Quantum information processing and cryptography

Laboratory of Quantum Information Processing and Communication concentrates on the
research and advising students of all levels in the area of quantum
information processing and communication as well as classical and quantum
cryptography.

There are three main goals of the research in this area that is one of the
hottest and most important area in informatics and also physics.

1. To discover laws, limitations and methods of using very specific resources
of the quantum world for the development of faster than classical algorithms
and protocols.

2. To develop new quantum information processing and communication technology and new
cryptography protocols that make clever use of inherently quantum phenomena in order to
get better than classical performance. To find also limitations of such
approaches.

3. To get better, information processing based, understanding of
quantum physics phenomena.

4. To develop new protocols for quantum and classical cryptography and their
analysis.

In order to achieve these goals a variety of special activities are performed.

1. A weekly quantum seminar is run on which members of the laboratory and guest
from other countries present their new results.

2. A special lecture is held to inform about hot topics and new direction/results in the
area of quantum information processing.

3. An annual workshop, CEQIP (Central European Quantum Information Processing, starting
with 2004) is held where, in addition to members of the laboratory,
about 40 researchers from abroad participate.

4. The quantum information processing group plays also leading role in annual
Asia Quantum Information Science conference held in Japan, China, Korea and
India.

The laboratory has very close cooperation contacts with groups in Bratislava,
Vienna, Lisbon, Tokyo, Seoul, and several groups in India as well in Singapore, Poland
and Hungary.

During the last 10 years members of the laboratory gave more than 200 talks
all over the world.

Internationally the area of quantum information processing is well supported and
excellent PhD students have a variety of options for postdoctoral positions.

Though the target of the research in quantum information processing
bridges informatics and physics, many specific research subjects require easy
to learn quantum physics.

Concerning quantum information processing, basic knowledge can be obtained
in the course IA066 (for detailed slides see http://www.fi.muni.cz/usr/gruska/quantum10f ). See also book J. Gruska: Quantum
computing, McGraw-Hill, 1999

Concerning basics of classical cryptography see the course IV054 (for detailed slides see
http://www.fi.muni.cz/usr/gruska/crypto10 and cryptographic seminar
(IV055)

5.10 Matej Pivoluska - Encryption with Weakly Random Keys Using Quantum Ciphertext

Weakly Random Keys Using Quantum Ciphertext

Matej Pivoluska, FI MUNI


Lack of perfect randomness can cause significant problems

in securing communication between two parties. McInnes and Pinkas

proved that unconditionally secure encryption is impossible when

the key is sampled from a weak random source. The adversary

can always gain some information about the plaintext,

regardless of the cryptosystem design.

Most notably, adversary can obtain full information

about the plaintext if only two bits of the source are

fixed (if the key is sampled from a distribution on n-bits,

for which the probability of each element is bounded from above by

1/(2^(n-2)).

In this paper we show that for every weak random

source there is a cryptosystem with a classical plaintext,

a classical key, and a quantum ciphertext that bounds the

adversary's probability to guess correctly the plaintext

strictly under the McInnes-Pinkas bound, except for a

single case, where it coincides with the bound. In

addition, regardless of the source of randomness, the

adversary's probability p is strictly smaller than 1 as

long as there is some uncertainty in the key

(Shannon/min-entropy is non-zero). These results

demonstrate that quantum information processing can solve

cryptographic tasks with strictly higher security than

classical information processing.