Cryptography 1 Crypto

Cryptography 2 Crypto  Cryptology  The art and science of making and breaking “secret codes”  Cryptography  making “secret codes”  Cryptanalysis  breaking “secret codes”  Crypto  all of the above (and more)

Cryptography 3 How to Speak Crypto  A cipher or cryptosystem is used to encrypt the plaintext  The result of encryption is ciphertext  We decrypt ciphertext to recover plaintext  A key is used to configure a cryptosystem  A symmetric key cryptosystem uses the same key to encrypt as to decrypt  A public key cryptosystem uses a public key to encrypt and a private key to decrypt (sign)

Cryptography 4 Crypto  Basis assumption o The system is completely known to Trudy o Only the key is secret  Also known as Kerckhoffs Principle o Crypto algorithms are not secret  Why do we make this assumption? o Experience has shown that secret algorithms are weak when exposed o Secret algorithms never remain secret o Better to find weaknesses before using

Cryptography 5 Symmetric Key Notation  Encrypt plaintext P with symmetric key K C = E(P,K)  Decrypt ciphertext C with symmetric key K P = D(C,K)  Encrypt and decrypt are inverses D(E(P,K),K) = E(D(P,K),K) = P  Note that same key K is used to encrypt and to decrypt

Cryptography 6 Symmetric Key Encryption  Must agree on key K in advance  How to do this securely?  This is a big problem! AliceBob E(Bob’s data, K) E(Alice’s data, K)

Cryptography 7 Symmetric Ciphers  Popular symmetric key ciphers include o DES o 3DES (aka triple DES) o AES o Blowfish o RC6 o TEA

Cryptography 8 Uses for Symmetric Crypto  Confidentiality o Transmitting data over insecure channel o Secure storage on insecure media  Integrity ( MAC )  Authentication protocols (later…)  Anything you can do with a hash function (upcoming chapter…)

Cryptography 9 Public Key Cryptography  There are 2 keys o Public key used to encrypt o Private key used to decrypt  Also have digital signatures o Private key to sign o Public key to verify signature

Cryptography 10 Public Key Notation  Encrypt message M with Alice’s public key C = {M} Alice  Decrypt ciphertext with Alice’s private key M = [C] Alice  Private key and public key are inverses {[M] Alice } Alice = [{M} Alice ] Alice = M

Cryptography 11 Digital Signature  Encrypt message M with Alice’s public key C = {M} Alice  To decrypt the ciphertext use private key M = [C] Alice  Sign message M with Alice’s private key S = [M] Alice  To verify the signature use public key o To verify, show that M = {S} Alice

Cryptography 12 Public Key Encryption  Bob’s public key is public  Alice’s public key is public  So no need to agree on key in advance  A huge advantage over symmetric key AliceBob {M} Alice {M} Bob

Cryptography 13 Digital Signature  Bob verifies signature using Alice’s public key (which is public) AliceBob M, [M] Alice

Cryptography 14 Public Key Cryptosystems  The most popular is RSA o Named after Rivest, Shamir and Adleman  RSA can do encryption and signatures  A few other public key systems are used o But not many!  There are a lots of symmetric ciphers  Why so few public key systems?

Cryptography 15 Diffie-Hellman  A “key exchange” algorithm  Only used to establish a shared symmetric key  Not for encryption or signing  Considered a public key system o Some public info is used to agree on key

Cryptography 16 Diffie-Hellman  Alice computes (g b ) a = g ab mod p  Bob computes (g a ) b = g ab mod p  The shared key is g ab mod p Alice secret a Bob secret b g b mod p g a mod p

Cryptography 17 Diffie-Hellman  Trudy can see g a mod p and g b mod p  Trudy wants g ab mod p  She can compute o (g a )(g b ) = g a+b  g ab mod p  If Trudy can find a or b, she wins  But finding a from g a mod p is hard o The “discrete log” problem

Cryptography 18 Diffie-Hellman  Subject to man-in-the-middle (MiM) attack Alice, a Bob, b g a mod p g b mod p Trudy, t g t mod p  Trudy shares secret g at mod p with Alice  Trudy shares secret g bt mod p with Bob  Alice and Bob don’t know Trudy exists!

Cryptography 19 Uses for Public Key Crypto  Confidentiality o Transmitting data over insecure channel o Secure storage on insecure media  Authentication (later)  Digital signature provides integrity and non-repudiation o No non-repudiation with symmetric keys

Cryptography 20 Symmetric vs Public Key  Advantages of symmetric key o Efficiency o No public key infrastructure (PKI)  Advantages of public key o No key distribution problem o Digital signatures

Cryptography 21 Real World Confidentiality  Hybrid cryptosystem: best of both worlds o Public key crypto to establish a key o Symmetric key crypto to encrypt data AliceBob {K} Bob E(Bob’s data, K) E(Alice’s data, K)  Can Bob be sure he’s talking to Alice?

Cryptography 22 Crypto Hash Function  Crypto hash function h(x) provides o Compression  output length is small o Efficiency  h(x) easy to computer for any x o One-way  given a value y it is infeasible to find an x such that h(x) = y o Collision resistance  can’t find any x and y, with x  y such that h(x) = h(y) o Collisions must exist, but hard to find one

Cryptography 23 Popular Crypto Hashes  MD5  invented by Rivest o 128 bit output (collision recently found)  SHA-1  A US government standard (similar to MD5) o 180 bit output  Tiger  192 bit output  Many others hashes, but MD5 and SHA-1 most widely used  Hashes work by hashing message in blocks

Cryptography 24 Hash Uses  Authentication ( HMAC )  Message integrity ( HMAC )  Message fingerprint  Data corruption detection  Digital signature efficiency  Anything you can do with symmetric crypto

Cryptography 25 Online Auction  Suppose Alice, Bob and Charlie are bidders  Alice plans to bid A, Bob B and Charlie C  They don’t trust that bids will stay secret  Solution? o Alice, Bob, Charlie submit hashes h(A), h(B), h(C) o All hashes received and posted online o Then bids A, B and C revealed  Hashes don’t reveal bids (one way)  Can’t change bid after hash sent (collision)

Cryptography 26 Signing and Hashing  Suppose Alice signs M o Alice sends M and S = [M] Alice to Bob o Bob verifies that M = {S} Alice  If M is big, [M] Alice is costly to compute o Sending M and S also wastes bandwidth  Instead, Alice signs h(M) o Alice sends M and S = [h(M)] Alice to Bob o Bob verifies that h(M) = {S} Alice

Cryptography 27 Digital Signature  Bob verifies signature using Alice’s public key (which is public) AliceBob M, [h(M)] Alice