# Cryptography Overview

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1 Cryptography Overview

2 Cryptography Is n A tremendous tool n The basis for many security mechanisms Is not n The solution to all security problems n Reliable unless implemented properly n Reliable unless used properly n Something you should try to invent yourself unless w you spend a lot of time becoming an expert w you subject your design to outside review

3 Auguste Kerckhoffs A cryptosystem should be secure even if everything about the system, except the secret key, is public knowledge. baptised as Jean-Guillaume-Hubert-Victor-François- Alexandre-Auguste Kerckhoffs von Nieuwenhof

4 Goal 1:secure communication Step 1: Session setup to exchange key Step 2: encrypt data HTTPS

5 Goal 2: Protected files Disk Alice File 1 Alice File 2 No eavesdropping No tampering Analogous to secure communication: Alice today sends a message to Alice tomorrow

6 Symmetric Cryptography Assumes parties already share a secret key

7 Building block: sym. encryption Alice m, n E(k,m,n)=c E nonce Bob c, n D(k,c,n)=m D k k E, D: cipher k: secret key (e.g. 128 bits) m, c: plaintext, ciphertext n: nonce (aka IV) Encryption algorithm is publicly known Never use a proprietary cipher

8 Use Cases Single use key: (one time key) Key is only used to encrypt one message encrypted No need for nonce (set to 0) new key generated for every Multi use key: (many time key) Key used to encrypt multiple messages SSL: same key used to encrypt many packets Need either unique nonce or random nonce

9 First example: One Time Pad (single use key) Vernam (1917) Key: Plaintext: Ciphertext: Shannon 49: n OTP is secure against ciphertext-only attacks

10 Stream ciphers (single use key) Problem: OTP key is as long the message Solution: Pseudo random key -- stream ciphers key PRG c PRG(k) m message ciphertext Stream ciphers: RC4 (113MB/sec), SEAL (293MB/sec)

11 Dangers in using stream ciphers One time key!! Two time pad is insecure: C1 m1 PRG(k) C2 m2 PRG(k) Eavesdropper does: C1 C2 m1 m2 Enough redundant information in English that: m1 m2 m1, m2

12 Block ciphers: crypto work horse n Bits PT Block n Bits E, D CT Block Key k Bits Canonical examples: 1. 3DES: n= 64 bits, k = 168 bits 2. AES: n=128 bits, k = 128, 192, 256 bits IV handled as part of PT block

13 Building a block cipher Input: (m, k) Repeat simple mixing operation several times DES: Repeat 16 times: ml mr mr mlf(k,mr) AES-128: Mixing step repeated 10 times Difficult to design: must resist subtle attacks differential attacks, linear attacks, brute-force,

14 Block Ciphers Built by Iteration key k key expansion k1 k2 k3 kn m R(k1, ) R(k2, ) R(k3, ) R(kn, ) c R(k,m): round function for DES (n=16), for AES (n=10)

15 Incorrect use of block ciphers Electronic Code Book (ECB): PT: m1 m2 CT: c1 c2 Parallel encryption of the various blocks through the same key Problem: n if m1=m2 then c1=c2

16 In pictures

17 Correct use of block ciphers I: CBC mode E a secure PRP. Cipher Block Chaining with random IV: IV m[0] m[1] m[2] m[3] E(k,) E(k,) E(k,) E(k,) IV c[0] c[1] c[2] c[3] ciphertext Q: how to do decryption?

18 Use cases: choosing an IV Single use key: no IV needed (IV=0) Multi use key: (CPA Security) Best: use a fresh random IV for every message Can use unique IV (e.g counter) but then first step in CBC must be IV E(k1,IV) benefit: may save transmitting IV with ciphertext

19 CBC with Unique IVs unique IV means: (k,iv) pair is used for only one message may be predictable so use E(k1,) as PRF IV m[0] m[1] m[2] m[3] IV E(k1,) E(k,) E(k,) E(k,) E(k,) IV c[0] c[1] c[2] c[3] ciphertext

20 In pictures

21 Correct use of block ciphers II: CTR mode Counter mode with a random IV: (parallel encryption) IV m[0] m[1] E(k,IV) E(k,IV+1) m[l] E(k,IV+L) IV c[0] c[1] c[l] ciphertext

22 Performance: Crypto [ Wei Dai ] Pentium 4, 2.1 GHz ( on Windows XP SP1, Visual C ) Cipher Block/key size Speed (MB/sec) RC4 113 SEAL 293 3DES 64/168 9 AES 128/128 61

23 Data integrity

24 Message Integrity: MACs Goal: message integrity. No confidentiality. n ex: Protecting public binaries on disk. k k Alice Generate tag: tag S(k, m) Message m tag Bob Verify tag:? V(k, m, tag) = `yes note: non-keyed checksum (CRC) is an insecure MAC!!

25 Secure MACs Attacker information: chosen message attack n for m1,m2,,mq attacker is given ti S(k,mi) Attacker s goal: existential forgery. n produce some new valid message/tag pair (m,t). (m,t) { (m1,t1),, (mq,tq) } A secure PRF gives a secure MAC: n S(k,m) = F(k,m) n V(k,m,t): `yes if t = F(k,m) and `no otherwise.

26 Construction 1: ECBC m[0] m[1] m[2] m[3] E(k,) E(k,) E(k,) E(k,) Raw CBC key = (k, k1) E(k1,) tag

27 Construction 2: HMAC (Hash-MAC) Most widely used MAC on the Internet. H: hash function. example: SHA-256 ; output is 256 bits Building a MAC out of a hash function: Standardized method: HMAC S( k, m ) = H( kopad H( kipad m ))

28 SHA-256: Merkle-Damgard m[0] m[1] m[2] m[3] IV h h h h H(m) h(t, m[i]): compression function Thm 1: Thm 2 : if h is collision resistant then so is H if h is a PRF then HMAC is a PRF PRF=pseudo random function

29 Construction 3: PMAC parallel MAC ECBC and HMAC are sequential. PMAC: m[0] m[1] m[2] m[3] P(k,0) P(k,1) P(k,2) P(k,3) F(k,) F(k,) F(k,) F(k,) F(k1,) tag

30 These MAC constructions are secure n No time to prove it Why the last encryption step in ECBC? n CBC (aka Raw-CBC) is not a secure MAC: n Given tag on a message m, attacker can deduce tag for some other message m n How: good crypto exercise

31 Authenticated Encryption: Encryption + MAC

32 Combining MAC and ENC (CCA) Encryption key KE MAC key = KI Option 1: MAC-then-Encrypt (SSL) MAC(M,KI) Enc KE Msg M Msg M MAC Option 2: Encrypt-then-MAC (IPsec) Enc KE Secure on general ground s Msg M Option 3: Encrypt-and-MAC (SSH) Enc KE Msg M MAC(C, KI) MAC MAC(M, KI) MAC

33 OCB offset codebook mode More efficient authenticated encryption m[0] m[1] m[2] m[3] checksum P(N,k,0) P(N,k,1) P(N,k,2) P(N,k,3) P(N,k,0) E(k,) E(k,) E(k,) E(k,) E(k,) P(N,k,0) P(N,k,1) P(N,k,2) P(N,k,3) auth c[0] c[1] c[2] c[3] c[4] Rogaway,

34 Public-key Cryptography

35 Public key encryption: (Gen, E, D) Gen pk sk m c c m E D

36 Applications Session setup (for now, only eavesdropping security) Alice Generate (pk, sk) x pkalice E(pk, x) Bob choose random x (e.g. 48 bytes) Non-interactive applications: (e.g. ) Bob sends to Alice encrypted using pkalice Note: Bob needs pkalice (public key management)

37 Applications Encryption in non-interactive settings: Encrypted File Systems write read ska Alice Bob E(kF, File) E(pkA, KF) E(pkB, KF) File

38 Applications Encryption in non-interactive settings: Key escrow: data recovery without Bob s key Bob write E(pkescrow, KF) Escrow Service skescrow E(kF, File) E(pkB, KF)

39 Trapdoor functions (TDF) A trapdoor func. X Y is a triple of efficient algs. (G, F, F-1) G(): randomized alg. outputs key pair (pk, sk) F(pk, ): det. alg. that defines a func. X Y F-1(sk, ): Y X that inverts F(pk, ) Security: F(pk, ) is one-way without sk

40 Public-key encryption from TDFs (G, F, F-1): secure TDF X Y (Es, Ds) : symm. auth. encryption with keys in K H: X K a hash function We construct a pub-key enc. system (G, E, D): Key generation G: same as G for TDF

41 Public-key encryption from TDFs (G, F, F-1): secure TDF X Y (Es, Ds) : symm. auth. encryption with keys in K H: X K a hash function We construct a pub-key enc. system (G, E, D): Key generation G: same as G for TDF

42 Public-key encryption from TDFs (G, F, F-1): secure TDF X Y (Es, Ds) : symm. auth. encryption with keys in K H: X K a hash function E( pk, m) : x X, y F(pk, x) k H(x), c Es(k, m) output (y, c) D( sk, (y,c) ) : x F-1(sk, y), k H(x), m Ds(k, c) output m

43 Digital Signatures Public-key encryption n Alice publishes encryption key n Anyone can send encrypted message n Only Alice can decrypt messages with this key Digital signature scheme n Alice publishes key for verifying signatures n Anyone can check a message signed by Alice n Only Alice can send signed messages

44 Digital Signatures from TDPs (G, F, F-1): secure TDP X X H: M X a hash function Sign( sk, m X) : output sig = F-1(sk, H(m) ) Verify( pk, m, sig) : output 1 if H(m) = F(pk, sig) 0 otherwise Security: existential unforgeability under a chosen message attack in the random oracle model

45 Public-Key Infrastructure (PKI) Anyone can send Bob a secret message n Provided they know Bob s public key How do we know a key belongs to Bob? n If imposter substitutes another key, can read Bob s mail One solution: PKI n n n Trusted root Certificate Authority (e.g. Symantec) w Everyone must know the verification key of root CA w Check your browser; there are hundreds!! Root authority signs intermediate CA Results in a certificate chain

46 Back to SSL/TLS Version, Crypto choice, nonce Version, Choice, nonce, Signed certificate containing server s public key Ks C Secret key K encrypted with server s key Ks S switch to negotiated cipher Hash of sequence of messages Hash of sequence of messages data transmission

47 Limitations of cryptography Most security problems are not crypto problems n n This is good w Cryptography works! This is bad w People make other mistakes; crypto doesn t solve them Misuse of cryptography is fatal for security n n WEP ineffective, highly embarrassing for industry Occasional unexpected attacks on systems subjected to serious review

48

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