1. Opracowanie językowe dr inż. J. Jarnicki
Internet Engineering
Czesław Smutnicki
Discrete Mathematics – Cryptography

2. CONTENTS DES algorithm Triple-DES algorithm RSA algorithm
MD5 algorithm
CRC algorithm
ssh service

3. SECURITY IN COMPUTER NETWORKS
Cryptography
Algorithms with symmetrical keys
Algorithms with public (non-symmetrical) keys
Digital signature
Management of public keys
Security of communications
Trustworthiness protocols
Security of
Security of www
Social aspects of computer networks

4. CRYPTOGRAPHY
Introduction: encryption = transformation (bit-after-bit, character-after-character), coding = replacing, open text, algorithm, key, encrypted text, intruder, cryptoanalysis, cryptology
Substituting ciphers
Transposition ciphers
Once-used keys (XOR of data and key)
Quantized cryptography: phaeton, polarisation, strigth linear basis, diagonal basis, qubit, once-used key
Fundamental rules of cryptography: redundancy, timeliness

5. ALGORITHMS WITH SYMMETRICAL KEYS
P-box, S-box, cascade
DES
Triple DES
AES
Encryption modes: coding book, linking of coding blocks, feedback, streaming code, counting method
Other coding: IDEA, RC4, RC5, Rijndael, Serpent, Twofish
Cryptoanalysis: differential, linear

6. ALGORITHM WITH SYMMETRICAL KEYS
P-box: 8 lines
S-box: 3 lines
Aggregate (cascade): 12 lines S1 S5 S9 S2 S6
S10 P1 P2 P3 P4 S3 S7
S11
Decoder 8->3 S4 S8
S12
Decoder 3->8
P-box
permutation=key
cascade: lines, >18 stages (hardware),
>8 (software), 1 stage=iteration=P+S

7. DES = DATA ENCRYPTION STANDARD
open text 64 bits
L 32 bits (i-1)
P 32 bits (i-1)
starting transposition
iteration 1
Key 56 bits
iteration 2 .
L(i) XOR f(P(i-1),K(i))
iteration 16
transposition of 32-bit halves
final transposition
inverse to starting
encrypted data 64 bits
L 32 bits (i)
P 32 bits (i)

8. DES cont. L 32 bits (i-1) P 32 bits (i-1) 32 bits
32 bits -> 48 bits
indirect key
XOR K
S-box: in 8 x 6
L(i) XOR f(P(i-1),K(i)) S1 S2 S3 S4 S5 S6 S7 S8
S-box: out 8 x 4
P-box
indirect key has been obtained by certain transformation of
fundamental key of 56 bits.
Applied is so-called whitening operation (additional
random keys)
L 32 bits (i)
P 32 bits (i)

9. TRIPLE DES
2 keys
encryption(K1)-decryption(K2)-encryption(K1)

10. AES= ADAVANCED ENCRYPTION STANDARD
Competition
Symmetrical key
Public project
Keys 128, 192, 256-bits
Easily implementable (hardware, software)
Free-access licence
Rijndael (86), Serpent (59), Twofish (31), RC6 (23), MARS (13)

11. ALGORYITHM WITH PUBLIC KEYS: RSA
Choose two prime numbers p i q
Find n=p*q and z=(p-1)*(q-1)
Find any d relatively prime with z
Find any number e such that (e*d) mod z=1
Public key (e,n)
Private key (d,n)
Encryption of message P decryption of hiden text C

12. DIGITAL SIGNATURE
Receiver can verify the authentity of Sender signature
Sender cannot renege of sending the message with this contents
Receiver cannot change the obtained message contents
Signature based on symmetric keys (certification institution)
Signature based on public keys (secret key theft, changing of secret key)
Message shortcut (hashing): MD5, SHA-1,

13. MANAGEMENT OF PUBLIC KEYS
Certificates
Standard X.509
Infrastructure of public keys: confidence chain, certfication track, confidence anchors, certificate cancel,

14. SECURITY OF COMMUNICATION
IPsec: transport mode, tunel mode, trafic analysis
Firewalls, packet filter, application gateway, DoS attack, DDoS
Private virtual networks
Security in wireless networks: WEP (RC4), Bluetooth (SAFER+)

15. TRUSTWORTHINESS PROTOCOLS
Trustworthiness on the base of shared secret key
Setting shared secret key: key exchange
Trustworthiness with the use of key distribution center
Trustworthiness based on Kerberos
Trustworthiness with the use of public keys

16. SECURITY OF
PGP
PEM
S/MIME

17. SECURITY OF WWW
Emergences
Secure names
SSL
Security of movable code

18. SOCIAL ASPECTS OF COMPUTER NETWORKS
Privacy protection policy
Freedom of a word
Intelectual property rigths

19. Thank you for your attention
DISCRETE MATHEMATICS
Czesław Smutnicki