Cryptography Basics

Attacks

There are two ways to break cryptography system:

• brute force - protection against it is to have so many password possibilities that it’d be infeasible to try to break it. Another way is to limit the amount of attacks that may be performed in a period of time
• finding the algorithm weakness

An algorithm is well designed if its security does not depend on keeping the algorithm itself secret.

Hash

Examples: MD5 (broken), SHA-1 (broken), SHA-2, SHA-3

Hash function turns some data into an irreversible digest. It’s used mostly to check if data is correct - if it matches a known hash/digest (data integrity).

SHA-256 is a good enough choice, but SHA-3 is recommended.

Hash functions have the following properties:

• pre-image resistance - we can’t get back from the result to the initial form
• second pre-image resistance - given some input and output, we’ll not find another input with the same output
• collision resistance - there are no two different inputs that result in the same output.

MAC

Examples: HMAC, KMAC

Uses hash function together with a private key (known to both the sender and the receiver). It’s mostly used to verify that the received data is correct (when we create MAC by ourselves, it matches the received MAC) and sent by authorized entity (it had to know the secret to create a MAC). The received data consists of raw data and a MAC. The receiver should calculate the MAC from the raw data and compare it with the received MAC.

MAc can be used for cookies. After login, we can return a cookie containing a MAC of the login name. Since only the server knows the secret that is used to produce a MAC, users cannot provide fake MACs.

HMAC

A way to generate a MAC. It uses a pair of a hashing function and a secret key to generate a MAC from some message.

Encryption does not guarantee integrity. The receiver of encrypted data does not know if the received string has not been altered by someone (that someone would not know the plain text, though). It’s a good practice to first encrypt the plain text and then HMAC it to get a MAC of the encrypted data. A receiver can check if the encrypted string is correct and then they can decrypt it. Then the receiver would need to know two secrets - HMAC secret and the encryption key. Or, a seed might be used.

Nonce

A number attached to the message. There shouldn’t be two messages with the same nonces. It guards against replay attacks.

Symmetric Encryption

Examples: AES (128, 192, or 256 bits)

The bits in the algorithm name refer to the amount of bits in the key.

AES-128 is commonly used, it provides good enough encryption.

Authenticated Symmetric Encryption

Ciphers generated with AES may be tempered with, and the result of decryption might be invalid. That’s why we call it Unauthenticated encryption - we don’t know if the cipher is valid.

Authenticated encryption is used instead to provide some guarantees about validity of the cipher. AES-GCM and ChaCha20-Poly1305 are used most often.

Asymmetric Encryption

Examples: Diffie-Hellman (DH), RSA, ECDH (Elliptic Curve DH) (recommended)

Calculating a public key from a private key is simple. The opposite is computationally infeasible.

Encrypting some data with a private key is called signing. Everyone can decrypt it, but they can be sure that it was encrypted by the owner of the private key. It helps to establish trust. If we trust the signer, then we can trust the content of the message that was signed.

Encrypting some data with a public key ensures that only an owner of the private key will be able to read it.

The size of data to be encrypted cannot be too big (~500 characters). Usually, the symmetric key gets encrypted with a public key, and then the parties use that symmetric key to encrypt the actual messages. Additionally, symmetric encryption/decryption is much faster than asymmetric operations.

Authenticated Encryption

Similarly to symmetric encryption, we need a way to be sure that we got a public key of the entity we believe we got it from. If we don’t have a way to verify that then the key exchange is unauthenticated.

Asymmetric communication can be authenticated (one-sided authentication) or mutually authenticated.

Digital Signature

Signing a piece of data creates a digital signature. It is similar to the MAC. Such a signature provides a proof of authenticity and integrity (like MAC). Additionally, it:

• allows to verify the signature by anyone. MAC requires the verifier to have the private key
• only the trusted sender could generate the signature, because the private key was needed. In case of MAC, both the sender and receiver know the secret. The receiver cannot prove that the MAC was generated by the sender and not the receiver themselves.

Typically, signatures are created based on digests of the original data due to size limitations in asymmetric encryption. The receiver applies hash to the plain text data to compare it with the signed hash.

X.509

X.509 is a format of digital certificates. It includes:

• the public key part of asymmetric pair - that key is being certified
• attributes of that key

The certificate must be signed by a CA (by its private key). CA’s public key may be signed by another CA, which creates a hierarchy - a certificate chain. At the top, there’s a root certificate, which is trusted unconditionally.

TPM does not generate or consume X.509 certificates. It can store them though. There are some certification processes within TPM:

• TPM vendor and platform manufacturer may provision TPM with Endorsement Keys (EKs) and corresponding certificates before shipping to the end user. the certificates assert respectively that the TPM is produced by the vendor and included by the manufacturer in their platform. They are in X.509 format.
• the EKs (and their certs) may be used to certify other keys (if EKs are signing). TPM can create certificates (but not in X.509 format, it’s too complex for TPMs).

Resources

• Real-World Cryptography by David Wong
• http://jrruethe.github.io/blog/2014/10/25/cryptography-primer/