladd, 2005).

What is Cryptography ?Transmitting information with access restricted to the intended recipient even if the message is intercepted by others.

Cryptography is of increasing importance in our technological age using broadcast, network communications, Internet ,e-mail, cell phones which may transmit sensitive information related to finances, politics, business and private confidential matters

CLASSICAL versus QUANTUM CRYPTOGRAPHY

Security of classical cryptography is based on unproven assumptions of computational complexity (and it can be jeopardize by progress in algorithms and/or technology). Security of quantum cryptography is based on laws of quantum physics that allow to build systems where undetectable eavesdropping is impossibleSince classical cryptography is volnurable to technological improvements it has to be designed in such a way that a secret is secure with respect to future technology, during the whole period in which the secrecy is required.Quantum key generation, on the other hand, needs to be designed only to be secure against technology available at the moment of key generation.

public-key Cryptography• Encryption of data for many IT systems today relies on public-

key cryptography. The concept of public-key cryptography was introduced by Whitfield Diffie and Martin Hellman in 1976

• This new method of encryption had two main purposes, encryption and digital signatures. It entails that each person (or communicating system) gets a pair of keys, one was dubbed the public key and the other was named the private key.

• The public key is shared between the two parties and is used for identifying the end-user while the private key remains a secret and is never transmitted. Encrypted information is sent using the public key to identify the source but only a receiver that possesses the private key is able to decode the message. Unfortunately, the private key, while kept a secret from prying eyes, is linked to the public key through a mathematical algorithm

Company's developing QKD System

• In 2002 - Swiss company called id Quantique

• In 2003 -American company called MagiQ Technologies

Methods of Cryptography in Quantum Computer

Cryptographers are discussing alternatives to today’s methods and have agreed that there are four major candidates that would provide immunity from a quantum computer attack. The four possible replacement methods include: - error-correcting codes - hash-functions- lattice cryptography systems- multivariate public-key cryptography system

Commercial quantum key distribution products exist

Current State of Affairs

Current fiber-based distance record: 200 km (Takesue et al)

Current State of Affairs

Demonstrated free-space link: 10 km

Current State of Affairs

CONCLUSIONQuantum cryptography ensure secure communication by providing security based on the fundamental law of physics, intend of the current state of mathematical algorithms or computing technology unlike classical encryption algorithm quantum cryptography does not depend factoring large integers into primes but on the fundamental principles of quantum physics. Quantum cryptography is more secure, because an intruder is not able to replicate the photon to recreate the key.Integrating QKD in TLS protocol will ensure financial transaction. Instead of using RSA, in TLS protocol .We can use Quantum Cryptography securely exchange the secret data and avoid an attack of intruder

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