Introduction to Security and Crypto

1. Introduction to Security and Crypto

2. Agenda • Basics of security • Basics of cryptography • Symmetric Crypto • DES example, block chaining • Key exchange, Asymetric Crypto • RSA example • Public Key Infrastructure • Trust Provisionning • Attacks and how to cope with it • Attacks on Algorithms • Attacks on Implementations • Attacks on Protocols • Two Examples • A7 FS-application Trust provisioning + Offline Authentication • TLS and support of A70CM

3. Embedded NFC Basics of Security

4. Tue, at 10 at my place. Alice Mon, at 10 at my place. Alice At 10 at my place Alice At 10 at my place Anneliese Alice Security Goals Confidentiality: Eavesdropping possible? Authenticity: Sender correct? Integrity: Message modified? Non-Repudiation: Message signed? But also: Availability (i.e.: preventing denial of service), Privacy (personal data towards merchant or third parties)

5. Security Goals and Algorithms Authenticity: Asymmetric Crypto / Signature / Hash Confidentiality: Symmetric Crypto Integrity: Hash / Signature / MAC Non-repudiation: Hash / Signature

6. There is no such thing as „perfect security“ There is no such thing as “perfect security” – A secure system makes an attack more expensive than the value of the advantage gained by the attacker.

7. Attacks & Principles • Kerckhoffs’ principle: The attacker always knows the algorithm; the only information unknown to him/her is the key. • Brute force attack • Exhaustive search over all keys • Single plaintext-ciphertext-pair may be enough to determine the correct key • Cannot be avoided • Goal: Make it practically infeasible, i.e. key space is so large that the search takes more than a lifetime • Side Channel Attacks: • Even if a cryptographic algorithm offers high level of security, its implementation may still leak information about secrets or keys: timing behavior, current consumption, electromagnetic radiation etc establish so called side channels for secret information. • There is no such thing as “perfect security” – A secure system makes an attack more expensive than the value of the advantage gained by the attacker.

8. There is no such thing as „perfect security“

9. Embedded NFC Basics of Cryptography Symmetric Crypto

10. Symmetric Encryption Key Key Plaintext Plaintext Ciphertext Encryption DES Triple-DES AES Decryption DES-1 Triple-DES-1 AES-1  Confidentiality: Eavesdropping not easily possible

11. Introduction - What is Android ? Platform Architecture Platform Components Platform Initialization How to get Android sources A bit of history… The Caesar cipher

12. Introduction - What is Android ? Platform Architecture Platform Components Platform Initialization How to get Android sources Block Ciphers DES Block Chaining

13. Symmetric Encryption : DES

14. Algorithm Block m4 Block m3 Block c2 Block c1 Symmetric block ciphers: DES and AES • Plaintextisdividedintoblocks m1, m2, ... ofthe same length • Every block isencryptedunderthe same key. • Typical block lengths: DES – 64 bit, AES – 128 bit • Typicalkeylengths: DES – 56 bit; AES – 128, 192, 256 bit

15. L0 R0 Input 64 bit K1 Key 56 bit F Permutation IP L1 R1 round i Round key i round 16 Round key 16 Permutation IP –1 L15 R15 K16 Output 64 bit F L16 R16 R16 DES - Data Encryption Standard • Most important example for Feistel ciphers (ie: same operations to encrypt and decrypt) • Published in 1977 as a standard for the American governmental institutions • Significant weakness: 56 bit key is too short 1999 Deep Crack: 100.000 PCs computed key within 22 hours and 15 minutes

16. Block m4 Block m3 Block c2 Block c1 Algorithm Modes of Operation • Modes of Operation • How to ensure that the ordering of blocks is not changed by an attacker? • Dependencies between encrypted blocks: Cipher Block Chaining (CBC)

17. Problems of block encryption ECB-Example: Electronic Code Book Mode: Identical blocks are identically encrypted. m1 m2 m3 (3)DES Enciphering (3)DES Enciphering (3)DES Enciphering c1 c2 c3

18. m1 m2 m3 IV (3)DES Enciphering (3)DES Enciphering (3)DES Enciphering c1 c2 c3 CBC Mode CBC-Example: Cipher Block Chaining Mode: Identical blocks are differently encrypted.

19. Triple-DES • Triple-DES = triple encryption using DES with two or three external keys: DES(k1, DES-1(k2, DES(k1,m))) • Question: Why is the decryption DES-1 in the middle? Compatibility: When implementing Triple-DES and choosing k1 = k2, then one gets the single DES. Therefore, only one algorithm needs to be implemented to get Triple-DES and single DES. • Question: Why is not Double-DES used instead of Triple-DES? Meet-in-the-middle attack! • Security comparison • Two keys – NIST estimation: effectively 80 bits • Three keys – NIST estimation: effectively 112 bits

20. plaintext  Round key 0 Round 1 (round key 1) Round 2 (round key 2) Round n (round key n) ciphertext ByteSub ShiftRow MixColumn AddRoundKey AES – Scheme • AES is standardized for key lengths of 128 bit, 192 bit, 256 bit, and block size of 128 bit. • The number of rounds depends on key length used: 10 up to 14 • Round Function:

21. Security Goals andAlgorithms; HASH Function Authentication: Asymmetric Crypto / Signature / Hash Confidentiality: Symmetric Crypto Integrity: Hash / Signature / MAC Non-repudiation: Hash / Signature

22. Hashfunctions • Analogy: digital fingerprints • Compression: Data ofarbitrarylengthismappedto n bits. (Typicalvalues: 128/160 bits) • Cryptographicproperties • Preimageof a hashishardto find. • Twodataelementswiththe same hashvaluearehardto find (Collisions). Data Hash

23. m m' m m m' Hashfunctions • Compression: Data ofarbitrarylengthismappedto n bits. • Preimageof a hashishardto find.One-wayness: Givenh(m) findingmisinfeasible. • Twodataelementswiththe same hashvaluearehardto find (Collisions).Collisionresistance:Itisinfeasibleto find mandm‘whicharemappedtothe same value. (birthday paradox; outputshouldbeat least 160 bits) h(m)

24. Secure Hash Algorithm (SHA) • First version: SHA-0 (160 bit output) in early 90s • SHA-1 only a minor change to SHA-0 • Chinese Research Group attacked SHA-1: • On collision resistance only expected effort: 280, real effort 263 (Birthday paradox) • Applicability highly depends on application • SHA-224,256,512 etc … xxx giving the length of output • SHA-3 in reviewandselectionprocess

25. At 10 at my place Alice At 10 at my place Anneliese Authentication The active attacker: Who is the origin of a message? Message Authentication Codes: MAC, HASH K m, MAC Message Authentication Code (“symmetric signature”) A authenticates her message by computing a tagMAC and sends it together with the message to B.B can verify this tag by re-computing it and checkwhether the two results match. m, K computesMAC= HK(m) verifiesMAC = HK(m) ? The function H can be either a hash function (SHA, MD5), or a symetric block cipher based on DES or AES (CMAC,…).  Integrity: Message can’t be easily modified

26. Introduction - What is Android ? Platform Architecture Platform Components Platform Initialization How to get Android sources Key Exchange Asymmetric Crypto

27. What about the Keys? • Alice and Bob need to share the same key. How to share it securely? • Pre distribution? (ie: keys exchanges in a “secure environment”) • Trust provisionning (see later) • Secured Key Exchange • Diffie Hellman and asymetric cryptography

28. Diffie Hellmann Key Exchange Private “keys” Public “keys”

29. Asymmetric Crypto: The Idea Bob‘s Public Key Bob‘s Private Key Plaintext Plaintext Ciphertext Encryption RSA ECC Decryption RSA ECC

30. AsymmetricCrypto: Signatures Bob‘s Private Key Bob‘s Public Key Plaintext, Hash Plaintextverified Plaintext, Hash, Signature Signature Generation (Decryption) RSA ECC SignatureVerification (Encryption andComparewith Hash) RSA ECC

31. Everyone can put a letter into Bob‘s mailbox.Everyone can encrypt message for Bob.Everyonecan verify Bob’s signature Encryption Decryption Hello Bob, .... ... Hello Bob, .... ... Bob Principles of Asymmetric Encryption Only Bob can open his mailbox with his private key.Only Bob can decrypt with his private key. Only Bob can create his own signature

32. Comparison Symmetric - Asymmetric

33. Introduction - What is Android ? Platform Architecture Platform Components Platform Initialization How to get Android sources Asymmetric Crypto: RSA

34. dB A: nA,eA B: nB,eB C : nC,eC dC dA RSA • Based on the so called factorization problem: • Given two prime numbers, it is easy to multiply them. Given the product, it is difficult to find the prime numbers. • RSA Keys – Every participant has • a modulus n = p*q (public), the product of two large prime numbers • a public exponent e(for performance reasons, one often chooses small prime numbers with few 1’s) • a private exponent d.

35. RSA - Operation Encryption Decryption The sender computes c = me mod n, where m is the message, (n, e)is the public key of the receiver, and cis the cipher text. The receiver computes cd mod n, where c is the cipher text and d is the private key of the receiver. It holds:cd mod n = med mod n = m. • For signing it is the other way round: • Signing is the same operation as decrypting • Verifying a signature is the same operation as encrypting

36. RSA – SomeMath c = memod n and m = cdmod n - Why? • Primes p, q ; n = p*q • Thus, φ(n) = (p-1)*(q-1) = |{ x | x and n arecoprime }|. • Euler‘s Theorem: cφ(n) mod n = 1 mod n • Let e, d such that • e andφ(n) arecoprime, thus inverse of e modφ(n) exists • e*d = 1 modφ(n) • Let‘sprove RSA: • cdmod n = (me)dmod n = medmod n // substitution = m1+k*φ(n)mod n = m1 * mk*φ(n)mod n // definitionmodulo = m1 * (mφ(n)) k mod n = m * 1kmod n // Euler‘s Theorem= m

37. RSA • Size of the RSA keys • The bit length of the modulus is called the size of an RSA key. The public exponent is usually a lot shorter; the private exponent is of the same length as the modulus. • Today, everything larger than 1024 2048 bit is considered to be secure. • Implementation • Chinese Remainder Theorem (CRT) is a mathematical fact that allows to make decryption and signing significantly more efficient. Has to be carefully implemented in order to be secure. • Implementation without CRT is often called “straight forward” – significantly less performance, but usually less security issues as well

38. Embedded NFC Public Key Infrastructure

39. A : E A B : E B E X C : E CU : E U V : E V Threat: Authenticity of Public Keys • AttackMr. X replaces B’s public key EB by his own public key EX. • Consequences: • Encryption: Only X can read messages that are meant for B. • Signature: B’s signatures are not verifiable – B’s signatures are invalid! X can sign messages that are verified as Bob’s signatures.

40. DCA Certificates DA A, EA Cert(A) • Name and public key are signed by a trustworthy institution (certification authority, CA). • Message (name, public key) and the CA’s signature on it are called “certificate”: Cert(A) = {A, EA}, DCA{A, EA} • Format of Certificates have to be specified – X.509 for example • Tree-likestructurepossible – pathoftrust

41. Random numbers • Facts: • In cryptography, often “unpredictable” numbers are needed (for keys for example). • Example: Generate a 128 bit AES key – required is, that even if an attacker “knows” 127 bits of this key, he should not be able to guess the missing bit with a better probability than ½. • There is NO mathematical way to determine whether the outcome of an “random number generator” is unpredictable!!!! • The best thing offered by mathematicians are statistical tests: but they can only test whether a sequence of random numbers has a specific structure or property (and hence is NOT unpredictable). A statistical test never gives a POSITIVE result. Passing a test, only means a sequence does not have one specific (of many) negative properties.

42. Unpredictablerandomnumbers

43. Block Diagram of Random Number Generator