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

Network Security Network security can be roughly divided into 4 areas: • Secrecy: keep 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

Network Security (cont’d) Network security functionality can be distributed across several protocol layers: • 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)

Traditional Cryptography Passive intruder (listens only) Plaintext P Encryption key K Active intruder (alters Traditional Cryptography Passive intruder (listens only) Plaintext P Encryption key K Active intruder (alters message) EK( P) DK( EK( P)) = P Decryption key K • 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

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

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

Substitution Cipher • Caesar cipher – Every letter is shifted by k positions, e. 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: ciphertext: abcdefghijklmnopqrstuvwxyz QWERTYUIOPASDFGHJKLZXCVBNM – The key space is 26! » 4 x 1026 – 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)

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

Transposition Ciphers M 7 p a e d o b u o E 4 Transposition Ciphers M 7 p a e d o b u o E 4 l n m o m a n t G 5 e s i l y n t w A 1 a f l l s k s o B 2 s e l a w a i a U 8 e r i c x b C 3 t o o s s c t c K 6 r n n t s o w d Plaintext pleasetransferonemilliondollarsto myswissbankaccountsixtwotwo Ciphertext AFLLSKSOSELAWAIATOOSSCTCLNMOMANT ESILYNTWRNNTSOWDPAEDOBUOERIRICXB • 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

Two Fundamental Cryptographic Principles • First principle – All encrypted messages must contain redundancy 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

Secret-Key Algorithms P-box (Permutation) Encoder: 8 to 3 Decoder: 3 to 8 • Consists Secret-Key Algorithms P-box (Permutation) Encoder: 8 to 3 Decoder: 3 to 8 • Consists of sequence of transpositions and S-box (Substitution) substitutions S 1 P 1 S 2 S 6 Product cipher S 5 S 3 S 4 P 2 S 7 S 8 P 3

Data Encryption Standard (DES) • Plaintext is encrypted in blocks of 64 bits • 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 56 -bit key Initial transposition K 1 Iteration 1 K 16 Iteration 16 Li-1 Å f(Ri-1, Ki) 32 bit swap Inverse transposition 64 bit ciphertext 32 bits Li 32 bits Ri

DES Chaining • DES may be vulnerable to active intruders Name Bonus Leslie $0000010 DES Chaining • DES may be vulnerable to active intruders Name Bonus Leslie $0000010 Kimberly $0100000 8 bytes Intruder may copy the block to one row above 8 bytes • DES chaining P 0 P 1 P 2 P 3 C 0 C 1 C 2 C 3 IV # # D D # # P 0 P 1 P 2 P 3 Key E E C 0 C 1 C 2 C 3 Exclusive OR

Breaking DES • Exhaustive search of key space = 256 » 7 x 1016 Breaking DES • Exhaustive search of key space = 256 » 7 x 1016 – 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 » 5 x 1033 – but it still can be broken by the “meet-in-the-middle” attack in Q (257) time, because Ci = EK 2 (EK 1 (Pi)) DK 2(Ci) = EK 1(Pi)

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

Public-Key Algorithms • Encryption (E) and Decryption (D) algorithms must meet the following requirements 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 P 1 EB(P 1) EB DB DA(EA(P 2)) = P 2 DA EA(P 2) EA DB(EB(P 1)) = P 1 P 2

Principles of Public-Key Cryptosystems Principles of Public-Key Cryptosystems

Principles of Public-Key Cryptosystems (cont’d) • Requirements for PKC – – – easy for 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 C and KUb (useful but not necessary) M = DKRb(EKUb(M)) = EKUb(DKRb(M)) (true for RSA and good for authentication)

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

Principles of Public-Key Cryptosystems (cont’d) • The idea of PKC was first proposed by 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

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

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

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

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

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

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

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

RSA Algorithms • Developed by Rivest, Shamir, and Adleman at MIT in 1978 • 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 2 k < 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)

The RSA Algorithm (cont’d) • Format’s Little Theorem: If p is prime and a 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

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

The RSA Algorithm (cont’d) • Example 1 – – Select two prime numbers, p 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.

The RSA Algorithm (cont’d) • The RSA Algorithm (cont’d) •

The RSA Algorithm (cont’d) • The security of RSA – brute force: This involves 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.

The RSA Algorithm (cont’d) • To avoid brute force attacks, a large key space 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 < n 1/4

The RSA Algorithm (cont’d) • To make n difficult to factor (cont’d) – p The RSA Algorithm (cont’d) • To make n difficult to factor (cont’d) – p and q should best be strong primes, where p is a strong prime if • there exist two large primes p 1 and p 2 such that p 1|p-1 and p 2|p+1 • there exist four large primes r 1, s 1, r 2 and s 2 such that r 1|p 11, s 1|p 1+1, r 2|p 2 -1 and s 2|p 2+1 – e should not be too small, e. g. for e = 3 and C = M 3 mod n, if M 3 < n then M can be easily calculated

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

The RSA Algorithm (cont’d) • Major threats – the continuing increase in computing power 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)

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

RSA Algorithms (cont’d) • The security of RSA is based on the difficulty of RSA Algorithms (cont’d) • The security of RSA is based on the difficulty of factoring large numbers – It takes 4 x 109 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

The RSA Algorithm (cont’d) The RSA Algorithm (cont’d)

Key Management • The distribution of public keys – – public announcement publicly available 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

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

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

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

Key Management (cont’d) • Publicly available directory (cont’d) – elements of the scheme • 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

Key Management (cont’d) • Publicly available directory (cont’d) – disadvantages • need of a 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 (globalscaled disaster if the private key of the directory authority is compromised) • vulnerability of the directory records

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

Key Management (cont’d) • Public-key authority (cont’d) – stronger security for public-key distribution can 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

Key Management (cont’d) • Public-key certificates Key Management (cont’d) • Public-key certificates

Key Management (cont’d) • Public-key certificates (cont’d) – to use certificates that can be Key Management (cont’d) • Public-key certificates (cont’d) – to use certificates that can be used by participants to exchange keys without contacting a public-key authority – requirements on the scheme • any participant can read a certificate to determine the name and public key of the certificate’s owner • any participant can verify that the certificate originated from the certificate authority and is not counterfeit • only the certificate authority can create & update certificates • any participant can verify the currency of the certificate

Key Management (cont’d) • Public-key certificates (cont’d) – advantages • to use certificates that Key Management (cont’d) • Public-key certificates (cont’d) – advantages • to use certificates that can be used by participants to exchange keys without contacting a public-key authority • in a way that is as reliable as if the key were obtained directly from a public-key authority • no on-line bottleneck effect – disadvantages: need of a certificate authority

Key Management (cont’d) • Simple secret key distribution Key Management (cont’d) • Simple secret key distribution

Key Management (cont’d) • Simple secret key distribution (cont’d) – advantages • simplicity • Key Management (cont’d) • Simple secret key distribution (cont’d) – advantages • simplicity • no keys stored before and after the communication • security against eavesdropping – disadvantages • lack of authentication mechanism between participants • vulnerability to an active attack (opponent active only in the process of obtaining Ks) • leak of the secret key upon such active attacks

Key Management (cont’d) • Secret key distribution with confidentiality and authentication Key Management (cont’d) • Secret key distribution with confidentiality and authentication

Key Management (cont’d) • Secret key distribution with confidentiality and authentication (cont’d) – provides Key Management (cont’d) • Secret key distribution with confidentiality and authentication (cont’d) – provides protection against both active and passive attacks – ensures both confidentiality and authentication in the exchange of a secret key – public keys should be obtained a priori – more complicated

Diffie-Hellman Key Exchange • First public-key algorithm published • Limited to key exchange • Diffie-Hellman Key Exchange • First public-key algorithm published • Limited to key exchange • Dependent for its effectiveness on the difficulty of computing discrete logarithm

Diffie-Hellman Key Exchange (cont’d) • Diffie-Hellman key exchange – n, g: large prime number Diffie-Hellman Key Exchange (cont’d) • Diffie-Hellman key exchange – n, g: large prime number with additional conditions • n and g may be made public 1 n, g, gx mod n 2 gy mod n Bob Alice computes (gy mod n)x = gxy mod n Alice – x, y: large (say, 512 -bit) numbers – gxy mod n = the secret key – it is very difficult to find x given gx mod n Bob computes (gx mod n)y = gxy mod n

Diffie-Hellman Key Exchange (cont’d) • Define a primitive root of of a prime number Diffie-Hellman Key Exchange (cont’d) • Define a primitive root of of a prime number p as one whose powers generate all the integers from 1 to p-1. • If a is a primitive root of the prime number p, then the numbers a mod p, a 2 mod p, …, ap-1 mod p are distinct and consists of the integers from 1 to p-1 in some permutation. • Not every number has a primitive root.

Diffie-Hellman Key Exchange (cont’d) • For any integer b and a primitive root a Diffie-Hellman Key Exchange (cont’d) • For any integer b and a primitive root a of prime number p, one can find a unique exponent i such that b = ai mod p, where 0 i (p-1). • The exponent is referred to as the discrete algorithm, or index, of b for the base a, mod p. • This value is denoted as inda, p(b).

Diffie-Hellman Key Exchange (cont’d) Diffie-Hellman Key Exchange (cont’d)

Diffie-Hellman Key Exchange (cont’d) • Example: q = 97 and a primitive root a Diffie-Hellman Key Exchange (cont’d) • Example: q = 97 and a primitive root a = 5 is selected. XA = 36 and XB = 58 (both 97). YA = 536 = 50 mod 97 and YB = 558 = 44 mod 97. K = (YB) X mod 97 = 4436 mod 97 = 75 mod 97. K = (YA) X mod 97 = 5058 mod 97 = 75 mod 97. 75 cannot easily be computed by the opponent. A B

Diffie-Hellman Key Exchange (cont’d) • How the algorithm works Diffie-Hellman Key Exchange (cont’d) • How the algorithm works

Diffie-Hellman Key Exchange (cont’d) Diffie-Hellman Key Exchange (cont’d)

Diffie-Hellman Key Exchange (cont’d) • q, a, YA and YB are public. • To Diffie-Hellman Key Exchange (cont’d) • q, a, YA and YB are public. • To attack the secrete key of user B, the opponent must compute XB = inda, q(YB). [YB = a. X mod q. ] • The effectiveness of this algorithm therefore depends on the difficulty of solving discrete logarithm. B

Attack on Diffie-Hellman Key Exchange • Bucket brigade attack Alice picks x 1 Trudy Attack on Diffie-Hellman Key Exchange • Bucket brigade attack Alice picks x 1 Trudy picks z Bob picks y n, g, gx mod n gy mod n Bob Trudy Alice gz mod n n, g, gz mod n 4 3 2 – (gxz mod n) becomes the secret key between Alice and Trudy, while (gyz mod n) becomes the secret key between Trudy and Bob

Authentication Protocols • Authorization – verifies what a process is permitted to do • Authentication Protocols • Authorization – verifies what a process is permitted to do • Authentication – verifies the identity of the process that you are talking to – public and private keys are used for authentication, and for establishing the session key (a secret key) – all data communicated is then encrypted using secret key cryptography

Authentication Based on a Shared Secret Key • Challenge-response protocol Alice KAB = shared Authentication Based on a Shared Secret Key • Challenge-response protocol Alice KAB = shared secret key between Alice and Bob 2 3 4 5 After step 5, Alice verifies Bob’s identity 6 A RB KAB(RB) RA KAB(RA) KAB(KS) Challenge Response Session key if needed Bob 1 After step 3, Bob verifies Alice’s identity

Authentication Based on a Shared Secret Key (cont’d) • Can we reduce the number Authentication Based on a Shared Secret Key (cont’d) • Can we reduce the number of messages exchanged, e. g. , 2 3 A, RA RB, KAB(RA) KAB(RB) Challenge Response/ Challenge Bob Alice 1 Response – Only three, instead of five, messages are exchanged

Authentication Based on a Shared Secret Key (cont’d) • The shortened protocol can be Authentication Based on a Shared Secret Key (cont’d) • The shortened protocol can be defeated by a reflection attack Trudy 2 3 4 5 A, RT First session RB, KAB(RT) A, RB Bob 1 Second session RB 2, KAB(RB) First session

Authentication Using a Key Distribution Center A, KA(B, KS) 2 KB(A, KS) Bob 1 Authentication Using a Key Distribution Center A, KA(B, KS) 2 KB(A, KS) Bob 1 KDC Alice • Need a trusted Key Distribution Center (KDC) • Wide-mouth frog: simplest KDC authentication protocol • Replay attack – an intruder can just replay message 2 (and any following messages) to Bob later, and Bob has no way to tell if it is a second connection from Alice

Authentication Using Public-Key • Assume both sides already know each other’s public keys – Authentication Using Public-Key • Assume both sides already know each other’s public keys – This is not a trivial assumption as explained previously 2 3 EB(A, RA) EA(RA, RB, KS) Ks(RB) Bob Alice verified Bob’s identity Alice 1 Bob verified Alice’s identity

Digital Signatures • What is needed is a system by which one party can Digital Signatures • What is needed is a system by which one party can send a “signed” message to another party such that – The receiver can verify the claimed identity of the sender – The sender cannot later repudiate the contents of the message – The receiver cannot possibly have concocted the message itself

Secret-Key Signatures KB(A, RA, t, P, KBB(A, t, P)) Bob A, KA(B, RA, t, Secret-Key Signatures KB(A, RA, t, P, KBB(A, t, P)) Bob A, KA(B, RA, t, P) BB Alice • Assumes a central authority, say Big Brother (BB), that knows everyone’s secret key • Bob has KBB(A, t, P), which is proof that Alice sent message P at time t • To guard against replaying attack – A message is discarded if its timestamp is too old – For a recent message, it is discarded if RA is duplicate

Public-Key Signatures • Assumes both D(E(P)) = P and E(D(P)) = P (RSA algorithm Public-Key Signatures • Assumes both D(E(P)) = P and E(D(P)) = P (RSA algorithm has such property) Alice’s computer P Alice’s private key DA DA(P) Bob’s public key EB EB(DA(P)) Bob’s computer Transmission line Bob’s private key DB DA(P) Alice’s public key EA P • Bob has P and DA(P), which is proof that Alice sent P

Message Digests • It is often desirable to send signed plaintext documents because encrypting Message Digests • It is often desirable to send signed plaintext documents because encrypting the complete document may take too much time • Message Digest (MD): hash plaintext to a fixed-length bit string such that – Given P, it is easy to compute MD(P) – Given MD(P), it is effectively impossible to find P – No one can generate two messages that have the same message digest m bits P MD(P)

Message Digests (cont’d) P, DA(MD(P)) Bob Alice • Public-key message digest • Most widely Message Digests (cont’d) P, DA(MD(P)) Bob Alice • Public-key message digest • Most widely used message digest functions – MD 5 – SHA (Secure Hash Algorithm) • An m-bit MD system may be possibly broken in Q (2 m/2) time (referred as birthday attack in text)