Lecture: SS 2002 Introduction to cryptography

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Lecture SS 2002Introduction to cryptography

• Dr. Tsuyoshi Takagi
• Darmstadt University of Technology
• Department of Computer Science
• Research group of Prof. J. Buchmann

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Lecture Plan
I will explain the content of the book J.
Buchmann, Introduction to cryptography,
Springer, 1998.

• Introduction
• Mathematic basics
• Encryption schemes
• Perfect secret
• DES or AES
• Public-key encryption
• Hash function
• Digital signatures

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Attacks to an e-mail system
Company B
Company A
(1) Confidentiality. - Attacker can
eavesdrop the contract. (2) Authentication.
- Attacker can send a different contract to
company B. (3) Integrity. - Attacker can
modify the contract (100 Euro to 1000 Euro).
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attacker
eavesdropping
Sender
Receiver
Pretending
Altering/Forgery
attacker
attacker
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Security Techniques

• Encryption
• - Symmetric Cryptosystem (Secret-Key
  Cryptosystem)
• - Asymmetric Cryptosystem (Public-Key
  Cryptosystem)
• Signature
• - Symmetry (Message Authentication Code)
• - Asymmetry (Digital Signature)

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Symmetric cryptosystem
d a common secret key between the user
and the bank Ed encryption function, Ed-1
decryption function, m Ed-1(Ed(m))
Receiver
Sender
m message
Encryption using d
Ed(m) cipher text
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Public-key cryptosystem
(e public key , d secret key ) of
the receiver (Bank) Ee encryption function, Dd
decryption function, m Dd(Ee(m))
Receiver
Sender
m message
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Advantage of PKC

• The number of secret keys is reduced

n is the number of users.
SKC
PKC
n
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No common key is required
From Thomas.Koenig_at_ciw.uni-karlsruhe.de Newsgroup
s comp.security.unix,comp.security.misc,sci.crypt
,comp.answers,sci.ans wers,news.answers Subject
SSH (Secure Shell) FAQ - Frequently Asked
Questions Followup-To comp.security.unix,comp.sec
urity.misc Date Mon, 27 May 1996 112305
JST Organization University of Karlsruhe,
Germany -----BEGIN PGP
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Disadvantage of PKC

• The speed of encryption/decryption is slow
  compared with symmetric cryptosystems
• - The arithmetic of PKC is complicated.
• - A special coprocessor is required for the
  implementation over smartcards.

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Efficiency is important
For the sake of high security, a secret key is
stored on a smart card (tamper-resistant).
A special coprocessor is required for the
computation on a smart card, which is very
expensive.
Currently no public-key cryptosystems are used
for a large scale market, such as cash cards or
SIM cards for mobile phones
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Examples of encryption schemes

• Symmetric cryptosystem
• - 3DES, IDEA, AES, etc.
• Asymmetric cryptosystem
• - RSA, Elliptic Curve Cryptosystem, etc.

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Message Authentication Code
(d a common secret key ) of signer and
verifier Sd signing function, Vd verification
function, Vd(m) Sd(m)
Verifier
Signer
m message
m message
Signing using d
Verification using d
Sd(m) hash value
Vd (m)Sd(m)
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Digital Signature
(e public key , d secret key ) of a
signer Sd signing function, Vs verification
function, m Vs(Sd(m))
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Examples of Signature Schemes

• Message Authentication Code
• - hash functions MD5, SHA, etc.
• Digital Signature
• - RSA, DSA, Elliptic Curve Cryptosystem, etc.

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Typical Usage

• A common secret key is shared by PKC.
• Data is encrypted by symmetric cryptosystem.
• Digital signature is used for integrity.

PKC
Data
Data
Symmetric cryptosystem
Digital Signature
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Internet Banking (Web-Zugang)
Internet banking client
Internet banking server
PIN (1205)
PIN
PIN (1205)

• Confidentiality
• - Attacker can eavesdrop the PIN and data.
• (2) User Authentication
• - If the attacker knows the PIN, she/he
  can pretend to be the user.

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SSL (Secure Sockets Layer)
Which algorithms are used?
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Secure E-Mail
Secure IP Network
PGP
Secure Payment
IPv6
Mobile Network
S/MIME
SET
i-mode
IPSEC
WAP
iKP
SSL
TSL
Secure Devices
Digital Signature
Public-Key Cryptosystem
NF
RSA
Lattice
Factoring
EC