Quantum computers attack

Branislav Majerník@oracle.com

18.5.2015 Oracle Security day Bratislava

TopicsCryptography today

Introduction to Quantum computing today

Post quantum cryptography

Cryptography todayRSA, ElGamal, Elliptic curves systems, Lattice systems

Based on hard to compute problems(polynomial vs. exponential)

(N-1)!/2O(n) O(2n)

Search telephone number in DB

Traveling salesman problem

Hard to compute (polynomial vs. exponential)

n (amount of data)

Number of

Operations

O(n log n)

O(log n)

Hard to compute (sub)exponential IFP problem

Hard to compute (sub)exponential DLP problem

Is IFP and DLP same?

Given a group G, a subgroup H ≤ G, and a set X, we say a function f : G → X hides the subgroup H if for all g1, g2 G, f(g1) = f(g2) if and only if g1H = g2H for the cosets of H. Equivalently, the function f is constant on the ∈cosets of H, while it is different between the different cosets of H.Hidden subgroup problem: Let G be a group, X a finite set, and f : G → X a function that hides a subgroup H ≤ G. The function f is given via an oracle, which uses O(log |G|+log|X|) bits. Using information gained from evaluations of f via its oracle, determine a generating set for H.A special case is when X is a group and f is a group homomorphism in which case H corresponds to the kernel of f.

Both problems are special cases of the hidden subgroup problem over an abelian group.

http://www.eecs.berkeley.edu/Pubs/TechRpts/1984/CSD-84-186.pdf

Eric Bach: Discrete logarithms and factoring

ECDLP ? Hard to compute exponential

Public key, ABPrivate key, abA=aPB=bP

Message from B2AM= aB = abP = bA = baP

http://www.design-reuse.com/articles/7409/ecc-holds-key-to-next-gen-cryptography.html

Underlying mathematical problem & run times of public-key systems

http://www.design-reuse.com/articles/7409/ecc-holds-key-to-next-gen-cryptography.html

Public-key sizes with equivalent security levels

Why Oracle ? :)

http://theory.stanford.edu/~dfreeman/cs259c-f11/finalpapers/CDHandDLP.pdf

Oracle cryptographics engine ECDH (SunEC)

Introduction to QC today

Future of computers (physical limits)

0,1 nm a0 is size of atom, QM rules

Exponential problems become polynomial

Quantum computing

Realization of Qubit – single electron transistor

University of New South Wales (UNSW)

Realization of Qubit – photon with semiconductor quantum dots

Joint Quantum Institute

Realization of Qubit - superconducting

IFN-CNR, Rome

Realization of Qubit – superconducting, quantum annealing???

http://www.wired.com/2013/06/d-wave-quantum-computer-usc/

Realization of Qubits – problems: decoherence, noise errors

Realization of Qubits – Topological QC

Possible representations of Qubits – summary

Abelian hidden subgroup problem ( IFP, DLP...) solution

1. Transform problem to problem find a period of function – can be done on classical computer

Shor's algorithm

Abelian hidden subgroup problem ( IFP, DLP...) solution

2. Find period with quantum Fourier transformation - can be done on quantum computer

Shor's algorithm

Information set discovery problem (database search, inversion function, McEliece cryptography) solution

Via iteration find the eigenvalues = 1 for projection s to ω, f(ω) = 1

http://cr.yp.to/codes/grovercode-20091123.pdf

Grover's algorithm

Quantum cryptography

Secure distribution of secret key BB84 protocol

Private amplification

Secure distribution of secret key E91 protocol

Post scriptum

Quantum computers attack

Documents

Transcript of Quantum computers attack

Programming Quantum Computers (Modules)

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