Applied Cryptography Lecture 8 - Cryptography II PDF

Applied Cryptography Lecture #8 Public Key Cryptography II College of Computing and IT 1 Remember (Lect.07) Public key Private key Diffie–Hellman Key Exchange  The Diffie–Hellman key exchange (DHKE), proposed by Whitfield Diffie and Martin Hellman in 1976 provides a pract...

Applied Cryptography Lecture #8 Public Key Cryptography II College of Computing and IT 1 Remember (Lect.07) Public key Private key Diffie–Hellman Key Exchange  The Diffie–Hellman key exchange (DHKE), proposed by Whitfield Diffie and Martin Hellman in 1976 provides a practical solution to the key distribution problem.  It enables two parties to derive a common secret key by communicating over an insecure channel.  The security of the Diffie-Hellman key exchange is based on the discrete logarithm problem (DLP). Diffie–Hellman Key Exchange  DHKE Description  In this protocol we have two parties, Alice and Bob, who would like to establish a shared secret key.  It is possible that Alice or Bob generate the public parameters which are needed for the key exchange.  The DHKE consists of two protocols, the set- up protocol and the main protocol, which performs the actual key exchange. DHKE Description  The set-up protocol consists of the following steps:  These two values (p, α) are sometimes referred to as domain parameters. DHKE Description  If Alice and Bob both know the public parameters p and α computed in the set-up phase, they can generate a joint secret key k with the following key-exchange protocol: DHKE Description  Alice and Bob in fact compute the same session key kAB:  Thus Alice and Bob both share the session key kAB ≡ αab mod p. The key is used to establish a secure communication between Alice and Bob, e.g., by using kAB as key for a symmetric algorithm like AES or 3DES. DHKE Example  Example 1: The Diffie–Hellman domain parameters are p = 29 and α = 2.  The key-exchange protocol as follows: DHKE Example  During the actual protocol, we first have to choose the private keys a and b.  They should stem from a true random generator in order to prevent an attacker from guessing them.  The public keys A and B are typically precomputed.  The main computation that needs to be done for a key exchange is thus the exponentiation for the session key. Hash Functions  A hash function h usually means a function that compresses or compute a digest of a message which is a short, fixed-length bitstring. Hash Functions  The message digest, or hash value, can be seen as the fingerprint of a message, i.e., a unique representation of a message.  If the message digest is transmitted securely, then changes to the message can be detected.  Hash functions are used in many parts of cryptography, and there are many different types of hash functions, with differing security properties. Uses of Hash Functions  Message authentication  Integrity checks  Digital signature  Timestamping  Password hashing Uses of Hash Functions  Practical hash functions have output lengths between 128–512 bits.  The computed fingerprint should be highly sensitive to all input bits. That means even if we make minor modifications to the input x, the fingerprint should look very different. Hash Functions Properties  Hash Functions Properties 2. 2nd-preimage resistance—it is essential that two different messages do not hash to the same value. This means it should be computationally infeasible to create two different messages x1 ≠ x2 with equal hash values z1 = h(x1)= h(x2)= z2. Hash Functions Properties Hash Functions Properties 3. collision resistance—We call a hash function collision resistant or strong collision resistant if it is computationally infeasible to find two different inputs x1 ≠ x2 with h(x1)= h(x2). (Note that here there is free choice of both inputs.) Message-Digest Family (MD)  Family of cryptographic hash functions designed by Ron Rivest starting in 1989.  MD2: produces a 128-bit hash value, perceived as slower and less secure than MD4 and MD5.  MD4: produces a 128-bit hash of the message, using bit operations on 32-bit operands for fast implementation.  MD5: produces a 128-bit output, specified as Internet standard in 1992; till relatively recently was widely used. Secure Hash Algorithm Family (SHA)  SHA was designed by NIST and is the US federal standard for hash functions, specified in 1993. (SHA-0)  SHA-1, revised version of SHA, produces 160- bit hash values specified in 1995.  NIST have issued a revision that adds 3 additional hash algorithms: SHA-256, SHA-384, SHA-512, designed for compatibility with increased security provided by AES. Cryptographic Hash Functions  An overview of the main parameters of the cryptographic hash functions. SHA-256 Compression Function  The value of K[i] in all rounds is pre-initialized, W[i] is calculated individually for each block. Properties of Hash Functions  We summarize all important properties of hash functions h(x). Microsoft Hash  In a Windows machine, passwords aren't stored in cleartext, and they're not even stored in an encrypted format, they're actually stored as hashes.  Local Area Network (LAN) Manager (LM Hash): Original version of password hashing used by Windows that uses Data Encryption Standard (DES) and is limited to 14 characters.  Network LM Hash (NTLM Hash): Replacement for LM Hash that uses RC4 instead of DES and was released with Windows NT 3.1 in 1993. Microsoft Hash  NTLMv2 Hash: It relies on the HMAC-MD5 hash and is considered difficult to crack.  Hash-based Message Authentication Code (HMAC): is a cryptographic authentication technique that uses a hash function and a secret key.  Kerberos: using AES encryption for tickets in Kerberos authentication. Hashing Attacks  Pass the Hash: A technique that allows an attacker to authenticate to a remote server or service by using the underlying NTLM or LM hash instead of requiring the associated plaintext password.  Birthday Attack: occurs when an attacker is able to send two different messages through a hash algorithm and it results in the same identical hash digest causing a collision.  So, the hacker can use this as an attack against your system. Hashing Attacks  To prevent the Pass the Hash attack: 1. Only use a trusted operating systems 2. Use multifactor authentication 3. Patch/update workstations 4. Use least privilege Increasing Hash Security 1. Key Stretching: A technique that is used to mitigate a weaker key by increasing its effectiveness and thereby increasing the time needed to crack it. ◦ WiFi Protected Access (WPA), WPA2, and other algorithms utilize key stretching. ◦ A “nonce” is used to prevent password reuse. Increasing Hash Security 2. Salting: Adding random data into a one-way cryptographic hash to help protect against password cracking techniques. Exercise What is the common secret key of the Diffie-Hellman protocol works with the following parameters: p = 17, α = 3, a=7, b = 4 Thank you  Any questions? 31