Internet Security 1 ( IntSi1 )

Internet Security 1 (IntSi1) 9 Cryptographical Strength Prof. Dr. Andreas Steffen Institute for Internet Technologies andApplications (ITA)

Chat: Cryptographical Strength Needed Today? Recommended Algorithms Key Size True Strength SymmetricEncryption bits bits Data Integrity(HashFunction) bits bits Key Exchangebetween Peers bits bits Digital Signature bits bits Public Key Encryption bits bits User Password chars bits

Cryptographical Strength Needed Today? Recommended Algorithms Key Size True Strength SymmetricEncryption AES (CBC or Counter-Mode) 128 bits 128 bits Data Integrity /Hash Function SHA-256 256 bits 128 bits Key Exchangebetween Peers Diffie Hellmanwith Prime Modulus (MODP) 3072 bits 128 bits Digital Signature RSA / DSA 3072 bits 128 bits Public Key Encryption RSA / El Gamal 3072 bits 128 bits User Password Abbreviated Passphrase 13* chars ≈78 bits *22 base64 characterswouldberequiredfor 128 bitstrength but impossibletomemorize!

EquivalentCryptographicStrength 128 bitstrength: number of private keysignatures per second* RSA 3072 32 ECDSA 256 546 192 bitstrength: number of private keysignatures per second* RSA 8192 1 ECDSA 384 233 *measured on an Intel Core2Duo T9400 platform (onecore, 32 bitLinux OS)

Internet Security 1 (IntSi1) 9.1 NSA Suite B Cryptography

NSA Suite B Cryptography 2005 • The secure sharing of information motivates the need for widespread cryptographic interoperability that meet appropriate security standards to protect classified information at the SECRET level. • NSA has initiated three efforts to address these needs: • TheCryptographicInteroperabilityStrategy. • Expanding the use of GOTS products that meet a revised set ofsecurity standards to protect information up to the SECRET level. • Layered use of COTS products that meet a more robust set ofsecurity standards to protect information up to the SECRET level. • Several IETF protocol standards have been identified as having potential widespread use. IETF RFCs have been established to allow the use of Suite B Cryptography with these protocols.

NSA Suite B with 128 Bit Security Recommended Algorithms Key Size True Strength SymmetricEncryption AES 128 bits 128 bits Hash Function SHA-256 256 bits 128 bits AuthenticatedEncryption AES-GCM(Galois-Counter-Mode) 128 bits 128 bits Key Exchangebetween Peers Elliptic Curve Diffie Hellman(ECP) 256 bits 128 bits Digital Signature EllipticCurve DSA 256 bits 128 bits

NSA Suite B with 192 Bit Security (SECRET) * AES with 192 bit key is optional. Therefore AES with a 256 bit key is mandated. Recommended Algorithms Key Size True Strength SymmetricEncryption AES 256* bits 256 bits Data Integrity / Hash Function SHA-384 384 bits 192 bits Authenticated Encryption AES-GCM(Galois-Counter-Mode) 256* bits 256 bits Key Exchangebetween Peers Elliptic Curve Diffie Hellman(ECP) 384 bits 192 bits Digital Signature ECDSA 384 bits 192 bits

Microsoft Windows with Suite B Support • Windows Vista SP1 • Windows 7 • Windows Server 2008 • Windows Server 2008 R2

strongSwan VPN Solution with Suite B Support # ipsec.secrets for gateway moon : ECDSA moonKey.der # ipsec.conf for gateway moon conn rw keyexchange=ikev2 ike=aes256-sha384-ecp384,aes128-sha256-ecp256! esp=aes256gcm16,aes128gcm16! leftsubnet=10.1.0.0/24 leftcert=moonCert.der leftid=@moon.strongswan.org right=%any rightsourceip=10.3.0.0/24 auto=add rw[1]: ESTABLISHED 9 seconds ago, 192.168.0.1[moon.strongswan.org]... 192.168.0.100[carol@strongswan.org] rw[1]: IKE SPIs: 7c1dcd22a8266a3b_i 12bc51bc21994cdc_r*, rw[1]: IKE proposal: AES_CBC_128/HMAC_SHA2_256_128/PRF_HMAC_SHA2_256/ECP_256 rw{1}: INSTALLED, TUNNEL, ESP SPIs: c05d34cd_i c9f09b38_o rw{1}: AES_GCM_16_128, 84 bytes_i (6s ago), 84 bytes_o (6s ago), rw{1}: 10.1.0.0/24 === 10.3.0.1/32

Internet Security 1 (IntSi1) 9.2 Whatthe Heck are EllipticCurves!

What are Elliptic Curves? General form: y2 = x3 + ax + b Condition for distinctsingle roots: 4a3 +27b2 0 Example: y2 = x3 4x = x(x 2)(x +2)

What is an Algebraic Group <G,> ? A group is an algebraic system consisting of a set G and anoperation  such that for all elements a, b and c in G thefollowing conditions must be fulfilled: • Closure: a  b mustremain in G • Associativity: a  (b  c) = (a  b)  c • Neutral Element: a  e = e  a = a • Inverse Element: a  a'= a' a= e • Commutativity: a  b = b  a (Abelian Group) Examples: • Addition: <R, +> e = 0 , a'= -a • Multiplication: <R-{0}, · > e = 1 , a'= a-1

R P Q R' Points P(x,y) on an Elliptic Curve form a Group Group set: All points P(x,y) lyingon an elliptic curve Group operation: Point addition R = P+Q

P P' Neutral and Inverse Elements Inverse element: P'(x,-y) = P(x,y) is mirrored on x-axis Point addition with inverse element: P + P' = O results in a neutralelement O(x,)at infinity Neutral element: P + O = P O

R P R' Point Doubling – Adding a point to itself Point Doubling: Form the tangent in Point P(x,y) R = P+P =2P

2P P 3P Point Iteration – Adding a point k-1 times to itself Point Iteration: kP = P+P + ... +P

Elliptic curves can be defined in a finite or Galois field GFp: y2 = x3 + ax + b mod p where the field size p is a prime number and {0,1, ..., p-1} is an abelian group under addition mod p and {1, ..., p-1} is an abelian group under multiplication mod p. How can Geometry be useful for Cryptography?

Diffie-Hellman: Basis g and prime p A = gamod p Common secret: s = Ab = Ba= gabmod p B = gbmod p • Elliptic Curve Cryptosystem: ECC, basis point P and prime p QA = aP Common secret: S = bQA = aQB= abP QB = bP Cryptographic Application – Secret Key Exchange

Internet Security 1 (IntSi1) 9.3 Authenticated Encryption with Associated Data (AEAD)

AuthenticatedEncryptionwithAssociated Data • AEAD isbased on specialblock ciphermodes: • Block size: 128 bits • Key size: 128/256 bits • Tag size : 128/96/64 bits • Noncesize: 128 bits32 bits 64 bits 32 bits • Recommended AEAD Modes: AES-Galois/CounterModeAES-GMAC (auth. only) • Alternative AEAD Modes:AES-CCMCAMELLIA-GCMCAMELLIA-CCM Salt IV 2 Salt IV 0 Salt IV 1 Key K Key K Salt IV Counter HashSubkey Derivation 0………………..0 Key K HashSubkey H

Internet Security 1 (IntSi1) 9.4 Practical Passwords

Random Passwords with 128 Bits of Entropy • Digits (0..9): 39 digits  3.3 bits/digits • 39475 10485 98021 43380 05872 49759 70291 2634 • Hexadecimal (0..F): 32 nibbles  4 bits/nibble • 3F8A 84D1EA7B 5092 C64F 8EA6 73BD F01B • Alphabet (A..Z): 28 characters  4.7 bits/character • AWORH GHJBP IUCMX MLZFQ TZDOP ZJV • Alphabet & Digits (A..Z, 0..9): 25 symbols  5.2 bits/symbol • E5RGL UPQ7A 8F3ZP NWTIC 22JBM • Base64 (A..Z, a..z, 0..9, /, +): 22 symbols  6 bits/symbol • y5GNa Riq92 VCm4Q 1BOKl x0 • Cryptographically strong passwords are nearly impossibleto remember and very error-prone to type in blinded mode!

1 CPU A…Z A…Z, 0…9 A…Z, a…z, 0…9 Length 26 symbols 36 symbols 62 symbols 6 48 sec 6 min 2 hours 8 9 hours 5 days 1 year 10 251 days 18 years 4‘094 years Assumption: 2.2 GHz Intel Core Duo CPU  ca. 6’500'000 MD5 password hashes/sec 30 CPUs A…Z A…Z, 0…9 A…Z, a…z, 0…9 Length 26 symbols 36 symbols 62 symbols 6 2 sec 11 sec 5 min 8 18 min 4 hours 13 days Compromise 10 8 days 1 year 136 years Practical Passwords Example of a good 8 character pseudo-random password: Aufbruch zu neuen Horizonten um 4Uhr morgens: AznHu4Um change every month!

Internet Security 1 ( IntSi1 )