Chapter 8: Secret and Public Keys Study Notes

Chapter 8: Secret and Public Keys

Overview of Chapter 8

• Managing and Using Secret Keys: Discusses methodologies for effectively handling secret keys.

• Wrapping Techniques for Secret Keys: Details on how to secure secret keys during distribution.

• Detecting Errors and Protecting File Integrity: Mechanisms to monitor and maintain data integrity.

• Public-Key Cryptography: An overview of public-key cryptography and its future implications with quantum cryptography.

• Public-Key Techniques for Signing Data: How public keys can be used to sign and wrap data securely.

• Public-Key Certificates: The role and structure of public-key certificates in securing communications.

Key Management Challenges (Dr. Z)

• Protecting Secret Keys: Instead of protecting large amounts of secret data, it is more efficient to protect smaller secret keys according to Kerckhoffs's (or Shannon's) principle:

  • Kerckhoffs's Principle: The security of a cryptosystem should depend solely on the secrecy of the key, not the secrecy of the algorithm.

• Challenges include:

  • Key Distribution: Ensure secret keys are shared only with authorized individuals or systems.

  • Key Generation: Keys must be sufficiently random to resist guessing by attackers.

  • Key Handling: Keys must be managed and stored securely to prevent interception or leakage.

• Cryptonet: A group of entities sharing the same secret key, fostering a network of transitive trust. Trust in one member implies trust in all others.

Rekeying – Changing Old Keys

• Encryption Risk: The more data encrypted with a key, the greater the risk of exposure through cryptanalysis.

• Rekeying Strategy: To minimize risks, rekey periodically by replacing old keys with new ones.

  • Cryptoperiod: The defined time during which a key is deemed safe to use.

    • General Recommendations:

      • Rarely used keys should have a cryptoperiod of about 2 years.

      • Heavily used keys should be changed as frequently as practical.

  • Key Principle: Rekeying presents a trade-off between performance and security; shorter cryptoperiods enhance safety but require more frequent management.

Key Distribution Methods

• Person-to-Person Exchange: Safe but inefficient for large-scale systems.

• Common Methods:

  • Verbal Exchange: Effective for short, memorable keys.

  • Paper Exchange: Keys can be securely written and handed over but require protection against theft/loss.

  • Electronic Exchange: Convenient but risks include sniffing and unauthorized duplication. Secure methods for electronic exchange will be covered later.

• Key Questions to Address:

  • How to prevent sniffing or interception during transmission.

  • How to stop unauthorized copying of keys once distributed.

Crypto Keys in Text Format

• Useful for encrypting shared files, allowing for verbal or paper exchange.

• Key Conversion Question: How to convert text phrases into bits for digital encryption algorithms that operate on binary data. Any text-based key must be converted into bits before use in encryption.

Passphrase as Key: Simple Case (Dr. Z)

• Concern: Passwords may not fit key size exactly.

• Textual Keys vs. Binary Keys:

  • Textual keys are flexible and can be shared verbally or in text files.

  • Binary keys, especially large ones, are difficult to memorize. They often require secure storage which may risk exposure.

Passphrase as Key: Better Case

• Use of One-Way Hashes:

  • Passphrase is hashed to produce a key (Internal Key) before being used in encryption algorithms.

• Model:

  • Text Passphrase → Hash Value → Internal Key.

  • Data is encrypted using the Internal Key generating ciphertext.

Checklist for Secure Key Handling

• Use a password or a passphrase.

• Allow long passphrases for better security.

• Preserve the full entropy of the passphrase entire key operation.

• Erase the passphrase from memory immediately after use.

• Facilitate user retention of passphrases securely.

• Avoid storing passphrases on disk unless encrypted.

• Disable input echoing during passphrase entry to mask input.

• Utilize each internal key for a single file only.

Key Strength

• A longer key with a diverse character set yields more entropy.

• Entropy: The amount of randomness or unpredictability in the key which increases the search space against attacks.

• Memorization Trade-off::

  • Passwords with unusual characters or misspellings are hard to remember.

  • Longer passphrases with regular words and syntax are easier to recall.

The Reused Key Stream Problem

• Illustration of Problem:

  • Plaintext Key Stream and resulting Ciphertext demonstrate how reusing key streams can compromise security.

• Bit Management: XOR function combines duplicate ciphertexts, allowing recovery of original plaintext messages; key management hence requires separate keys for separate messages in stream ciphers.

Using a Nonce

• Nonce is introduced in the encryption process to prevent duplicate key streams during encryption using a key wrapped approach, through the use of hashes and keys leading to ciphertext.

Key Wrapping: A Building Block

• Random Source and Wrapped Keys: Key wrapping involves using a Key Encryption Key (KEK) which is made up of a one-way hash of the passkey to securely transmit a Data Encryption Key (DEK) (CEK) within the principle of encrypted files.

Key Splitting - Simplified Wrapping

• A method of securely sharing keys (CEK and KEK) individually, reducing the risk of interception by sealing away components from potential attackers.

Separation of Duty: A Principle

• Task division requiring multiple individuals to complete promotes security as it requires cooperation for illicit actions. Examples include:

• Business Example: Dual signature checks for financial approvals.

• Military Example: Launching nuclear missiles requires dual confirmations.

Public-Key Cryptography (Dr. Z)

• Techniques enable secure communication without prior shared secrets. Notable techniques:

  • Diffie-Hellman (Merkle): Allows the construction of a shared secret using public information.

  • Rivest-Shamir-Adleman (RSA): Encrypts data for recipient’s reading while providing means to verify senders’ signatures.

Public and Private Keys

• Users maintain a temporary secret for transactions:

  • Create and discard shared secret key post-transaction to minimize cryptanalysis exposures.

• Public/private key architecture:

  • Public keys are shareable, private keys are secured.

Constructing a Key Pair

• The process involves constructing both a public and private key for an entity (e.g., Alice) based on random input.

Diffie-Hellman Secret Sharing

• Process utilizing public keys shared between entities (e.g., Bob and Alice) to create a shared secret through mathematical methods.

Elliptic Curve Cryptography

• Similar to Diffie-Hellman, utilizes elliptic curve mathematics for secure key exchanges:

• Formula: (y² = x² + ax + b) (mod p).

• This approach allows for smaller key sizes while maintaining effective security.

Quantum Theory and Cryptography

• Quantum Key Distribution: Based on Heisenberg's Uncertainty Principle to detect eavesdropping.

• Quantum Cryptanalysis: Developments like Shor's algorithm can undermine traditional public-key systems; hence, post-quantum research does exist to confront these potential threats.

RSA In Practice

• RSA revolves around a fundamental calculation involving large integers: C = M^x ext{ mod } N where:

  • N is a product of two prime numbers.

  • e is a public exponent and d is a secret exponent.

  • M is the plaintext, and C is the resulting ciphertext.

  • Encryption and decryption require the appropriate keys (e or d).

Key Wrapping with RSA

• Utilizing RSA to wrap keys involves an encryption process where data keys are encapsulated into ciphertext for transport security.

Attacking Public Key Crypto

• The strength of public key systems resides in the large prime numbers used. Attack strategies focus on efficient factorization of these primes.

• Attacking RSA:

  • Vulnerability assessment includes small plain texts and timing analysis for capturing key information.

Data Integrity

• Encryption fails to guarantee data integrity; hence mechanisms are required to detect changes, whether malicious or accidental.

• Detection Methods: Utilizing hash functions similar to Error Detection Codes (EDCs).

Bit Flipping Attack on Ciphertext

• Example illustrated to show how modifying ciphertext can alter plaintext through deliberate changes in encrypted data.

Checking Data Protection

• A checksum is calculated post-encryption to verify data integrity, aiding in detecting unauthorized changes post-encryption.

Birthday Attack on a Check Value

• Demonstrates the theoretical framework for exploiting hash collisions to adjust values covertly within digital documents, impacting data integrity.

Alternative: Encrypting a Hash

• Efficiency in digital signing and integrity validation can be achieved by hashing content and then encrypting the hash rather than the full message.

Keyed Hash: More Efficient

• A secure method to ensure integrity while maintaining a level of efficiency with digital signatures related to the content.

Public Keys and Digital Signatures

• Mechanism outlined where Bob signs a transaction, which is subsequently verified through asymmetric techniques utilizing public keys to validate authenticity.

Constructing an RSA Digital Signature

• Process detailing how to create a digital signature using RSA securely, involving public/private keys and the signing function.

Verifying an RSA Digital Signature

• Steps taken to validate the authenticity of a digital signature, ensuring integrity and authenticity of the transaction or message.

The MITM or Bucket Brigade Attack

• Illustrates the concept of man-in-the-middle attacks where an attacker can impersonate another entity and intercept/alter communications, undermining trust.

Public-Key Certificates

• Certificates establish trust in public keys through digital signatures from Certificate Authorities (CAs) ensuring public key authenticity.

Interpreting Certificates

• Certificates can be organized hierarchically whereby root certificates validate subordinate certificates, ensuring an organized trust model.