Network Security Frank Yeong-Sung Lin Department of Information Management National Taiwan University

1. Network SecurityFrank Yeong-Sung LinDepartment of Information ManagementNational Taiwan University

2. Network Security Network security can be roughly divided into 4 areas: • Secrecy: keep information unrevealed • Authentication: determine the identity of whom you are talking to • Nonrepudiation: make sure that someone cannot deny the things he/she had done • Integrity control: make sure the message you received has not been modified

3. Network Security (cont’d) Network security functionality can be distributed across several protocol layers: • Physical layer: protect transmission link from wire tapping • Data link layer: link encryption • Network layer: firewall, packet filter • Application layer: authentication, nonrepudiation, integrity control, (and secrecy)

4. Traditional Cryptography Passive intruder (listens only) Active intruder (alters message) • The model depends on a stable public algorithm and a key • The work factor for breaking the system by exhaustive search of the key space is exponential in the key length • Two categories: Substitution ciphers vs. transposition ciphers DK( EK( P)) = P Plaintext P EK( P) Encryption Decryption key K key K

5. Traditional Cryptography (cont’d) • Simplified model of traditional cryptography

6. Traditional Cryptography (cont’d) • Model of traditional cryptography

7. Substitution Cipher • Caesar cipher • Every letter is shifted by k positions, e.g., k = 3 and “a” becomes “D”, b becomes “E”, … • For example, “attack” becomes “DWDDFN” • Monoalphabetic substitution Plaintext: abcdefghijklmnopqrstuvwxyz ciphertext: QWERTYUIOPASDFGHJKLZXCVBNM • The key space is 26! » 4x1026 • Still the cipher may be broken easily by taking advantage of the frequency statistics of English text (e.g., e, a, th, er, and, the appear very often)

8. Substitution Cipher (cont’d) • Relative frequency of letters in English text

9. Transposition Ciphers M E G A B U C K 7 4 5 1 2 8 3 6 p l e a s e t r a n s f e r o n e m i l l i o n d o l l a r s t o m y s w i s s b a n k a c c o u n t s i x t w o t w o a b c d • Plaintext is written horizontally, while the ciphertext is read out by column, starting with the lowest key column • To break the transposition cipher • guess a probable word or phrase (e.g., milliondollars) • try to determine the key length, then order the columns Plaintext pleasetransferonemilliondollarsto myswissbankaccountsixtwotwo Ciphertext AFLLSKSOSELAWAIATOOSSCTCLNMOMANT ESILYNTWRNNTSOWDPAEDOBUOERIRICXB

10. Two Fundamental Cryptographic Principles • First principle • All encrypted messages must contain redundancy to prevent active intruders from tricking the receiver into acting on a false message • However, the same redundancy makes it easier for passive intruders to break the system • Second principle • Some measures must be taken to prevent active intruders from playing old messages, e.g., use time stamp to • filter out duplicate messages within a certain time • incoming messages that are too old are discarded

11. Encoder: 8 to 3 Decoder: 3 to 8 S1 S5 S2 S6 P1 P2 P3 S3 S7 S4 S8 Secret-Key Algorithms • Consists of sequence of transpositions and substitutions S-box (Substitution) Product cipher P-box (Permutation)

12. Data Encryption Standard (DES) • Plaintext is encrypted in blocks of 64 bits • DES is basically a monoalphabetic substitution cipher using a 64-bit character 64 bit plaintext Li-1 Ri-1 Initial transposition K1 Iteration 1 56-bit key K16 Li-1 Å f(Ri-1, Ki) Iteration 16 32 bit swap Inverse transposition 32 bits Li 32 bits Ri 64 bit ciphertext

13. DES Chaining • DES may be vulnerable to active intruders Name Bonus Leslie $0000010 Intruder may copy the block to one row above Kimberly $0100000 8 bytes 8 bytes • DES chaining P0 P1 P2 P3 C0 C1 C2 C3 IV # # # # D D D D Exclusive OR Key # # # # E E E E C0 C1 C2 C3 P0 P1 P2 P3

14. Breaking DES • Exhaustive search of key space = 256» 7x1016 • can use multiple computers to do search in parallel • Running DES twice consecutively with two different 56-bit keys creates a key space of 2112» 5x1033 • but it still can be broken by the “meet-in-the-middle” attack in Q (257) time, because Ci = EK2 (EK1 (Pi)) DK2(Ci) = EK1(Pi)

15. Triple DES Encryption • Using EDE (2 encryption and 1 decryption) instead of EEE is for backward compatibility (when K1 = K2) with single-stage DES system • Using EEE with 3 different keys is basically unbreakable nowadays K1 K2 K1 K1 K2 K1 P C C P E D E D E D Encryption Decryption

16. Public-Key Algorithms • Encryption (E) and Decryption (D) algorithms must meet the following requirements • E and D are different • D(E(P)) = P • It is exceedingly difficult to deduce D from E • Everyone has a pair of keys: public key (E) and private key (D) • Public key is made known to the world • Private key is to be kept private all the time A B P1 EB(P1) DB(EB(P1)) = P1 EB DB DA(EA(P2)) = P2 EA(P2) P2 DA EA

17. Principles of Public-Key Cryptosystems

18. Principles of Public-Key Cryptosystems (cont’d) • Requirements for PKC • easy for B (receiver) to generate KUb and KRb • easy for A (sender) to calculate C = EKUb(M) • easy for B to calculate M = DKRb(C) = DKRb(EKUb(M)) • infeasible for an opponent to calculate KRb from KUb • infeasible for an opponent to calculate M from Cand KUb • (useful but not necessary) M = DKRb(EKUb(M)) = EKUb(DKRb(M)) (true for RSA and good for authentication)

19. Principles of Public-Key Cryptosystems (cont’d)

20. Principles of Public-Key Cryptosystems (cont’d) • The idea of PKC was first proposed by Diffie and Hellman in 1976. • Two keys (public and private) are needed. • The difficulty of calculating f-1 is typically facilitated by • factorization of large numbers • resolution of NP-completeness • calculation of discrete logarithms • High complexity confines PKC to key management and signature applications

21. Principles of Public-Key Cryptosystems (cont’d)

22. Principles of Public-Key Cryptosystems (cont’d)

23. Principles of Public-Key Cryptosystems (cont’d) • Comparison between conventional and public-key encryption

24. Principles of Public-Key Cryptosystems (cont’d) • Applications for PKC • encryption/decryption • digital signature • key exchange

25. Principles of Public-Key Cryptosystems (cont’d)

26. Principles of Public-Key Cryptosystems (cont’d)

27. Principles of Public-Key Cryptosystems (cont’d)

28. RSA Algorithms • Developed by Rivest, Shamir, and Adleman at MIT in 1978 • First compute the following parameters • Choose two large primes, p and q (typically > 10100) • Compute n = pxq and z = (p-1)x(q-1) • Choose d, which is a number relatively prime to z • Find e such that (exd) mod z = 1 • Divide the plaintext into blocks of k bits, where 2k < n • To encrypt P, compute C = Pe mod n • To decrypt C, compute P = Cd mod n • Public key = (e, n), private key = (d, n)

29. The RSA Algorithm (cont’d) • Format’s Little Theorem: If p is prime and a is a positive integer not divisible by p, then a p-1 1 mod p. Example: a = 7, p = 19 72 = 49  11 mod 19 74 = 121  7 mod 19 78 = 49  11 mod 19 716 = 121  7 mod 19 a p-1 = 718 = 716+2 711  1 mod 19

30. The RSA Algorithm (cont’d)

31. The RSA Algorithm (cont’d)

32. The RSA Algorithm (cont’d) • Example 1 • Select two prime numbers, p = 7 and q = 17. • Calculate n = p  q = 717 = 119. • Calculate Φ(n) = (p-1)(q-1) = 96. • Select e such that e is relatively prime to Φ(n) = 96 and less than Φ(n); in this case, e = 5. • Determine d such that d  e = 1 mod 96 and d < 96.The correct value is d = 77, because 775 = 385 = 496+1.

33. The RSA Algorithm (cont’d)

34. The RSA Algorithm (cont’d) • The security of RSA • brute force: This involves trying all possible private keys. • mathematical attacks: There are several approaches, all equivalent in effect to factoring the product of two primes. • timing attacks: These depend on the running time of the decryption algorithm.

35. The RSA Algorithm (cont’d) • To avoid brute force attacks, a large key space is required. • To make n difficult to factor • p and q should differ in length by only a few digits (both in the range of 1075 to 10100) • both (p-1) and (q-1) should contain a large prime factor • gcd(p-1,q-1) should be small • should avoid e < n and d < n1/4

36. The RSA Algorithm (cont’d) • To make n difficult to factor (cont’d) • p and q should best be strong primes, where p isa strong prime if • there exist two large primes p1 and p2 such that p1|p-1 and p2|p+1 • there exist four large primes r1, s1, r2 and s2 such that r1|p1-1, s1|p1+1, r2|p2-1 and s2|p2+1 • e should not be too small, e.g. for e = 3 and C = M3 mod n, if M3 < n then M can be easily calculated

37. The RSA Algorithm (cont’d)

38. The RSA Algorithm (cont’d) • Major threats • the continuing increase in computing power (100 or even 1000 MIPS machines are easily available) • continuing refinement of factoring algorithms (from QS to GNFS and to SNFS)

39. The RSA Algorithm (cont’d)

40. The RSA Algorithm (cont’d)

41. RSA Algorithms (cont’d) • The security of RSA is based on the difficulty of factoring large numbers • It takes 4x109 years for factoring a 200-digit number • It takes 1025 years for factoring a 500-digit number • RSA is too slow to actually encrypt large volumes of data, so it is primarily used for distributions of one-time session key for use with DES algorithms

42. The RSA Algorithm (cont’d)

43. Key Management • The distribution of public keys • public announcement • publicly available directory • public-key authority • public-key certificates • The use of public-key encryption to distribute secret keys • simple secret key distribution • secret key distribution with confidentiality and authentication

44. Key Management (cont’d) • Public announcement

45. Key Management (cont’d) • Public announcement (cont’d) • advantages: convenience • disadvantages: forgery of such a public announcement by anyone

46. Key Management (cont’d) • Publicly available directory

47. Key Management (cont’d) • Publicly available directory (cont’d) • elements of the scheme • {name, public key} entry for each participant in the directory • in-person or secure registration • on-demand entry update • periodic publication of the directory • availability of secure electronic access from the directory to participants • advantages: greater degree of security

48. Key Management (cont’d) • Publicly available directory (cont’d) • disadvantages • need of a trusted entity or organization • need of additional security mechanism from the directory authority to participants • vulnerability of the private key of the directory authority (global-scaled disaster if the private key of the directory authority is compromised) • vulnerability of the directory records

49. Key Management (cont’d) • Public-key authority

50. Key Management (cont’d) • Public-key authority (cont’d) • stronger security for public-key distribution can be achieved by providing tighter control over the distribution of public keys from the directory • each participant can verify the identity of the authority • participants can verify identities of each other • disadvantages • bottleneck effect of the public-key authority • vulnerability of the directory records