1 Types of Cryptosystems ECE 646 - Lecture 3 Implementation of Security Services Block vs. stream ciphers Types of Cryptosystems (1) Cryptosystem (Cipher) message ciphertext cryptographic key n bits m bits k bits2 Block vs. stream ciphers Stream cipher Internal state - IS Block cipher K K M1, M2, …, Mn m1, m2, …, mn C1, C2, …, Cn c1, c2, …, cn Ci=fK(Mi) ci = fK(mi, ISi) ISi+1=gK(mi, ISi) Every block of ciphertext is a function of only one corresponding block of plaintext Every block of ciphertext is a function of the current block of plaintext and the current internal state of the cipher Typical stream cipher Sender Receiver Pseudorandom Key Generator mi plaintext ci ciphertext ki keystream key initialization vector (seed) Pseudorandom Key Generator mi plaintext ci ciphertext ki keystream key initialization vector (seed) Secret-key vs. public-key ciphers Types of Cryptosystems (2)3 Secret-key (Symmetric) Cryptosystems key of Alice and Bob - KAB key of Alice and Bob - KAB Alice Bob Network Encryption Decryption Key Distribution Problem N - Users N · (N-1) 2 Keys Users Keys 100 5,000 1000 500,000 Digital Signature Problem Both corresponding sides have the same information and are able to generate a signature There is a possibility of the • receiver falsifying the message • sender denying that he/she sent the message4 Public Key (Asymmetric) Cryptosystems Public key of Bob - KB Private key of Bob - kB Alice Bob Network Encryption Decryption Classification of cryptosystems Terminology secret-key symmetric symmetric-key classical conventional public key asymmetric One-way function X f(X) Y f-1(Y) EXAMPLE: f: Y=f(X) = AX mod P where P and A are constants, P is a large prime, A is an integer smaller than P Number of bits of P Average number of multiplications necessary to compute f f -1 1000 1500 10305 Trap-door one-way function X f(X) Y f-1(Y) Whitfield Diffie and Martin Hellman “New directions in cryptography,” 1976 PUBLIC KEY PRIVATE KEY Key Distribution Alice Bob message ciphertext message ciphertext Bob’s public key Bob’s private key Bob’s public key message ciphertext Bob’s public key Intruder Digital Signature Alice Bob signature message signature message Alice’s public key Alice’s private key Alice’s public key signature message Alice’s public key Intruder signature message Alice’s public key Judge6 Implementation of Security Services Message Hash function Public key cipher Alice Signature Alice’s private key Bob Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes no Message Signature Hash function arbitrary length message hash function hash value h(m) h m fixed length7 Hash functions Basic requirements 1. Public description, NO key 2. Compression arbitrary length input → fixed length output 3. Ease of computation Hash functions Security requirements It is computationally infeasible Given To Find h(m) m m and h(m) m’ ≠ m, such that h(m’) = h(m) m’ ≠ m, such that h(m’) = h(m) Message Hash function Public key cipher Alice Signature Alice’s private key Bob Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes/no Message Signature8 Message Hash function Public key cipher Alice Signature Alice’s private key Bob Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes/no Message Signature Signature generation function Signature verification function Message Secret key algorithm Alice MAC Secret key of Alice and Bob Bob Secret key algorithm Authentication MAC’ MAC yes no Message MAC Secret key of Alice and Bob KAB KAB MAC - Message Autentication Codes (keyed hash functions) arbitrary length message MAC function MAC m fixed length secret key K9 MAC functions Basic requirements 1. Public description, SECRET key parameter 2. Compression arbitrary length input → fixed length output 3. Ease of computation MAC functions Security requirements Given zero or more pairs mi, MAC(mi) i = 1..k it is computationally impossible to find any new pair m’, MAC(m’) such that m’ ≠ mi i = 1..k CBC-MAC (Cipher Block Chaining MAC) Secret-key cipher KAB M1 KAB M2 . . . . KAB Mt 0 Message MAC Secret-key cipher Secret-key cipher10 Relations among security services INTEGRITY AUTHENTICATION NON-REPUDIATION CONFIDENTIALITY Message Hash function Public key cipher Alice Signature Alice’s private key Bob Hash function Alice’s public key Non-repudiation Hash value 1 Hash value 2 Hash value Public key cipher yes no Message Signature Message Secret key algorithm Alice MAC Secret key of Alice and Bob Bob Secret key algorithm Authentication MAC’ MAC yes no Message MAC Secret key of Alice and Bob KAB KAB11 Hybrid Systems Features required from today’s ciphers STRENGTH FUNCTIONALITY • easy key distribution • digital signatures PERFORMANCE Features of secret-key ciphers STRENGTH FUNCTIONALITY • easy key distribution • digital signatures PERFORMANCE12 Features of public-key ciphers STRENGTH FUNCTIONALITY • easy key distribution • digital signatures PERFORMANCE Average Decryption Speed for implementations based on the same technology AES deciphering speed RSA-1024 deciphering speed ≈ 100 ≈ 1000 software hardware Basic operations of secret key ciphers - S-box S-box n x m ROM Software Hardware C ASM WORD S[1<<n]= { 0x23, 0x34, 0x56 . . . . . . . . . . . . . . } S DW 23H, 34H, 56H ….. direct logic n m 2n words n-bit address m-bit output ... x1 x2 xn ... y1 y2 ym S Substitution13 Permutation C order of wires P Hardware Software ASM sequence of instructions <<, |, & sequence of instructions ROL, OR, AND n n x1 x2 x3 xn xn-1 . . . y1 y2 y3 yn yn-1 . . . Basic operations of secret key ciphers - P-box P-box n x n Basic Operations of the Public Key Cryptosystem RSA Encryption Decryption ciphertext = mod plaintext public key modulus public key exponent plaintext = mod ciphertext private key modulus private key exponent k-bits k-bits k-bits k-bits k-bits k-bits Alice Bob session key (random secret-key) Bob’s public key Hybrid Systems Bob’s private key Network Session key encrypted using Bob’s public key Message encrypted using session key14 Hybrid Systems - Sender’s Side (2) Alice session key random Bob’s public
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