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Ch03-Computer Security

Attaporn Ninsuwan
Attaporn Ninsuwan

The document discusses various cryptographic techniques including symmetric and asymmetric encryption. Symmetric encryption uses the same key for encryption and decryption, while asymmetric encryption uses two different keys. The document then describes the Data Encryption Standard (DES) algorithm and its variants, including Triple DES. It also covers the Advanced Encryption Standard (AES) algorithm, its design principles, and modes of operation for block ciphers like ECB, CBC, CFB and OFB.

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1 241-427-SV-2-2553-COE-PSU 1 241-427 Computer Security Chapter III: Cryptography Dr. Sangsuree Vasupongayya 241-427-SV-2-2553-COE-PSU 2 Cryptography mechanisms Symmetric-key encryption Same key for encrypt and decrypt Based on transformations Asymmetric-key encryption Two keys One for encrypt One for decrypt Based on mathematical functions 241-427-SV-2-2553-COE-PSU 3 Symmetric-key cipher Encryption: C = Ek(P) Decryption: P = Dk(C) Where Dk(Ek(x)) = Ek(Dk(x)) = x Bob and Alice will need another channel, a secured one, to exchange the secret key. 241-427-SV-2-2553-COE-PSU 4 Symmetric Encryption Same key used to encrypt and decrypt E(k) can be derived from D(k), and vice versa DES is most commonly used symmetric block- encryption algorithm (created by US Govt) Encrypts a block of data at a time Triple-DES considered more secure Advanced Encryption Standard (AES), twofish up and coming RC4 is most common symmetric stream cipher, but known to have vulnerabilities Encrypts/decrypts a stream of bytes (i.e wireless transmission) Key is a input to psuedo-random-bit generator Generates an infinite keystream 241-427-SV-2-2553-COE-PSU 5 Substitution-Permutation Ciphers Claude Shannon introduced idea of substitution- permutation (S-P) networks in 1949 paper form basis of modern block ciphers S-P nets are based on the two primitive cryptographic operations seen before: substitution (S-box) permutation (P-box) provide confusion & diffusion of message & key 241-427-SV-2-2553-COE-PSU 6 Confusion and Diffusion cipher needs to completely obscure statistical properties of original message a one-time pad does this more practically Shannon suggested combining S & P elements to obtain: diffusion – dissipates statistical structure of plaintext over bulk of ciphertext confusion – makes relationship between ciphertext and key as complex as possible
2 241-427-SV-2-2553-COE-PSU 7 Data Encryption Standard (DES) most widely used block cipher in world adopted in 1977 by NBS (now NIST) as FIPS PUB 46 encrypts 64-bit data using 56-bit key has widespread use has been considerable controversy over its security 241-427-SV-2-2553-COE-PSU 8 DES overview 241-427-SV-2-2553-COE-PSU 9 DES structure 241-427-SV-2-2553-COE-PSU 10 Initial and Final Permutations The initial and final permutations are straight P- boxes that are inverses of each other. They have no cryptography significance in DES. 241-427-SV-2-2553-COE-PSU 11 Initial and Final Permutations The initial and final permutations are straight P- boxes that are inverses of each other. They have no cryptography significance in DES. 241-427-SV-2-2553-COE-PSU 12 Rounds DES uses 16 rounds. Each round of DES is a Feistel cipher.
3 241-427-SV-2-2553-COE-PSU 13 DES function Applies a 48-bit key to the rightmost 32 bits (Ri-1) to produce a 32-bit output. Found sections: An expansion P-box, A whitener (need key), A group of S-boxes, A straight P-box 241-427-SV-2-2553-COE-PSU 14 Expansion P-box Expand 32-bit data to 48-bit data using P-box 241-427-SV-2-2553-COE-PSU 15 S-Boxes Do the real mixing (confusion) 241-427-SV-2-2553-COE-PSU 16 Straight Permutation Straight permutation with a 32-bit input and a 32- bit output 241-427-SV-2-2553-COE-PSU 17 241-427-SV-2-2553-COE-PSU 18 Key generation Create sixteen 48- bit keys out of a 56-bit cipher key.
4 241-427-SV-2-2553-COE-PSU 19 Parity-bit drop table Drop bit 8,16,24,32,40,48,56 & 64 241-427-SV-2-2553-COE-PSU 20 Shift left (circular shift) Round 1, 2, 9 and 16 shift 1 bit; other rounds shift 2 bits 241-427-SV-2-2553-COE-PSU 21 Compression Permutation Changes 56-bit to 48-bit, which are used as a key for a round. 241-427-SV-2-2553-COE-PSU 22 DES analysis Avalanche effect: a small change in the plaintext (or key) should create a significant change in the ciphertext. Completeness effect: each bit of the ciphertext needs to depend on many bits on the plaintext. A brute-force attack on DES is feasible with available technology and the possibility of parallel processing. 241-427-SV-2-2553-COE-PSU 23 Variants of DES Double DES (2DES) Use DES twice instead of 1 DES Vulnerable to a known-plain text attack Triple DES (3DES) the middle stage use reverse cipher With 2 keys (DES1 & DES3 use the same key) With 3 keys (e.g., PGP) 241-427-SV-2-2553-COE-PSU 24 Double-DES? could use 2 DES encrypts on each block C = EK2(EK1(P)) issue of reduction to single stage and have “meet-in-the-middle” attack works whenever use a cipher twice since X = EK1(P) = DK2(C) attack by encrypting P with all keys and store then decrypt C with keys and match X value can show takes O(256) steps
5 241-427-SV-2-2553-COE-PSU 25 Triple-DES with Two-Keys hence must use 3 encryptions would seem to need 3 distinct keys but can use 2 keys with E-D-E sequence C = EK1(DK2(EK1(P))) nb encrypt & decrypt equivalent in security if K1=K2 then can work with single DES standardized in ANSI X9.17 & ISO8732 no current known practical attacks 241-427-SV-2-2553-COE-PSU 26 Triple-DES with Two-Keys 241-427-SV-2-2553-COE-PSU 27 Triple-DES with Three-Keys although are no practical attacks on two-key Triple- DES have some indications can use Triple-DES with Three-Keys to avoid even these C = EK3(DK2(EK1(P))) has been adopted by some Internet applications, eg PGP, S/MIME 241-427-SV-2-2553-COE-PSU 28 designed by Rijment-Daemen in Belgium has 128/192/256 bit keys, 128 bit data designed to be: resistant against known attacks speed and code compactness on many CPUs design simplicity Basic Algebraic structures Groups Rings Fields Advanced Encryption Standard (AES) 241-427-SV-2-2553-COE-PSU 29 General Design of AES 241-427-SV-2-2553-COE-PSU 30 Data Units Bit: a binary digit with a value of 0 or 1 Byte: a group of 8 bits can be A row matrix (1x8), insert a bit from left to right A column matrix (8x1), insert a bit from top Word: a group of 32 bits can be A row matrix of 4 bytes A column matrix of 4 bytes Block: a group of 128 bits or a row matrix of 16 bytes
6 241-427-SV-2-2553-COE-PSU 31 Structure of round in AES 241-427-SV-2-2553-COE-PSU 32 Byte Substitution (ByteSub) a simple substitution of each byte uses one table of 16x16 bytes containing a permutation of all 256 8-bit values each byte of state is replaced by byte indexed by row (left 4-bits) & column (right 4-bits) eg. byte {95} is replaced by byte in row 9 column 5 which has value {2A} S-box constructed using defined transformation of values in GF(28) designed to be resistant to all known attacks 241-427-SV-2-2553-COE-PSU 33 Byte Substitution 241-427-SV-2-2553-COE-PSU 34 Shift Rows a circular byte shift in each row 1st row is unchanged 2nd row does 1 byte circular shift to left 3rd row does 2 byte circular shift to left 4th row does 3 byte circular shift to left decrypt inverts using shifts to right since state is processed by columns, this step permutes bytes between the columns 241-427-SV-2-2553-COE-PSU 35 Shift Rows 241-427-SV-2-2553-COE-PSU 36 Mix Columns each column is processed separately each byte is replaced by a value dependent on all 4 bytes in the column effectively a matrix multiplication in GF(28) using prime poly m(x) =x8+x4+x3+x+1
7 241-427-SV-2-2553-COE-PSU 37 Mix Columns 241-427-SV-2-2553-COE-PSU 38 Mix Columns can express each col as 4 equations to derive each new byte in col decryption requires use of inverse matrix with larger coefficients, hence a little harder have an alternate characterisation each column a 4-term polynomial with coefficients in GF(28) and polynomials multiplied modulo (x4+1) 241-427-SV-2-2553-COE-PSU 39 Add Round Key XOR state with 128-bits of the round key again processed by column (though effectively a series of byte operations) inverse for decryption identical since XOR own inverse, with reversed keys designed to be as simple as possible a form of Vernam cipher on expanded key requires other stages for complexity / security 241-427-SV-2-2553-COE-PSU 40 Add Round Key 241-427-SV-2-2553-COE-PSU 41 AES Round 241-427-SV-2-2553-COE-PSU 42 AES Key Expansion takes 128-bit (16-byte) key and expands into array of 44/52/60 32-bit words start by copying key into first 4 words then loop creating words that depend on values in previous & 4 places back in 3 of 4 cases just XOR these together 1st word in 4 has rotate + S-box + XOR round constant on previous, before XOR 4th back designed to resist known attacks
8 241-427-SV-2-2553-COE-PSU 43 AES Key Expansion 241-427-SV-2-2553-COE-PSU 44 Key Expansion Rationale design criteria included knowing part key insufficient to find many more invertible transformation fast on wide range of CPU’s use round constants to break symmetry diffuse key bits into round keys enough non-linearity to hinder analysis simplicity of description 241-427-SV-2-2553-COE-PSU 45 AES Decryption AES decryption is not identical to encryption since steps done in reverse but can define an equivalent inverse cipher with steps as for encryption but using inverses of each step with a different key schedule works since result is unchanged when swap byte substitution & shift rows swap mix columns & add (tweaked) round key 241-427-SV-2-2553-COE-PSU 46 Cipher and inverse cipher 241-427-SV-2-2553-COE-PSU 47 Implementation Aspects can efficiently implement on 8-bit CPU byte substitution works on bytes using a table of 256 entries shift rows is simple byte shift add round key works on byte XOR’s mix columns requires matrix multiply in GF(28) which works on byte values, can be simplified to use table lookups & byte XOR’s 241-427-SV-2-2553-COE-PSU 48 Implementation Aspects can efficiently implement on 32-bit CPU redefine steps to use 32-bit words can precompute 4 tables of 256-words then each column in each round can be computed using 4 table lookups + 4 XORs at a cost of 4Kb to store tables designers believe this very efficient implementation was a key factor in its selection as the AES cipher
9 241-427-SV-2-2553-COE-PSU 49 Modes of Operation block ciphers encrypt fixed size blocks eg. DES encrypts 64-bit blocks with 56-bit key need some way to en/decrypt arbitrary amounts of data in practise ANSI X3.106-1983 Modes of Use (now FIPS 81) defines 4 possible modes subsequently 5 defined for AES & DES have block and stream modes 241-427-SV-2-2553-COE-PSU 50 Electronic Codebook Book (ECB) message is broken into independent blocks which are encrypted each block is a value which is substituted, like a codebook, hence name each block is encoded independently of the other blocks Ci = DESK1(Pi) uses: secure transmission of single values 241-427-SV-2-2553-COE-PSU 51 Electronic Codebook Book (ECB) 241-427-SV-2-2553-COE-PSU 52 ECB Advantages & Limitations message repetitions may show in ciphertext if aligned with message block particularly with data such graphics or with messages that change very little, which become a code-book analysis problem weakness is due to the encrypted message blocks being independent main use is sending a few blocks of data 241-427-SV-2-2553-COE-PSU 53 Cipher Block Chaining (CBC) message is broken into blocks linked together in encryption operation each previous cipher blocks is chained with current plaintext block, hence name use Initial Vector (IV) to start process Ci = DESK1(Pi XOR Ci-1) C-1 = IV uses: bulk data encryption, authentication 241-427-SV-2-2553-COE-PSU 54 Cipher Block Chaining (CBC)
10 241-427-SV-2-2553-COE-PSU 55 Advantages and Limitations of CBC a ciphertext block depends on all blocks before it any change to a block affects all following ciphertext blocks need Initialization Vector (IV) which must be known to sender & receiver if sent in clear, attacker can change bits of first block, and change IV to compensate hence IV must either be a fixed value (as in EFTPOS) or must be sent encrypted in ECB mode before rest of message 241-427-SV-2-2553-COE-PSU 56 Cipher FeedBack (CFB) Size of the block in AES or DES is n Size of the plaintext is r; r <= n Encrypt or decrypt the contents of a shift register, S, of size n Encryption XOR r-bit plaintext w/ r-bits of the shift register 241-427-SV-2-2553-COE-PSU 57 Cipher FeedBack (CFB) 241-427-SV-2-2553-COE-PSU 58 CFB Advantages & Limitations appropriate when data arrives in bits/bytes most common stream mode limitation is need to stall while do block encryption after every n-bits note that the block cipher is used in encryption mode at both ends errors propogate for several blocks after the error 241-427-SV-2-2553-COE-PSU 59 Output FeedBack (OFB) Similar to CFB Each bit in the ciphertext is independent of the previous bit or bits 241-427-SV-2-2553-COE-PSU 60 Advantages and Limitations of OFB bit errors do not propagate more vulnerable to message stream modification a variation of a Vernam cipher hence must never reuse the same sequence (key+IV) sender & receiver must remain in sync originally specified with m-bit feedback subsequent research has shown that only full block feedback (ie CFB-64 or CFB-128) should ever be used
11 241-427-SV-2-2553-COE-PSU 61 Counter (CTR) similar to OFB but encrypts counter value rather than any feedback value must have a different key & counter value for every plaintext block (never reused) 241-427-SV-2-2553-COE-PSU 62 Advantages and Limitations of CTR efficiency can do parallel encryptions in h/w or s/w can preprocess in advance of need good for bursty high speed links random access to encrypted data blocks provable security (good as other modes) but must ensure never reuse key/counter values, otherwise could break (cf OFB) 241-427-SV-2-2553-COE-PSU 63 Asymmetric-key cryptosystem 241-427-SV-2-2553-COE-PSU 64 Conceptual differences slowfast numbers are manipulated (mathematical function) symbols are permuted or substituted only n personal secrets(n-1)n/2 shared secrets The secret is not sharedThe secret is shared asymmetricsymmetric 241-427-SV-2-2553-COE-PSU 65 General idea 241-427-SV-2-2553-COE-PSU 66 General idea (cont.) Bob must create two keys; distribute to others Eve should not be able to advertise her public key pretending to be Bob’s key Each key pair can be used for one-way communication Bob only needs one private key to receive message from anyone Bob needs n public keys to talk to n people (one for each person) The plaintext and ciphertext are treated as integers C = f(Kpublic, P) while P = g(Kprivate, C) And f must be a trapdoor one-way function
12 241-427-SV-2-2553-COE-PSU 67 Trapdoor one-way function One-way function f is easy given x compute y = f(x) is easy f-1 is difficult given y, it is computationally infeasible to calculate x = f-1(y) Trapdoor one-way function A one-way function that given y and a trapdoor (secret), x can be easily computed E.g., y = xk mod n when n is large 241-427-SV-2-2553-COE-PSU 68 y = xk mod n Given x, k and n, it is easy to calculate y Square-and multiply method Given y, k and n, it is very difficult to compute x Discrete logarithm problem However if a trapdoor k’ such that k’ • k = 1 mod Ф(n) is known x can be easily calculated by x = yk’ mod n This is used in RSA 241-427-SV-2-2553-COE-PSU 69 RSA cryptosystem Named for its inventors (Rivest, Shamir, Adleman) 241-427-SV-2-2553-COE-PSU 70 RSA: key generation Recommended size n should be at least 1024 bits e and d should be at least 512 bits Key generation 1. Select two large prime p and q 2. n ← p • q 3. Ф(n) = (p-1)(q-1) 4. Select e such that 1 < e < Ф(n) and gcd(e, Ф(n)) = 1 5. d ← e-1 mod Ф(n) {e,n} is the public key {d,n} is the private key 241-427-SV-2-2553-COE-PSU 71 Exponentiation can use the Square and Multiply Algorithm a fast, efficient algorithm for exponentiation concept is based on repeatedly squaring base and multiplying in the ones that are needed to compute the result look at binary representation of exponent only takes O(log2 n) multiples for number n eg. 75 mod 11 = 10 241-427-SV-2-2553-COE-PSU 72 square-and-multiply Square-and-multiply (x, k, n) y ← 1 for i=0 to nb-1 if(ki = 1) y ← x • y mod n x ← x2 mod n return y Where nb is the number of bits in k
13 241-427-SV-2-2553-COE-PSU 73 RSA Example - Key Setup 1. Select primes: p=17 & q=11 2. Compute n = pq =17 x 11=187 3. Compute ø(n)=(p–1)(q-1)=16 x 10=160 4. Select e: gcd(e,160)=1; choose e=7 5. Determine d: de=1 mod 160 and d < 160 Value is d=23 since 23x7=161= 10x160+1 6. Publish public key PU={7,187} 7. Keep secret private key PR={23,187} 241-427-SV-2-2553-COE-PSU 74 Attacking RSA possible approaches: brute force key search (infeasible given size of numbers) mathematical attacks (based on difficulty of computing ø(n), by factoring modulus n) timing attacks (on running of decryption) chosen ciphertext attacks (given properties of RSA) If the ciphertext is a permutation of the plaintext Continuous encryption of the ciphertext will eventually results in the plaintext 241-427-SV-2-2553-COE-PSU 75 Man-in-the-middle Attack 241-427-SV-2-2553-COE-PSU 76 Symmetric-key distribution How to distribute and maintain secret keys Two approach Use a trusted third party Use no third party 241-427-SV-2-2553-COE-PSU 77 Use a trusted third party Key-distribution center (KDC) Each user has a shared secret key wit the KDC Problems Not scale Bottleneck problem 241-427-SV-2-2553-COE-PSU 78 Example of KDC approach
14 241-427-SV-2-2553-COE-PSU 79 No third party Diffie-Hellman key agreement 241-427-SV-2-2553-COE-PSU 80 Diffie-Hellman Initial: choose two number p and g p: a large prime number > 300 decimal digits 1024 bits g: an integer < p such that foe every number n between 1 to p-1, there is a power k of g such that n = gk mod p Idea Key is gxy mod p where one party knows x and the other knows y Problems Discrete logarithm attack Man-in-the-middle attack 241-427-SV-2-2553-COE-PSU 81 Man-in-the-middle-attack 241-427-SV-2-2553-COE-PSU 82 Public-key distribution Public announcement simple and easy Subject to forgery Anyone can pretend to be anyone The key can be switched during the communication 241-427-SV-2-2553-COE-PSU 83 Public-key distribution (cont.) Trusted center: keep information of public key and dynamically updated the information Each user must prove his/her identity The user’s public key is kept at the trusted center 241-427-SV-2-2553-COE-PSU 84 Public-key distribution (cont.) Controlled trusted center
15 241-427-SV-2-2553-COE-PSU 85 Public-key distribution (cont.) Both trusted center models Create heavy load on the trusted center Objectives A person wants people to know his public-key Wants no one to accept a forged key as his Solutions Certification authority (CA): a federal or state organization that binds a public key to an entity and issues a certificate The CA checks Bob’s identity The CA issue the certificate by signing Bob’s public key using the center private key 241-427-SV-2-2553-COE-PSU 86 Certification authority 241-427-SV-2-2553-COE-PSU 87 Public-Key Infrastructures (PKI) A model for creating, distributing and revoking certificates based on the X.509 Duties Certificates’ issuing, renewal and revocation Keys’ storage and update: store members’ private keys and update these keys on members’ demands Providing services to other protocols e.g., IPSec, TLS Providing access control different access levels 241-427-SV-2-2553-COE-PSU 88 PKI: trust model Reason: not possible to have a single CA Q1: how user1 can trust user3? Q2: how user1 can trust user4? 241-427-SV-2-2553-COE-PSU 89 X.509 the Internationally accepted standard for how to construct a public key certificate used by S/MIME secure email, SSL/TLS secure Internet links (e.g., for secure web) 241-427-SV-2-2553-COE-PSU 90 X.509 Certificates
16 241-427-SV-2-2553-COE-PSU 91 X.509 Certificates issued by a Certification Authority (CA), containing: version (1, 2, or 3) serial number (unique within CA) identifying certificate signature algorithm identifier issuer X.500 name (CA) period of validity (from - to dates) subject X.500 name (name of owner) subject public-key info (algorithm, parameters, key) issuer unique identifier (v2+) subject unique identifier (v2+) extension fields (v3) signature (of hash of all fields in certificate) notation CA<<A>> : certificate for A signed by CA 241-427-SV-2-2553-COE-PSU 92 X.509: certificate revocation Reasons Compromised key The CA is no longer willing to certify the user The CA private key is compromised Actions: Issue a certificate revocation list (CRL) Before using any certificate, the user must check this list 241-427-SV-2-2553-COE-PSU 93 References W. Stallings, Cryptography and Network Security, 3rd ed. B.A. Forouzan, Cryptograhpy and Network Security, McGraw-Hill, 2008. A.Kahate, Cryptography and network Security, McGraw-Hill, 2003.

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Ch03-Computer Security

  • 1. 1 241-427-SV-2-2553-COE-PSU 1 241-427 Computer Security Chapter III: Cryptography Dr. Sangsuree Vasupongayya 241-427-SV-2-2553-COE-PSU 2 Cryptography mechanisms Symmetric-key encryption Same key for encrypt and decrypt Based on transformations Asymmetric-key encryption Two keys One for encrypt One for decrypt Based on mathematical functions 241-427-SV-2-2553-COE-PSU 3 Symmetric-key cipher Encryption: C = Ek(P) Decryption: P = Dk(C) Where Dk(Ek(x)) = Ek(Dk(x)) = x Bob and Alice will need another channel, a secured one, to exchange the secret key. 241-427-SV-2-2553-COE-PSU 4 Symmetric Encryption Same key used to encrypt and decrypt E(k) can be derived from D(k), and vice versa DES is most commonly used symmetric block- encryption algorithm (created by US Govt) Encrypts a block of data at a time Triple-DES considered more secure Advanced Encryption Standard (AES), twofish up and coming RC4 is most common symmetric stream cipher, but known to have vulnerabilities Encrypts/decrypts a stream of bytes (i.e wireless transmission) Key is a input to psuedo-random-bit generator Generates an infinite keystream 241-427-SV-2-2553-COE-PSU 5 Substitution-Permutation Ciphers Claude Shannon introduced idea of substitution- permutation (S-P) networks in 1949 paper form basis of modern block ciphers S-P nets are based on the two primitive cryptographic operations seen before: substitution (S-box) permutation (P-box) provide confusion & diffusion of message & key 241-427-SV-2-2553-COE-PSU 6 Confusion and Diffusion cipher needs to completely obscure statistical properties of original message a one-time pad does this more practically Shannon suggested combining S & P elements to obtain: diffusion – dissipates statistical structure of plaintext over bulk of ciphertext confusion – makes relationship between ciphertext and key as complex as possible
  • 2. 2 241-427-SV-2-2553-COE-PSU 7 Data Encryption Standard (DES) most widely used block cipher in world adopted in 1977 by NBS (now NIST) as FIPS PUB 46 encrypts 64-bit data using 56-bit key has widespread use has been considerable controversy over its security 241-427-SV-2-2553-COE-PSU 8 DES overview 241-427-SV-2-2553-COE-PSU 9 DES structure 241-427-SV-2-2553-COE-PSU 10 Initial and Final Permutations The initial and final permutations are straight P- boxes that are inverses of each other. They have no cryptography significance in DES. 241-427-SV-2-2553-COE-PSU 11 Initial and Final Permutations The initial and final permutations are straight P- boxes that are inverses of each other. They have no cryptography significance in DES. 241-427-SV-2-2553-COE-PSU 12 Rounds DES uses 16 rounds. Each round of DES is a Feistel cipher.
  • 3. 3 241-427-SV-2-2553-COE-PSU 13 DES function Applies a 48-bit key to the rightmost 32 bits (Ri-1) to produce a 32-bit output. Found sections: An expansion P-box, A whitener (need key), A group of S-boxes, A straight P-box 241-427-SV-2-2553-COE-PSU 14 Expansion P-box Expand 32-bit data to 48-bit data using P-box 241-427-SV-2-2553-COE-PSU 15 S-Boxes Do the real mixing (confusion) 241-427-SV-2-2553-COE-PSU 16 Straight Permutation Straight permutation with a 32-bit input and a 32- bit output 241-427-SV-2-2553-COE-PSU 17 241-427-SV-2-2553-COE-PSU 18 Key generation Create sixteen 48- bit keys out of a 56-bit cipher key.
  • 4. 4 241-427-SV-2-2553-COE-PSU 19 Parity-bit drop table Drop bit 8,16,24,32,40,48,56 & 64 241-427-SV-2-2553-COE-PSU 20 Shift left (circular shift) Round 1, 2, 9 and 16 shift 1 bit; other rounds shift 2 bits 241-427-SV-2-2553-COE-PSU 21 Compression Permutation Changes 56-bit to 48-bit, which are used as a key for a round. 241-427-SV-2-2553-COE-PSU 22 DES analysis Avalanche effect: a small change in the plaintext (or key) should create a significant change in the ciphertext. Completeness effect: each bit of the ciphertext needs to depend on many bits on the plaintext. A brute-force attack on DES is feasible with available technology and the possibility of parallel processing. 241-427-SV-2-2553-COE-PSU 23 Variants of DES Double DES (2DES) Use DES twice instead of 1 DES Vulnerable to a known-plain text attack Triple DES (3DES) the middle stage use reverse cipher With 2 keys (DES1 & DES3 use the same key) With 3 keys (e.g., PGP) 241-427-SV-2-2553-COE-PSU 24 Double-DES? could use 2 DES encrypts on each block C = EK2(EK1(P)) issue of reduction to single stage and have “meet-in-the-middle” attack works whenever use a cipher twice since X = EK1(P) = DK2(C) attack by encrypting P with all keys and store then decrypt C with keys and match X value can show takes O(256) steps
  • 5. 5 241-427-SV-2-2553-COE-PSU 25 Triple-DES with Two-Keys hence must use 3 encryptions would seem to need 3 distinct keys but can use 2 keys with E-D-E sequence C = EK1(DK2(EK1(P))) nb encrypt & decrypt equivalent in security if K1=K2 then can work with single DES standardized in ANSI X9.17 & ISO8732 no current known practical attacks 241-427-SV-2-2553-COE-PSU 26 Triple-DES with Two-Keys 241-427-SV-2-2553-COE-PSU 27 Triple-DES with Three-Keys although are no practical attacks on two-key Triple- DES have some indications can use Triple-DES with Three-Keys to avoid even these C = EK3(DK2(EK1(P))) has been adopted by some Internet applications, eg PGP, S/MIME 241-427-SV-2-2553-COE-PSU 28 designed by Rijment-Daemen in Belgium has 128/192/256 bit keys, 128 bit data designed to be: resistant against known attacks speed and code compactness on many CPUs design simplicity Basic Algebraic structures Groups Rings Fields Advanced Encryption Standard (AES) 241-427-SV-2-2553-COE-PSU 29 General Design of AES 241-427-SV-2-2553-COE-PSU 30 Data Units Bit: a binary digit with a value of 0 or 1 Byte: a group of 8 bits can be A row matrix (1x8), insert a bit from left to right A column matrix (8x1), insert a bit from top Word: a group of 32 bits can be A row matrix of 4 bytes A column matrix of 4 bytes Block: a group of 128 bits or a row matrix of 16 bytes
  • 6. 6 241-427-SV-2-2553-COE-PSU 31 Structure of round in AES 241-427-SV-2-2553-COE-PSU 32 Byte Substitution (ByteSub) a simple substitution of each byte uses one table of 16x16 bytes containing a permutation of all 256 8-bit values each byte of state is replaced by byte indexed by row (left 4-bits) & column (right 4-bits) eg. byte {95} is replaced by byte in row 9 column 5 which has value {2A} S-box constructed using defined transformation of values in GF(28) designed to be resistant to all known attacks 241-427-SV-2-2553-COE-PSU 33 Byte Substitution 241-427-SV-2-2553-COE-PSU 34 Shift Rows a circular byte shift in each row 1st row is unchanged 2nd row does 1 byte circular shift to left 3rd row does 2 byte circular shift to left 4th row does 3 byte circular shift to left decrypt inverts using shifts to right since state is processed by columns, this step permutes bytes between the columns 241-427-SV-2-2553-COE-PSU 35 Shift Rows 241-427-SV-2-2553-COE-PSU 36 Mix Columns each column is processed separately each byte is replaced by a value dependent on all 4 bytes in the column effectively a matrix multiplication in GF(28) using prime poly m(x) =x8+x4+x3+x+1
  • 7. 7 241-427-SV-2-2553-COE-PSU 37 Mix Columns 241-427-SV-2-2553-COE-PSU 38 Mix Columns can express each col as 4 equations to derive each new byte in col decryption requires use of inverse matrix with larger coefficients, hence a little harder have an alternate characterisation each column a 4-term polynomial with coefficients in GF(28) and polynomials multiplied modulo (x4+1) 241-427-SV-2-2553-COE-PSU 39 Add Round Key XOR state with 128-bits of the round key again processed by column (though effectively a series of byte operations) inverse for decryption identical since XOR own inverse, with reversed keys designed to be as simple as possible a form of Vernam cipher on expanded key requires other stages for complexity / security 241-427-SV-2-2553-COE-PSU 40 Add Round Key 241-427-SV-2-2553-COE-PSU 41 AES Round 241-427-SV-2-2553-COE-PSU 42 AES Key Expansion takes 128-bit (16-byte) key and expands into array of 44/52/60 32-bit words start by copying key into first 4 words then loop creating words that depend on values in previous & 4 places back in 3 of 4 cases just XOR these together 1st word in 4 has rotate + S-box + XOR round constant on previous, before XOR 4th back designed to resist known attacks
  • 8. 8 241-427-SV-2-2553-COE-PSU 43 AES Key Expansion 241-427-SV-2-2553-COE-PSU 44 Key Expansion Rationale design criteria included knowing part key insufficient to find many more invertible transformation fast on wide range of CPU’s use round constants to break symmetry diffuse key bits into round keys enough non-linearity to hinder analysis simplicity of description 241-427-SV-2-2553-COE-PSU 45 AES Decryption AES decryption is not identical to encryption since steps done in reverse but can define an equivalent inverse cipher with steps as for encryption but using inverses of each step with a different key schedule works since result is unchanged when swap byte substitution & shift rows swap mix columns & add (tweaked) round key 241-427-SV-2-2553-COE-PSU 46 Cipher and inverse cipher 241-427-SV-2-2553-COE-PSU 47 Implementation Aspects can efficiently implement on 8-bit CPU byte substitution works on bytes using a table of 256 entries shift rows is simple byte shift add round key works on byte XOR’s mix columns requires matrix multiply in GF(28) which works on byte values, can be simplified to use table lookups & byte XOR’s 241-427-SV-2-2553-COE-PSU 48 Implementation Aspects can efficiently implement on 32-bit CPU redefine steps to use 32-bit words can precompute 4 tables of 256-words then each column in each round can be computed using 4 table lookups + 4 XORs at a cost of 4Kb to store tables designers believe this very efficient implementation was a key factor in its selection as the AES cipher
  • 9. 9 241-427-SV-2-2553-COE-PSU 49 Modes of Operation block ciphers encrypt fixed size blocks eg. DES encrypts 64-bit blocks with 56-bit key need some way to en/decrypt arbitrary amounts of data in practise ANSI X3.106-1983 Modes of Use (now FIPS 81) defines 4 possible modes subsequently 5 defined for AES & DES have block and stream modes 241-427-SV-2-2553-COE-PSU 50 Electronic Codebook Book (ECB) message is broken into independent blocks which are encrypted each block is a value which is substituted, like a codebook, hence name each block is encoded independently of the other blocks Ci = DESK1(Pi) uses: secure transmission of single values 241-427-SV-2-2553-COE-PSU 51 Electronic Codebook Book (ECB) 241-427-SV-2-2553-COE-PSU 52 ECB Advantages & Limitations message repetitions may show in ciphertext if aligned with message block particularly with data such graphics or with messages that change very little, which become a code-book analysis problem weakness is due to the encrypted message blocks being independent main use is sending a few blocks of data 241-427-SV-2-2553-COE-PSU 53 Cipher Block Chaining (CBC) message is broken into blocks linked together in encryption operation each previous cipher blocks is chained with current plaintext block, hence name use Initial Vector (IV) to start process Ci = DESK1(Pi XOR Ci-1) C-1 = IV uses: bulk data encryption, authentication 241-427-SV-2-2553-COE-PSU 54 Cipher Block Chaining (CBC)
  • 10. 10 241-427-SV-2-2553-COE-PSU 55 Advantages and Limitations of CBC a ciphertext block depends on all blocks before it any change to a block affects all following ciphertext blocks need Initialization Vector (IV) which must be known to sender & receiver if sent in clear, attacker can change bits of first block, and change IV to compensate hence IV must either be a fixed value (as in EFTPOS) or must be sent encrypted in ECB mode before rest of message 241-427-SV-2-2553-COE-PSU 56 Cipher FeedBack (CFB) Size of the block in AES or DES is n Size of the plaintext is r; r <= n Encrypt or decrypt the contents of a shift register, S, of size n Encryption XOR r-bit plaintext w/ r-bits of the shift register 241-427-SV-2-2553-COE-PSU 57 Cipher FeedBack (CFB) 241-427-SV-2-2553-COE-PSU 58 CFB Advantages & Limitations appropriate when data arrives in bits/bytes most common stream mode limitation is need to stall while do block encryption after every n-bits note that the block cipher is used in encryption mode at both ends errors propogate for several blocks after the error 241-427-SV-2-2553-COE-PSU 59 Output FeedBack (OFB) Similar to CFB Each bit in the ciphertext is independent of the previous bit or bits 241-427-SV-2-2553-COE-PSU 60 Advantages and Limitations of OFB bit errors do not propagate more vulnerable to message stream modification a variation of a Vernam cipher hence must never reuse the same sequence (key+IV) sender & receiver must remain in sync originally specified with m-bit feedback subsequent research has shown that only full block feedback (ie CFB-64 or CFB-128) should ever be used
  • 11. 11 241-427-SV-2-2553-COE-PSU 61 Counter (CTR) similar to OFB but encrypts counter value rather than any feedback value must have a different key & counter value for every plaintext block (never reused) 241-427-SV-2-2553-COE-PSU 62 Advantages and Limitations of CTR efficiency can do parallel encryptions in h/w or s/w can preprocess in advance of need good for bursty high speed links random access to encrypted data blocks provable security (good as other modes) but must ensure never reuse key/counter values, otherwise could break (cf OFB) 241-427-SV-2-2553-COE-PSU 63 Asymmetric-key cryptosystem 241-427-SV-2-2553-COE-PSU 64 Conceptual differences slowfast numbers are manipulated (mathematical function) symbols are permuted or substituted only n personal secrets(n-1)n/2 shared secrets The secret is not sharedThe secret is shared asymmetricsymmetric 241-427-SV-2-2553-COE-PSU 65 General idea 241-427-SV-2-2553-COE-PSU 66 General idea (cont.) Bob must create two keys; distribute to others Eve should not be able to advertise her public key pretending to be Bob’s key Each key pair can be used for one-way communication Bob only needs one private key to receive message from anyone Bob needs n public keys to talk to n people (one for each person) The plaintext and ciphertext are treated as integers C = f(Kpublic, P) while P = g(Kprivate, C) And f must be a trapdoor one-way function
  • 12. 12 241-427-SV-2-2553-COE-PSU 67 Trapdoor one-way function One-way function f is easy given x compute y = f(x) is easy f-1 is difficult given y, it is computationally infeasible to calculate x = f-1(y) Trapdoor one-way function A one-way function that given y and a trapdoor (secret), x can be easily computed E.g., y = xk mod n when n is large 241-427-SV-2-2553-COE-PSU 68 y = xk mod n Given x, k and n, it is easy to calculate y Square-and multiply method Given y, k and n, it is very difficult to compute x Discrete logarithm problem However if a trapdoor k’ such that k’ • k = 1 mod Ф(n) is known x can be easily calculated by x = yk’ mod n This is used in RSA 241-427-SV-2-2553-COE-PSU 69 RSA cryptosystem Named for its inventors (Rivest, Shamir, Adleman) 241-427-SV-2-2553-COE-PSU 70 RSA: key generation Recommended size n should be at least 1024 bits e and d should be at least 512 bits Key generation 1. Select two large prime p and q 2. n ← p • q 3. Ф(n) = (p-1)(q-1) 4. Select e such that 1 < e < Ф(n) and gcd(e, Ф(n)) = 1 5. d ← e-1 mod Ф(n) {e,n} is the public key {d,n} is the private key 241-427-SV-2-2553-COE-PSU 71 Exponentiation can use the Square and Multiply Algorithm a fast, efficient algorithm for exponentiation concept is based on repeatedly squaring base and multiplying in the ones that are needed to compute the result look at binary representation of exponent only takes O(log2 n) multiples for number n eg. 75 mod 11 = 10 241-427-SV-2-2553-COE-PSU 72 square-and-multiply Square-and-multiply (x, k, n) y ← 1 for i=0 to nb-1 if(ki = 1) y ← x • y mod n x ← x2 mod n return y Where nb is the number of bits in k
  • 13. 13 241-427-SV-2-2553-COE-PSU 73 RSA Example - Key Setup 1. Select primes: p=17 & q=11 2. Compute n = pq =17 x 11=187 3. Compute ø(n)=(p–1)(q-1)=16 x 10=160 4. Select e: gcd(e,160)=1; choose e=7 5. Determine d: de=1 mod 160 and d < 160 Value is d=23 since 23x7=161= 10x160+1 6. Publish public key PU={7,187} 7. Keep secret private key PR={23,187} 241-427-SV-2-2553-COE-PSU 74 Attacking RSA possible approaches: brute force key search (infeasible given size of numbers) mathematical attacks (based on difficulty of computing ø(n), by factoring modulus n) timing attacks (on running of decryption) chosen ciphertext attacks (given properties of RSA) If the ciphertext is a permutation of the plaintext Continuous encryption of the ciphertext will eventually results in the plaintext 241-427-SV-2-2553-COE-PSU 75 Man-in-the-middle Attack 241-427-SV-2-2553-COE-PSU 76 Symmetric-key distribution How to distribute and maintain secret keys Two approach Use a trusted third party Use no third party 241-427-SV-2-2553-COE-PSU 77 Use a trusted third party Key-distribution center (KDC) Each user has a shared secret key wit the KDC Problems Not scale Bottleneck problem 241-427-SV-2-2553-COE-PSU 78 Example of KDC approach
  • 14. 14 241-427-SV-2-2553-COE-PSU 79 No third party Diffie-Hellman key agreement 241-427-SV-2-2553-COE-PSU 80 Diffie-Hellman Initial: choose two number p and g p: a large prime number > 300 decimal digits 1024 bits g: an integer < p such that foe every number n between 1 to p-1, there is a power k of g such that n = gk mod p Idea Key is gxy mod p where one party knows x and the other knows y Problems Discrete logarithm attack Man-in-the-middle attack 241-427-SV-2-2553-COE-PSU 81 Man-in-the-middle-attack 241-427-SV-2-2553-COE-PSU 82 Public-key distribution Public announcement simple and easy Subject to forgery Anyone can pretend to be anyone The key can be switched during the communication 241-427-SV-2-2553-COE-PSU 83 Public-key distribution (cont.) Trusted center: keep information of public key and dynamically updated the information Each user must prove his/her identity The user’s public key is kept at the trusted center 241-427-SV-2-2553-COE-PSU 84 Public-key distribution (cont.) Controlled trusted center
  • 15. 15 241-427-SV-2-2553-COE-PSU 85 Public-key distribution (cont.) Both trusted center models Create heavy load on the trusted center Objectives A person wants people to know his public-key Wants no one to accept a forged key as his Solutions Certification authority (CA): a federal or state organization that binds a public key to an entity and issues a certificate The CA checks Bob’s identity The CA issue the certificate by signing Bob’s public key using the center private key 241-427-SV-2-2553-COE-PSU 86 Certification authority 241-427-SV-2-2553-COE-PSU 87 Public-Key Infrastructures (PKI) A model for creating, distributing and revoking certificates based on the X.509 Duties Certificates’ issuing, renewal and revocation Keys’ storage and update: store members’ private keys and update these keys on members’ demands Providing services to other protocols e.g., IPSec, TLS Providing access control different access levels 241-427-SV-2-2553-COE-PSU 88 PKI: trust model Reason: not possible to have a single CA Q1: how user1 can trust user3? Q2: how user1 can trust user4? 241-427-SV-2-2553-COE-PSU 89 X.509 the Internationally accepted standard for how to construct a public key certificate used by S/MIME secure email, SSL/TLS secure Internet links (e.g., for secure web) 241-427-SV-2-2553-COE-PSU 90 X.509 Certificates
  • 16. 16 241-427-SV-2-2553-COE-PSU 91 X.509 Certificates issued by a Certification Authority (CA), containing: version (1, 2, or 3) serial number (unique within CA) identifying certificate signature algorithm identifier issuer X.500 name (CA) period of validity (from - to dates) subject X.500 name (name of owner) subject public-key info (algorithm, parameters, key) issuer unique identifier (v2+) subject unique identifier (v2+) extension fields (v3) signature (of hash of all fields in certificate) notation CA<<A>> : certificate for A signed by CA 241-427-SV-2-2553-COE-PSU 92 X.509: certificate revocation Reasons Compromised key The CA is no longer willing to certify the user The CA private key is compromised Actions: Issue a certificate revocation list (CRL) Before using any certificate, the user must check this list 241-427-SV-2-2553-COE-PSU 93 References W. Stallings, Cryptography and Network Security, 3rd ed. B.A. Forouzan, Cryptograhpy and Network Security, McGraw-Hill, 2008. A.Kahate, Cryptography and network Security, McGraw-Hill, 2003.