Quantum computers attack

Copyright © 2014 Oracle and/or its affiliates. All rights reserved. |Copyright © 2014 Oracle and/or its affiliates. All rights reserved. |
Quantum computers attack
Branislav Majerník
@oracle.com
18.5.2015 Oracle Security day Bratislava

Copyright © 2014 Oracle and/or its affiliates. All rights reserved. |
Topics
Cryptography today
Introduction to Quantum computing today
Post quantum cryptography
Q & A
1
2
3
4

Cryptography today
RSA, 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(2n
)
O(1)
O(n log n)
O(log n)
O(n2
)
O(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, AB
Private key, ab
A=aP
B=bP
Message from B2A
M= aB = abP = bA =
baP
D
L

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

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