Cryptography

• cryptanalysis (ניתוח הצפנה)

  • brute-force attack (or exhaustive key search)

• cipher (or cypher) (צופן)

• key (מפתח הצפנה)

• encryption (הצפנה)

• decryption (פענוח)

• plaintext (טקסט גלוי)

• ciphertext (טקסט מוצפן)

• cryptographic primitives

• Kerckhoffs’s principle

  • Shannon’s maxim: The enemy knows the system

• known-plaintext attack (KPA) (התקפת גלוי-ידוע)

• ciphertext-only attack (COA) (or known ciphertext attack)

• chosen-plaintext attack (CPA) (התקפת גלוי-נבחר)

• side-channel attack

Key exchange

• Diffie–Hellman (DH) key exchange
  • Alice and Bob publicly agree on a prime $p$ and a base $g$ (which is a primitive root modulo $p$)
  • Alice’s private key: $a$
  • Bob’s private key: $b$
  • Alice’s public key: $A=g^a\mathrm{mod}p$
  • Bob’s public key: $B=g^b\mathrm{mod}p$
  • Secret shared key: $s=A^b\mathrm{mod}p=B^a\mathrm{mod}p=g^{ab}\mathrm{mod}p$

Symmetric cryptography

• symmetric-key (or symmetric) cryptography
  • shared key (or secret key)

Block ciphers

• block cipher
  • plaintext $P$ of size $n$ bits (block size)
  • key $K$ of size $k$ (key size)
  • key space: $\{0,1{\}}^k$
  • ciphertext $C$ of size $n$ bits
  • encryption function: $E(K,P):\{0,1{\}}^k\times \{0,1{\}}^n\to \{0,1{\}}^n$
  • decryption function: $D(K,C):\{0,1{\}}^k\times \{0,1{\}}^n\to \{0,1{\}}^n$
  • $E^{-1}(K,C)=D(K,C)$
    • $\forall P\in \{0,1{\}}^n,K\in \{0,1{\}}^k:D(K,E(K,P))=P$
• block cipher mode of operation
  • electronic codebook (ECB)
  • cipher block chaining (CBC)
    • initialization vector (IV)
  • counter mode (CTR)

Stream cipher

• stream cipher

examples

• Data Encryption Standard (DES)
• Advanced Encryption Standard (AES)
• ChaCha20
• authenticated encryption (AE)
  • authenticated encryption with associated data (AEAD)

Asymmetric cryptography

• public-key (or asymmetric) cryptography

  • public key
  • private key

• RSA (Rivest–Shamir–Adleman) cryptosystem

• privacy-enhanced mail (PEM)

• Edwards-curve Digital Signature Algorithm (EdDSA)

  • Ed25519

• Elliptic Curve Digital Signature Algorithm (ECDSA)

• Digital Signature Algorithm (DSA)

• Elliptic-curve cryptography (ECC)

• Elliptic-curve Diffie–Hellman (ECDH)

• Public Key Cryptography Standards (PKCS)

  • PKCS #1
  • PKCS #8

• SHA-2 (Secure Hash Algorithm 2)

  • SHA-256

CHF

• A cryptographic hash function (CHF) is a hash function $h:\{0,1{\}}^{\ast }\to \{0,1{\}}^n$ that satisfies the following properties:
  • (pre-image resistance) for a given hash value $y$, it is computationally infeasible to find any input $x$ such that $h(x)=y$
  • (second pre-image resistance) for a given input $x_1$, it is computationally infeasible to find another input $x_2$ such that $x_1\ne x_2$ and $h(x_1)=h(x_2)$
  • (collision resistance) it is computationally infeasible to find any two distinct inputs $x_1$ and $x_2$ such that $h(x_1)=h(x_2)$
• The output of a CHF is called the message digest (or hash value) of the input message.

Digital signature

• digital signature
  • using message digest (MD)
    • given:
      • both sender and receiver know the CHF $h$
      • the sender has a public-private key pair: $(pk,sk)$ for encryption/decryption functions $E$ and $D$ (such that $E_{pk}(D_{sk}(m))=m$ for any message $m$)
    • sender:
      • (plaintext) $P$
      • (message digest) $h(P)$
      • (signature) $S=D_{sk}(h(P))$
      • (sends to receiver) $(P,S)$
    • receiver:
      • computes $h(P)$
      • computes $E_{pk}(S)$
      • verifies that $h(P)=E_{pk}(S)$

Public key infrastructure

• public key infrastructure (PKI)

• registration authority (RA)

• validation authority (VA)

• certificate authority (or certification authority) (CA) (רשות אישורים, רשות אישור)

• public-key certificate (or digital certificate or identity certificate) – binds a public key to an identity

  • X.509
  • domain validated certificate (DV)

• certificate signing request (CSR or certification request) – “a message sent from an applicant to a CA of the PKI in order to apply for a digital certificate”

• cryptographic protocol

  • Transport Layer Security (TLS)

• see also:

  • Certificate Authority Authorization (CAA)

Classical ciphers

• substitution cipher
• Caesar cipher (or shift cipher)
• one-time pad (OTP)