Audun Jøsang

42 Pages·2017·1.73 MB·English

by  Audun Jøsang

Post-Quantum Crypto Challenges
Prof. Audun Jøsang
Universitetet i Oslo
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Audun Jøsang - 2018 PQ Crypto Challenges 2
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Audun Jøsang - 2018 PQ Crypto Challenges 3
Principle for Quantum Computing
• Quantum Computing (QC) uses quantum superpositions
instead of binary bits to perform computations.
• Quantum algorithms, i.e. algorithms for quantum computers,
can solve certain problems much faster than classical
algorithms.
Audun Jøsang - 2018 PQ Crypto Challenges 4
Quantum Computers
Audun Jøsang - 2018 PQ Crypto Challenges 5
QC Threat to Traditional Cryptography
• Shor’s Quantum Algorithm (1994) can factor integers and
compute discrete logarithms efficiently. It has also been
extended to the crack ECC. Together, these attacks would be
devastating to traditional public key crypto algorithms.
• Grover’s Quantum Search Algorithm (1996) can be used to
brute-force search for a k-bit secret key with an effort of only
2k = 2k/2
which effectively doubles the required key sizes for ciphers.
• QC has been dismissed by most cryptographers until recent
years. General purpose quantum computers do not currently
exist, but are expected to be built in foreseeable future.
Audun Jøsang - 2018 PQ Crypto Challenges 6
Cryptographic Security Services
Symmetric
Confidentiality
encryption
Authentcity / Integrity
Hash-
functions
Non-repudiation
PKI / key distribution
Asymmetric
T
encryption & Confidentiality
digital signature
(Traditional)
Quantum Threat
Audun Jøsang - 2018 PQ Crypto Challenges 7
Cryptographic Security Services
Symmetric
Confidentiality
encryption
Authentcity / Integrity
Hash-
functions
Non-repudiation
PKI / key distribution
Asymmetric
PQ
encryption & Confidentiality
digital signature
(Post-Quantum)
PKIs can survive
Audun Jøsang - 2018 PQ Crypto Challenges 8
Non-repudiation only possible with PKI
The MAC was made
with the secret key,
Shared
so I know that Alice
Alice secret key Bob
sent the message.
But you have the
Symmetric
same secret key,
authentication
so maybe you
sent the message.
MAC
Private key The message was
Pulic key
Alice Bob signed by Alice,
so I know that she
sent the message.
Non-repudiatable
authentication
You are right, only
Alice could have
Digital signature
signed the message.
Audun Jøsang - 2018 PQ Crypto Challenges 9
SKI (Symmetric Key Infrastructure)
as alternative to PKI
Root-CA Master-node
PKI SKI
2 3
Sub-CA Sub-node
1 4
Direct Client
nodes
A B 1 C A B 5 C
Indirect
CA certificate
Pre-distributed shared secret keys
Forklaring:
Send encrypted secret session key
Shared secret session key
Audun Jøsang - 2018 PQ Crypto Challenges 10