# Overview of Cryptographic Tools for Data Security. Murat Kantarcioglu

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1 UT DALLAS Erik Jonsson School of Engineering & Computer Science Overview of Cryptographic Tools for Data Security Murat Kantarcioglu Pag. 1 Purdue University

2 Cryptographic Primitives We will discuss the following primitives in this course Symmetric Encryption Message Authentication Public Key Cryptography Digital Signatures Pseudo-random Number Generators

3 Block Ciphers Consider a block cipher as a permutation defined on n bit strings to n bit strings based on the secret key. It is assumed that if the key is secret the output of the block cipher will look like random

4 Iterated Block Cipher Requires the specification of an invertible round function g and key schedule function Ks and Number of rounds Nr. F(K,x) { (K 1,...K Nr ) Ks(K) w 0 x w i g(w i 1,K i 1 )fornr i 1 Returnw Nr }

5 Inverting an Iterated Block Cipher Since function g is invertible. We can easily decipher the output of an iterated cipher F 1 (K,y) { (K 1,...K Nr ) Ks(K) w Nr y w i 1 g 1 (w i,k i )fornr>i 1 Returnw 0 }

6 History of AES Due to limitations of DES (small key and block sizes), NIST started a open process to select a new block cipher. 15 proposals submitted to NIST around Rijndael from Belgium chosen as the AES in 2001 after an open process. Rijndael is chosen because of its security, performance, efficiency, implementability, and flexibility.

7 Overview of AES AES has 128 bits block size AES has three allowable key sizes K ={128,192,256} AES has variable number of rounds If K =128 then Nr=10 If K =192 then Nr=12 If K =256 then Nr=14

8 Block Ciphers Block length is fixed (n-bit) How to encrypt large messages? Partition into n-bit blocks Choose mode of operation Electronic Codebook (ECB), Cipher-Block Chaining (CBC), Cipher Feedback (CFB), Output Feedback (OFB), Counter (CTR) Padding schemes

9 Evaluation criteria Identical messages under which conditions ciphertext of two identical messages are the same Chaining dependencies how adjacent plaintext blocks affect encryption of a plaintext block Error propagation resistance to channel noise Efficiency preprocessing parallelization: random access

10 Notation Message x consists of plaintext blocks of size n x = x 1 x 2 x t Ciphertext of plaintext block x i denoted as c i Chaining requires an initialization vector that first plaintext block x 1 will depend on. Initialization vector denoted as IV. IV should be selected randomly for each message (x)

11 Electronic Codebook (ECB) Plaintext Plaintext Key Block Cipher Encryption Key Block Cipher Encryption Ciphertext Ciphertext Each block encrypted independently Identical plaintexts encrypted similarly No chaining, no error propagation

12 Electronic Codebook (ECB) Does not hide data patterns, unsuitable for long messages Wiki example: pixel map using ECB Susceptible to replay attacks Example: a wired transfer transaction can be replayed by resending the original message)

13 Cipher-Block Chaining (CBC) Plaintext Plaintext Initialization Vector (IV) Key Block Cipher Encryption Key Block Cipher Encryption Ciphertext Ciphertext Allows random access to ciphertext Decryption is parallelizable Plaintext block x j requires ciphertext blocks c j and c j-1

14 Cipher-Block Chaining (CBC) Identical messages: changing IV or the first plaintext block results in different ciphertext Chaining: Ciphertext block c j depends on x j and all preceding plaintext blocks (dependency contained in c j-1 ) Error propagation: Single bit error on c j may flip the corresponding bit on x j+1, but changes x j significantly. IV need not be secret, but its integrity should be protected

15 Counter (CTR) Nonce c43acb23 Counter Nonce c43acb23 Counter Nonce c43acb23 Counter Key Block Cipher Encryption Key Block Cipher Encryption Key Block Cipher Encryption Plaintext Plaintext Plaintext Ciphertext Preprocessing possible (inc/decrement and enc/decrypt counter) Allows random access Ciphertext Ciphertext

16 Data Integrity and Source Authentication Encryption does not protect data from modification by another party. Need a way to ensure that data arrives at destination in its original form as sent by the sender and it is coming from an authenticated source.

17 Cryptographic Hash Functions A hash function maps a message of an arbitrary length to a m-bit output output known as the fingerprint or the message digest if the message digest is transmitted securely, then changes to the message can be detected A hash is a many-to-one function, so collisions can happen.

18 Requirements for Cryptographic Hash Functions Given a function h:x Y, then we say that h is: preimage resistant (one-way): if given y Y it is computationally infeasible to find a value x X s.t. h(x) = y 2-nd preimage resistant (weak collision resistant): if given x X it is computationally infeasible to find a value x X, s.t. x x and h(x ) = h(x) collision resistant (strong collision resistant): if it is computationally infeasible to find two distinct values x,x X, s.t. h(x ) = h(x)

19 Uses of hash functions Message authentication Software integrity One-time Passwords Digital signature Timestamping Certificate revocation management

20 SHA1 (Secure Hash Algorithm) SHA was designed by NIST and is the US federal standard for hash functions, specified in FIPS-180 (1993). SHA-1, revised version of SHA, specified in FIPS (1995) use with Secure Hash Algorithm). It produces 160-bit hash values. NIST have issued a revision FIPS that adds 3 additional hash algorithms: SHA-256, SHA-384, SHA-512, designed for compatibility with increased security provided by AES.

21 Limitation of Using Hash Functions for Authentication Require an authentic channel to transmit the hash of a message anyone can compute the hash value of a message, as the hash function is public not always possible How to address this? use more than one hash functions use a key to select which one to use

22 Hash Family A hash family is a four-tuple (X,Y,K,H ), where X is a set of possible messages Y is a finite set of possible message digests K is the keyspace For each K K, there is a hash function h K H. Each h K : X Y Alternatively, one can think of H as a function K X Y

23 Message Authentication Code A MAC scheme is a hash family, used for message authentication MAC = C K (M) The sender and the receiver share K The sender sends (M, C k (M)) The receiver receives (X,Y) and verifies that C K (X)=Y, if so, then accepts the message as from the sender To be secure, an adversary shouldn t be able to come up with (X,Y) such that C K (X)=Y.

24 HMAC Goals Use available hash functions without modification. Preserve the original performance of the hash function without incurring a significant degradation. Use and handle keys in a simple way. Allow easy replacement of the underlying hash function in the event that faster or more secure hash functions are later available. Have a well-understood cryptographic analysis of the strength of the authentication mechanism based on reasonable assumptions on the underlying hash function.

25 HMAC HMAC K = Hash[(K + opad) Hash[(K + ipad) M)]] K + is the key padded out to input block size of the hash function and opad, ipad are specified padding constants Key size: L/2 < K < L MAC size: at least L/2, where L is the hash output

26 HMAC Overview

27 Limitation of Secret Key (Symmetric) Cryptography Secret key cryptography symmetric encryption confidentiality (privacy) MAC (keyed hash) authentication (integrity) Sender and receiver must share the same key needs secure channel for key distribution impossible for two parties having no prior relationship Other limitation of authentication scheme cannot authenticate to multiple receivers does not have non-repudiation 27

28 Public Key Cryptography Overview Proposed in Diffie and Hellman (1976) New Directions in Cryptography public-key encryption schemes public key distribution systems Diffie-Hellman key agreement protocol digital signature Public-key encryption was proposed in 1970 by James Ellis in a classified paper made public in 1997 by the British Governmental Communications Headquarters Diffie-Hellman key agreement and concept of digital signature are still due to Diffie & Hellman 28

29 Public Key Encryption Public-key encryption each party has a PAIR (K, K -1 ) of keys: K is the public key and K -1 is the secret key, such that D K -1[E K [M]] = M Knowing the public-key and the cipher, it is computationally infeasible to compute the private key Public-key crypto system is thus known to be asymmetric crypto systems The public-key K may be made publicly available, e.g., in a publicly available directory Many can encrypt, only one can decrypt 29

30 Public Key Cryptography Overview Public key distribution systems two parties who do not share any private information through communications arrive at some secret not known to any eavesdroppers Authentication with public keys: Digital Signature the authentication tag of a message can only be computed by one user, but can be verified by many called one-way message authentication in [Diffie & Hellman, 1976] 30

31 Digital Signatures: The Problem Consider the real-life example where a person pays by credit card and signs a bill; the seller verifies that the signature on the bill is the same with the signature on the card Contracts, they are valid if they are signed. Can we have a similar service in the electronic world? 31

32 Digital Signatures Digital Signature: a data string which associates a message with some originating entity. Digital Signature Scheme: for each key, there is a SECRET signature generation algorithm and a PUBLIC verification algorithm. Services provided: Authentication Data integrity Non-Repudiation (MAC does not provide this.) 32

33 RSA Signature Key generation (as in RSA encryption): Select 2 large prime numbers of about the same size, p and q Compute n = pq, and Φ = (q - 1)(p - 1) Select a random integer e, 1 < e < Φ, s.t. gcd(e, Φ) = 1 Compute d, 1 < d < Φ s.t. ed 1 mod Φ Public key: (e, n) Secret key: d, p and q must also remain secret 33

34 RSA Signature (cont.) Signing message M M must verify 0 < M < n Use private key (d) compute S = M d mod n Verifying signature S Use public key (e, n) Compute S e mod n = (M d mod n) e mod n = M Note: in practice, a hash of the message is signed and not the message itself. 34

35 Implementing Cryptosystems is Hard Crypto is not easy! Simple changes in the algorithm could make the underlying system insecure! CryptoSystems usually fail because of implementation. Unlike theory, in practice cryptosystems do not work in isolation.

36 Possible Implementation Pitfalls Not using publicly tested algorithms Do not use any algorithm that has not been tested by the crypto community extensively. Remember what happened to original DVD encryption Not using algorithms correctly I.e., Using AES in ECB mode or RSA function directly. Not generating randomness correctly. Note that CBC mode could be insecure if the IV is not generated randomly.

37 More on Random Number Generation Generic pseudo-random number generation is not secure. Must use provably-secure pseudo-random number generators (see the Anderson book for details.)

38 Issues Related to Key Management Secret keys should be generated randomly. Secret keys should be protected. Your implementation should not leave keys in memory. Need to consider the trust model carefully. i.e., can someone easily access the secret key files? What happens if you have trojan on your computer? What happens if there is a system failure?

39 Weakest Link: Users Users choose easy to guess passwords. Always make sure that chosen passwords are strong. They can be easily tricked into revealing passwords Consider two, three factor authentication methods.

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