CSE4303 Introduction to Computer Security (Exam Review)

Details

Time and location

– In class exam – Thursday, 3/5 at 11:30 AM – What is allowed: - One 8.5” X 11” paper of notes, single-sided only, typed or hand-written

Topics covered:

– Security fundamentals – TCP/IP network stack – Crypto fundamentals – Symmetric key cryptography – Hash functions – Asymmetric key cryptography

Security fundamentals

Defining security

• Understand principles of security analysis
  • The security of a system, application, or protocol is always relative to
    • A set of desired properties
    • An adversary with specific capabilities (“threat model”)

Key security concepts

C.I.A. triad:

• Integrity: Prevent unauthorized modification of data, and/or detect if modification occurred.
  • ARP poisoning (ARP spoofing)
  • Authentication codes
• Confidentiality: Prevent unauthorized parties from learning the contents of data (in transit or at rest).
  • Packet sniffing / eavesdropping
  • Data encryption
• Availability: Ensure systems and data are accessible to authorized users when needed.
  • Denial-of-Service (DoS) / Distributed DoS (DDoS)
  • Rate limiting + traffic filtering (often with DDoS protection/CDN)

Other security goals:

• Authenticity: identity of an entity (issuer of info/message) is verified
• Anonymity: identity of an entity remains unknown
• Non-repudiation: messages can’t be denied or taken back (e.g. online transaction commitments)

Modeling attacks

Common components:

• System being attacked (usually a model, with assumptions and abstractions)
• Threat model
• Attack surface: what can be attacked
  • Open ports and exposed services
  • Public APIs and their parameters
  • Web endpoints, forms, cookies
  • File system permissions
  • Hardware interfaces (USB, JTAG)
  • User roles and privilege boundaries
• Attack vector: how the attacker attacks
  • SQL injection via POST /login
  • Phishing to steal credentials, then SSH login
  • Buffer overflow in a network daemon
  • Cross-site scripting through a comment field
  • Supply-chain poisoning of a dependency
• Vulnerability: what the attacker can do
• Exploit: how the attacker exploits the vulnerability
• Damage: what the attacker can do
• Mitigation: mitigate vulnerability
• Defense: close vulnerability gap

Importance of correct modeling

• Attack-surface awareness guides defenses
  • E.g. pre-Covid-19 vs. post-Covid attack surface of company servers
• Match resources to expected threat actors
  • “Script kiddie”: individual or group running off-the-shelf attacks
    • Caveat: off-the-shelf attacks can still be quite powerful! Metasploit, Shodan, dark web market.
  • “Insider attack”: employee with access to internal machines/networks
  • “Advanced Persistent Threat (APT)”: nation-state level resources and patience
  • All these threats have different motivations, require different defenses/responses!
• Reevaluate often
  • Threat capabilities change over time

TCP/IP network stack

Local and interdomain routing

• TCP/IP for routing and messaging
• BGP for routing announcements

Domain Name System

• Find IP address from symbolic name (cse.wustl.edu)

Layer Summary

Application: the actual sending message Transport (TCP, UDP): segment Network (IP): packet Data Link (Ethernet): frame

Types of Addresses in Internet

• Media Access Control (MAC) addresses in the network access layer
  • Associated w/ network interface card (NIC)
  • 00-50-56-C0-00-01
• IP addresses for the network layer
  • IPv4 (32 bit) vs IPv6 (128 bit)
  • 128.1.1.3 vs fe80::fc38:6673:f04d:b37b%4
• IP addresses + ports for the transport layer
  • E.g., 10.0.0.2:8080
• Domain names for the application/human layer
  • E.g., www.wustl.edu 

Routing and Translation of Addresses

(All of them are attack surfaces)

• Translation between IP addresses and MAC addresses
  • Address Resolution Protocol (ARP) for IPv4
  • Neighbor Discovery Protocol (NDP) for IPv6
• Routing with IP addresses
  • TCP, UDP for connections, IP for routing packets
  • Border Gateway Protocol for routing table updates
• Translation between IP addresses and domain names
  • Domain Name System (DNS)

Summary for security

• Confidentiality
  • Packet sniffing
• Integrity
  • ARP poisoning
• Availability
  • Denial of service attacks
• Common
  • Address translation poisoning attacks (DNS, ARP)
  • Packet spoofing
• Core protocols not designed for security
  • Eavesdropping, packet injection, route stealing, DNS poisoning
  • Patched over time to prevent basic attacks
• More secure variants exist:
  • IP $\to$ IPsec (IPsec is )
  • DNS $\to$ DNSsec
  • BGP $\to$ sBGP

Crypto fundamentals

• Well-defined statement about difficulty of compromising a system
  • …with clear implicit or explicit assumptions about:
    • Parameters of the system
    • Threat model
    • Attack surfaces
• Example: “A one-time pad cipher is secure against any cryptanalysis, including a brute-force attack, assuming:
  • the key is the same length as the plaintext,
  • the key is truly random, and
  • the key is never re-used.”

Common roles in cryptography

Alice and Bob: Sender and receiver

Eve: Adversary that can see but not create any packets

Mallory: Man in the middle, can create and modify packets

The message M is called the plaintext.

Alice will convert plaintext M to an encrypted form using an encryption algorithm E that outputs a ciphertext C for M.

Cryptography goals

Confidentiality:

• Mallory and Eve cannot recover original message from ciphertext

Integrity:

• Mallory cannot modify message from Alice to Bob without detection by Bob

Threat models

• Attacker may have (with increasing power):
  • a) collection of ciphertexts (ciphertext-only attack)
  • b) collection of plaintext/ciphertext pairs (known plaintext attack: KPA)
  • c) collection of plaintext/ciphertext pairs for plaintexts selected by the attacker (chosen plaintext attack: CPA)
  • d) collection of plaintext/ciphertext pairs for ciphertexts selected by the attacker (chosen ciphertext attack: CCA/CCA2)

Symmetric key cryptography

Classical cryptography

Techniques: substitution and transposition

• Substitution: 1:1 mapping of alphabet onto itself

• Transposition: permutation of elements (i.e. rearrange letters)

• Caesar cipher: rotate each letter by k positions (k is fixed)

• Vigenère cipher: If length of key is known, split letters into groups based on index within key and do frequency analysis within groups

The three steps in cryptography:

• Precisely specify threat model
• Propose a construction
• Prove that breaking construction under threat mode will solve an underlying hard problem

Perfect secrecy

Ciphertext attack reveal no “info” about plaintext under ciphertext only attack

Def: A cipher $(E, D)$ over $(K, M, C)$ has perfect secrecy if

• $\forall m_0, m_1 \in M$ $(|m_0| = |m_1|)$ and $\forall c \in C$,
  • $\Pr[E(k, m_0) = c] = \Pr[E(k, m_1) = c]$ where $k \leftarrow K$

XOR One-time pad (perfect secrecy)

Assumptions:

• Key is as long as message
• Key is random
• Key is never re-used

In practice, relax this assumption gets “Stream ciphers”

Stream cipher

• Use pseudorandom generator as keystream for xore encryption (security is guaranteed by pseudorandom generator)

Security abstraction:

1. XOR transfers randomness of keystream to randomness of CT regardless of PT’s content
2. Security depends on G being “practically” indistinguishable from random string and “practically” unpredictable
3. Idea: shouldn’t be able to predict next bit of generator given all bits seen so far

Semantic security

• $(E, D)$ has semantic secrecy if $\forall m_0, m_1 \in M$ $(|m_0| = |m_1|)$,
  • $\{E(k, m_0)\} \approx_p \{E(k, m_1)\}$ where $k \leftarrow K$
• …and the adversary exhibits $m_0, m_1 \in M$ explicitly

The advantage of adversary is defined as the probability of distinguishing $E(k, m_0)$ from $E(k, m_1)$.

Weakness for stream ciphers

• Week pseudorandom generator
• Key re-use
• Predicable effect of modifying ciphertext or decrypted plaintext.

Block cipher

View cipher as a Pseudo-Random Permutation (PRP)

Pseudorandom permutation

• PRP defined over $(K, X)$:

  • $E: K \times X \to X$
  • such that:
    1. There exists an “efficient” deterministic algorithm to evaluate $E(k, x)$.
    2. The function $E(k, \cdot)$ is one-to-one.
    3. There exists an “efficient” inversion algorithm $D(k, y)$.

• i.e. a PRF that is an invertible one-to-one mapping from message space to message space

Security of block ciphers

Intuition: a PRP is secure if: a random function in $Perms[X]$ is indistinguishable from a random function in $SF$ (real random permutation function)

The adversarial game is to let adversary decide $x$, then we choose random key $k$ and give $E(k,x)$ and real random permutation $Perm(X)$ to let adversary decide which is which.

Block cipher constructions: Feistel network

Forward network:

• Forward (round $i$): given $(L_{i-1}, R_{i-1}) \in \{0,1\}^n \times \{0,1\}^n$,

  • $L_i = R_{i-1}$
  • $R_i = L_{i-1} \oplus f_i(R_{i-1})$

• Proof (construct the inverse):

  • Suppose we are given the output of round $i$, namely $(L_i, R_i)$.
  • Recover the previous right half immediately:
    • $R_{i-1} = L_i$
  • Then recover the previous left half by undoing the XOR:
    • $L_{i-1} = R_i \oplus f_i(R_{i-1}) = R_i \oplus f_i(L_i)$
  • Therefore each round map is invertible, with inverse transformation:
    • $R_{i-1} = L_i$
    • $L_{i-1} = f_i(L_i) \oplus R_i$
  • Applying this inverse for $i=d,d-1,\ldots,1$ recovers $(L_0,R_0)$ from $(L_d,R_d)$, so the whole Feistel network $F$ is invertible.

• Notation sketch (each wire is $n$ bits):

  • Input: $(L_0, R_0)$
  • Rounds:
    • $L_1 = R_0,\ \ R_1 = L_0 \oplus f_1(R_0)$
    • $L_2 = R_1,\ \ R_2 = L_1 \oplus f_2(R_1)$
    • $\cdots$
    • $L_d = R_{d-1},\ \ R_d = L_{d-1} \oplus f_d(R_{d-1})$
  • Output: $(L_d, R_d)$

Block ciphers: block modes: ECB

New attacker model for multi-use keys (e.g. multiple blocks): CPA (Chosen Plaintext)-capable, not just CT-only

• Attacker sees many PT/CT pairs for same key
• Conservative model: attacker submits arbitrary PT (hence “C”PA)
• Cipher goal: maintain semantic security against CPA

CPA indistinguishability game

• Updated adversarial game for a CPA attacker:

  • Let $E = (E, D)$ be a cipher defined over $(K, M, C)$. For $b \in \{0,1\}$ define $\operatorname{EXP}(b)$ as:

• Experiment $\operatorname{EXP}(b)$:

  • Challenger samples $k \leftarrow K$.
  • For each query $i = 1,\ldots,q$:
    • Adversary outputs messages $m_{i,0}, m_{i,1} \in M$ such that $|m_{i,0}| = |m_{i,1}|$.
    • Challenger returns $c_i \leftarrow E(k, m_{i,b})$.

• Encryption-oracle access (CPA):

  • If the adversary wants $c = E(k, m)$, it queries with $m_{j,0} = m_{j,1} = m$ (so the response is $E(k,m)$ regardless of $b$).

Semantic security under CPA

• Def: $E$ is semantically secure under CPA if for all “efficient” adversaries $A$,
  • $\operatorname{Adv}^{\operatorname{CPA}}[A,E] = \left|\Pr[\operatorname{EXP}(0)=1] - \Pr[\operatorname{EXP}(1)=1]\right|$
  • is negligible.

Summary for symmetric encrption

1. Stream ciphers
   • Rely on secure PRG
   • No key re-use
   • Fast, low-mem, less robust
2. Block ciphers
   • Rely on secure PRP
   • Allow key re-use (usually only across blocks, not sessions)
   • Provide authenticated encryption in some modes (e.g. GCM)
   • Slower, higher-mem, more robust
   • Used in practice for most crypto tasks (including secure network channels)

Hash functions

Hash function security properties

• Given a function $h:X \to Y$, we say that $h$ is:

• 1. Preimage resistant (one-way) if:
  • given $y \in Y$ it is computationally infeasible to find a value $x \in X$ s.t. $h(x) = y$
• 2. 2nd preimage resistant (weak collision resistant) if:
  • given a specific $x \in X$ it is computationally infeasible to find a value $x' \in X$ s.t. $x' \ne x$ and $h(x') = h(x)$
• 3. Collision resistant (strong collision resistant) if:
  • it is computationally infeasible to find any two distinct values $x', x \in X$ s.t. $h(x') = h(x)$

Collision resistance: adversarial definition

• Let $H: M \to T$ be a hash function ($|M| \gg |T|$).
• A function $H$ is collision resistant if for all (explicit) “efficient” algorithms $A$,
  • $\operatorname{Adv}^{\operatorname{CR}}[A,H] = Pr[$A outputs a collision for $H$ $]$
  • is negligible

Hash function integrity applications

1. Delayed knowledge verification
2. Password storage
3. Trusted timestamping / blockchains
4. Integrity check on software

File integrity with secure read-only space

• When user downloads package, can verify that contents are valid
• $H$ collision resistant $\Rightarrow$ attacker cannot modify package without detection
• No encryption needed (public verifiability) if publisher has secure read-only space (e.g. trusted website, social media account)

Symmetric-crypto message authentication

• Context: Assume no secure RO space (insecure channel only)

  • Need means of message authentication

• Idea: add tag to message

• System: Message Authentication Code (MAC)

• Def: a MAC $I=(S,V)$ defined over $(K,M,T)$ is a pair of algorithms:

  • $S(k,m)$ outputs $t \in T$ // “Sign”
  • $V(k,m,t)$ outputs yes' or no’ // “Verify”

• Symmetric-crypto message authentication:

  • Alice and Bob share secret key $k$
  • Generate tag: $\text{tag} \leftarrow S(k,m)$
  • Verify tag: $V(k,m,\text{tag}) = \texttt{yes}?$

MAC security model

• For a MAC $I=(S,V)$ and adversary $A$, define a MAC game as:

• Def: $I=(S,V)$ is a secure MAC if for all “efficient” $A$,

  • $\operatorname{Adv}^{\operatorname{MAC}}[A,I] = \Pr[\text{Chal. outputs }1]$
  • is negligible

• MAC game (sketch):

  • Challenger samples $k \leftarrow K$
  • Adversary makes queries $m_1,\ldots,m_q \in M$
    • For each $i$, challenger returns $t_i \leftarrow S(k,m_i)$
  • Adversary outputs a candidate forgery $(m,t)$
  • Challenger outputs $b=1$ if:
    • $V(k,m,t)=\texttt{yes}$ and
    • $(m,t) \notin \{(m_1,t_1),\ldots,(m_q,t_q)\}$
  • Otherwise challenger outputs $b=0$

• MAC security example: secure PRF not sufficient

  • Suppose $F: K \times X \to Y$ is a secure PRF with $Y=\{0,1\}^{10}$.
  • Is the derived MAC $I_F$ a secure MAC system?
    • No: tags are too short, anyone can guess the tag for any message

MACs from PRFs: sufficient security condition

• Thm: If $F: K \times X \to Y$ is a secure PRF and $1/|Y|$ is negligible (i.e. $|Y|$ is large), then $I_F$ is a secure MAC.
• In particular, for every efficient MAC adversary $A$ attacking $I_F$, there exists an efficient PRF adversary $B$ attacking $F$ such that:
  • $\operatorname{Adv}^{\operatorname{MAC}}[A, I_F] \le \operatorname{Adv}^{\operatorname{PRF}}[B, F] + 1/|Y|$
• Therefore $I_F$ is secure as long as $|Y|$ is large, e.g. $|Y| = 2^{80}$.

MACs from collision resistance

• Let $I=(S,V)$ be a MAC for short messages over $(K,M,T)$ (e.g. AES).
• Let $H: M_{\text{big}} \to M$.
• Def: $I_{\text{big}}=(S_{\text{big}},V_{\text{big}})$ over $(K,M_{\text{big}},T)$ as:
  • $S_{\text{big}}(k,m) = S(k, H(m))$
  • $V_{\text{big}}(k,m,t) = V(k, H(m), t)$
• Thm: If $I$ is a secure MAC and $H$ is collision resistant, then $I_{\text{big}}$ is a secure MAC.
• Example: $S(k,m) = \operatorname{AES2\text{-}block\text{-}cbc}(k, \operatorname{SHA\text{-}256}(m))$ is a secure MAC.

Using HMACs for confidentiality + integrity

• Confidentiality:
  • Semantic security under a CPA
  • Encryption secure against eavesdropping only
• Integrity:
  • Existential unforgeability under a CPA
  • CBC-MAC, HMAC
  • Hash functions
• Confidentiality + integrity:
  • CCA security
  • Secure against tampering
  • Method: Authenticated Encryption (AE)
  • Encryption + MAC, in correct form

Authenticated Encryption: security defs

• An authenticated encryption system $(E,D)$ is a cipher where:
  • $E: K \times M \times N \to C$
  • $D: K \times C \times N \to M \cup$ cipher text rejected
• Security: the system must provide
  • semantic security under a CPA attack, and
  • ciphertext integrity: attacker cannot create new ciphertexts that decrypt properly

Ciphertext integrity

• Let $(E,D)$ be a cipher with message space $M$.

• Def: $(E,D)$ has ciphertext integrity if for all “efficient” $A$,

  • $\operatorname{Adv}^{\operatorname{CI}}[A,E] = \Pr[\text{Chal. outputs }1]$
  • is negligible

• Security model: ciphertext integrity (sketch):

  • Challenger samples $k \leftarrow K$
  • Adversary makes encryption queries $m_1,\ldots,m_q \in M$
    • For each $i$, challenger returns $c_i \leftarrow E(k,m_i)$
  • Adversary outputs a ciphertext $c$
  • Challenger outputs $b=1$ if:
    • $D(k,c) \ne \bot$ and
    • $c \notin \{c_1,\ldots,c_q\}$
  • Otherwise challenger outputs $b=0$

Authenticated encryption implies CCA security

• Thm: Let $(E,D)$ be a cipher that provides AE. Then $(E,D)$ is CCA secure.

• In particular, for any $q$-query efficient adversary $A$, there exist efficient $B_1,B_2$ such that:

  • $\operatorname{Adv}^{\operatorname{CCA}}[A,E] \le 2q \cdot \operatorname{Adv}^{\operatorname{CI}}[B_1,E] + \operatorname{Adv}^{\operatorname{CPA}}[B_2,E]$

• Interpretation: CCA advantage is $\le O(\text{CT-integrity advantage}) + \text{CPA advantage}$.

• AE implication: authenticity

  • Attacker cannot fool Bob into thinking a message was sent from Alice
  • If attacker cannot create a valid ciphertext $c \notin \{c_1,\ldots,c_q\}$, then whenever $D(k,c) \ne \bot$ Bob knows the message is from someone who knows $k$ (but it could be a replay)

• DS construction example: signing a certificate

Comparison: integrity/authentication approaches

• 1. Collision resistant hashing: need a read-only public space
  • Allows public verification if the hash is published in a small read-only public space
• 2. MACs: must compute a new MAC for every client/user
  • Must manage a long-term secret key per user to verify MACs (depending on application)
  • Typically useful when one party signs, one verifies
• 3. Digital signatures: must manage a long-term secret key
  • E.g. vendor’s signature on software is shipped with software
  • Allows software to be downloaded from an untrusted distribution site
  • Public-key verification/rejection works, provided public key distribution is trustworthy
  • Typically useful when one party signs, many verify

Asymmetric key cryptography

Asymmetric crypto overview

• Parties: sender, recipient, attacker (eavesdropping)
• Goal: sender encrypts a plaintext to a ciphertext using a public key; recipient decrypts using a private key.

Public-key encryption system

• Def: a public-key encryption system is a triple of algorithms $(G, E, D)$:
  • $G()$: randomized algorithm that outputs a key pair $(pk, sk)$
  • $E(pk, m)$: randomized algorithm that takes $m \in M$ and outputs $c \in C$
  • $D(sk, c)$: deterministic algorithm that takes $c \in C$ and outputs $m \in M$ or $\bot$
• Consistency: for all $(pk, sk)$ output by $G$, for all $m \in M$,
  • $D(sk, E(pk, m)) = m$

Trapdoor function

• Def: a trapdoor function $X \to Y$ is a triple of efficient algorithms $(G, F, F^{-1})$:
  • $G()$: randomized algorithm that outputs a key pair $(pk, sk)$
  • $F(pk, \cdot)$: deterministic algorithm that defines a function $X \to Y$
  • $F^{-1}(sk, \cdot)$: defines a function $Y \to X$ that inverts $F(pk, \cdot)$
• More precisely: for all $(pk, sk)$ output by $G$, for all $x \in X$,
  • $F^{-1}(sk, F(pk, x)) = x$

Symmetric vs. asymmetric security: attacker models

• Symmetric ciphers: two security notions for a passive attacker
  • One-time security (stream ciphers: ciphertext-only)
  • Many-time security (block ciphers: CPA)
  • One-time security $\Rightarrow$ many-time security
  • Example: ECB mode is one-time secure but not many-time secure
• Public-key encryption: single notion for a passive attacker
  • Attacker can encrypt by themselves using the public key
  • Therefore one-time security $\Rightarrow$ many-time security (CPA)
  • Implication: public-key encryption must be randomized
  • Analogous to secure block modes for block ciphers

Semantic security of asymmetric crypto (IND-CPA)

IND-CPA game for public-key encryption

• For $b \in \{0,1\}$ define experiments $\operatorname{EXP}(0)$ and $\operatorname{EXP}(1)$:

• Experiment $\operatorname{EXP}(b)$:

  • Challenger runs $(pk, sk) \leftarrow G()$
  • Challenger sends $pk$ to adversary $A$
  • Adversary outputs $m_0, m_1 \in M$ such that $|m_0| = |m_1|$
  • Challenger returns $c \leftarrow E(pk, m_b)$
  • Adversary outputs a bit $b' \in \{0,1\}$ (often modeled as outputting 1 if it “guesses $b=1$“)

Semantic security (IND-CPA)

• Def: $E = (G, E, D)$ is semantically secure (a.k.a. IND-CPA) if for all efficient adversaries $A$,
  • $\operatorname{Adv}^{\operatorname{SS}}[A, E] = \left|\Pr[\operatorname{EXP}(0)=1] - \Pr[\operatorname{EXP}(1)=1]\right|$
  • is negligible
• Note: inherently multiple-round because the attacker can always encrypt on their own using $pk$ (CPA power is “built in”).

RSA cryptosystem: overview

• Setup:

  • $n = pq$, with $p$ and $q$ primes
  • Choose $e$ relatively prime to $\phi(n) = (p-1)(q-1)$
  • Choose $d$ as the inverse of $e$ in $\mathbb{Z}_{\phi(n)}$

• Keys:

  • Public key: $K_E = (n, e)$
  • Private key: $K_D = d$

• Encryption:

  • Plaintext $M \in \mathbb{Z}_n$
  • $C = M^e \bmod n$

• Decryption:

  • $M = C^d \bmod n$

• Example:

  • Setup:
    • $p = 7$, $q = 17$
    • $n = 7 \cdot 17 = 119$
    • $\phi(n) = 6 \cdot 16 = 96$
    • $e = 5$
    • $d = 77$
  • Keys:
    • public key: $(119, 5)$
    • private key: $77$
  • Encryption:
    • $M = 19$
    • $C = 19^5 \bmod 119 = 66$
  • Decryption:
    • $M = 66^{77} \bmod 119 = 19$

• Security intuition:

  • To invert RSA without $d$, attacker must compute $x$ from $c = x^e \pmod n$.
  • Best known approach:
    • Step 1: factor $n$ (hard)
    • Step 2: compute $e$-th roots modulo $p$ and $q$ (easy once factored)
  • Notes (as commonly stated in lectures):
    • 1024-bit RSA is within reach; 2048-bit is recommended usage

Diffie-Hellman key exchange (informal)

• Fix a large prime $p$ (e.g., 2000 bits)

• Fix an integer $g \in \{1,\ldots,p\}$

• Protocol:

  • Alice chooses random $a \in \{1,\ldots,p-1\}$ and sends $A = g^a \bmod p$
  • Bob chooses random $b \in \{1,\ldots,p-1\}$ and sends $B = g^b \bmod p$
  • Shared key:
    • Alice computes $k_{AB} = B^a \bmod p = g^{ab} \bmod p$
    • Bob computes $k_{AB} = A^b \bmod p = g^{ab} \bmod p$

• Hardness assumptions:

  • Discrete log problem: given $p, g, y = g^x \bmod p$, find $x$
  • Diffie-Hellman function: $\operatorname{DH}_g(g^a, g^b) = g^{ab} \bmod p$

Diffie-Hellman: security notes

• As described, the protocol is insecure against active attacks:
  • A man-in-the-middle (MiTM) can insert themselves and create 2 separate secure sessions
• Fix idea: need a way to bind identity to a public key
  • In practice: web of trust (e.g., GPG) or Public Key Infrastructure (PKI)

Implementing trapdoor functions securely

• Never encrypt by applying $F$ directly to plaintext:

  • Deterministic: cannot be semantically secure
  • Many attacks exist for concrete TDFs
  • Same plaintext blocks yield same ciphertext blocks

• Naive (insecure) sketch:

  • $E(pk, m)$: output $c \leftarrow F(pk, m)$
  • $D(sk, c)$: output $F^{-1}(sk, c)$

Public-key encryption from TDFs

• Components:

  • $(G, F, F^{-1})$: secure TDF $X \to Y$
  • $(E_s, D_s)$: symmetric authenticated encryption over $(K, M, C)$
  • $H: X \to K$: a hash function

• Construction of $(G, E, D)$ (with $G$ same as in the TDF):

  • $E(pk, m)$:
    • sample $x \leftarrow X$, compute $y \leftarrow F(pk, x)$
    • derive $k \leftarrow H(x)$, compute $c \leftarrow E_s(k, m)$
    • output $(y, c)$
  • $D(sk, (y, c))$:
    • compute $x \leftarrow F^{-1}(sk, y)$
    • derive $k \leftarrow H(x)$, compute $m \leftarrow D_s(k, c)$
    • output $m$

• Visual intuition:

  • header: $y = F(pk, x)$
  • body: $c = E_s(H(x), m)$

• Security theorem (lecture-style statement):

  • If $(G, F, F^{-1})$ is a secure TDF, $(E_s, D_s)$ provides authenticated encryption, and $H$ is modeled as a random oracle, then $(G, E, D)$ is CCA-secure in the random oracle model (often denoted CCA-RO).
  • Extension exists to reach full CCA (outside the RO idealization).

Wrapup: symmetric vs. asymmetric systems

• Symmetric: faster, but key distribution is hard
• Asymmetric: slower, but key distribution/management is easier
• Application: secure web sessions (e.g., online shopping)
  • Use symmetric-key encrypted sessions for bulk traffic
  • Exchange symmetric keys using an asymmetric scheme
  • Authenticate public keys (PKI or web of trust)

Key exchange: summary

• Symmetric-key encryption challenges:

  • Key storage: one per user pair, $O(n^2)$ total for $n$ users
  • Key exchange: how to do it over a non-secure channel?

• Possible solutions:

• 1. Trusted Third Party (TTP)
  • All users establish separate secret keys with the TTP
  • TTP helps manage user-user keys (storage and secure channel)
  • Applicability:
    • Works for local domains
    • Popular implementation: Kerberos for Single Sign On (SSO)
  • Challenges:
    • Scale: central authentication server is not suitable for the entire Internet
    • Latency: requires online response from central server for every user-user session
• 2. Public/private keys with certificates
  • All users have a single stable public key (helps with key storage and exchange)
  • Users exchange per-session symmetric keys via a secure channel using public/private keys
  • Trusting public keys: binding is validated by a third-party authority (Certificate Authority, CA)
    • Why better than TTP? CAs can validate statically by issuing certificates, then be uninvolved
  • CA/certificate process covered in a future lecture

Appendix for additional algorithms and methods

Feistel network (used by several items below)

A Feistel network splits a block into left/right halves and iterates rounds of the form $(L_{i+1},R_{i+1})=(R_i, L_i\oplus F(R_i,K_i))$, so decryption reuses the same structure with subkeys in reverse order.

Feistel-based here: DES, 3DES, CAMELLIA, SEED, GOST 28147-89 (and thus GOST89MAC uses a Feistel block cipher internally).

Key exchange and authentication selectors (not symmetric encryption, not MAC)

These describe *how keys are negotiated- and/or how the peer is authenticated, not whether payload is a block/stream cipher.

RSA / DH / ECDH families

• kRSA, RSA — (key exchange) the premaster secret is sent encrypted under the server’s RSA public key (classic TLS RSA KX).
• aRSA, aECDSA, aDSS, aGOST, aGOST01 — (authentication) the server identity is proven via a certificate signature scheme (RSA / ECDSA / DSA / GOST).
• kDHr, kDHd, kDH — (key exchange) *static- DH key agreement using DH certificates (obsolete/removed in newer OpenSSL).
• kDHE, kEDH, DH / DHE, EDH / ECDHE, EECDH / kEECDH, kECDHE, ECDH — (key exchange) *ephemeral- (EC)DH derives a fresh shared secret each handshake; “authenticated” variants bind it to a cert/signature.
• aDH — (authentication selector) indicates DH-authenticated suites (DH certs; also removed in newer OpenSSL).

PSK family

• PSK — (keying model) uses a pre-shared secret as the authentication/secret basis.
• kPSK, kECDHEPSK, kDHEPSK, kRSAPSK — (key exchange) PSK combined with (EC)DHE or RSA to derive/transport session keys.
• aPSK — (authentication) PSK itself authenticates endpoints (except RSA_PSK where cert auth may be involved).

Symmetric encryption / AEAD (this is where “block vs stream” applies)

AES family

• AES128 / AES256 / AES — encryption/decryption; block cipher; core algorithm: AES is an SPN (substitution–permutation network) of repeated SubBytes/ShiftRows/MixColumns/AddRoundKey rounds.
• AES-GCM — both encryption + message authentication (AEAD); both (AES block cipher used in counter mode + auth); core algorithm: encrypt with AES-CTR and authenticate with GHASH over ciphertext/AAD to produce a tag.
• AES-ECB: Functionality is encryption/decryption (confidentiality only) using a block cipher mode; core algorithm encrypts each 128-bit plaintext block independently under the same key, which deterministically leaks patterns because equal plaintext blocks map to equal ciphertext blocks.
• AES-CBC: Functionality is encryption/decryption (confidentiality only) using a block cipher mode; core algorithm XORs each plaintext block with the previous ciphertext block (starting from a fresh unpredictable IV) before AES-encrypting, which hides repetitions but requires correct IV handling and padding for non-multiple-of-block messages.
• AES-OFB — encryption; both (stream-like); repeatedly AES-encrypts an internal state to generate a keystream and XORs it with plaintext, where the state evolves independently of the plaintext/ciphertext.
• AESCCM / AESCCM8 — both encryption + message authentication (AEAD); both; core algorithm: compute CBC-MAC then encrypt with CTR mode, with 16-byte vs 8-byte tag length variants.

ARIA family

• ARIA128 / ARIA256 / ARIA — encryption/decryption; block cipher; core algorithm: ARIA is an SPN-style block cipher with byte-wise substitutions and diffusion layers across rounds.

CAMELLIA family

• CAMELLIA128 / CAMELLIA256 / CAMELLIA — encryption/decryption; block cipher; core algorithm: Camellia is a Feistel network with round functions plus extra FL/FL$^{-1}$ layers for nonlinearity and diffusion. (Feistel: yes)

ChaCha20

• CHACHA20 — encryption/decryption; stream cipher; core algorithm: ChaCha20 generates a keystream via repeated ARX (add-rotate-xor) quarter-rounds on a 512-bit state and XORs it with plaintext.

DES / 3DES

• DES — encryption/decryption; block cipher; core algorithm: DES is a 16-round Feistel network using expansion, S-boxes, and permutations. (Feistel: yes)
• 3DES — encryption/decryption; block cipher; core algorithm: applies DES three times (EDE or EEE) to increase effective security while retaining the Feistel DES core. (Feistel: yes)

RC4

• RC4 — encryption/decryption; stream cipher; core algorithm: maintains a 256-byte permutation and produces a keystream byte-by-byte that is XORed with plaintext.

RC2 / IDEA / SEED

• RC2 — encryption/decryption; block cipher; core algorithm: mixes key-dependent operations (adds, XORs, rotates) across rounds with “mix” and “mash” steps (not Feistel).
• IDEA — encryption/decryption; block cipher; core algorithm: combines modular addition, modular multiplication, and XOR in a Lai–Massey-like structure to achieve diffusion/nonlinearity (not Feistel).
• SEED — encryption/decryption; block cipher; core algorithm: a 16-round Feistel network with nonlinear S-box-based round functions. (Feistel: yes)

Hash / MAC / digest selectors (message authentication side)

These are not “ciphers” but are used for integrity/authentication (often as HMAC, PRF, signatures).

• MD5 — message authentication component (typically via HMAC, historically); cipher method: N/A; core algorithm: iterated Merkle–Damgård hash compressing 512-bit blocks into a 128-bit digest (now considered broken for collision resistance).
• SHA1, SHA — message authentication component (typically HMAC-SHA1 historically); N/A; core algorithm: Merkle–Damgård hash producing 160-bit output via 80-step compression (collisions known).
• SHA256 / SHA384 — message authentication component (HMAC / TLS PRF / signatures); N/A; core algorithm: SHA-2 family Merkle–Damgård hashes with different word sizes/output lengths (256-bit vs 384-bit).
• GOST94 — message authentication component (HMAC based on GOST R 34.11-94); N/A; core algorithm: builds an HMAC tag by hashing inner/outer padded key with the message using the GOST hash.
• GOST89MAC — message authentication; block-cipher-based MAC (so “block” internally); core algorithm: computes a MAC using the GOST 28147-89 block cipher in a MAC mode (cipher-based chaining). (Feistel internally via GOST 28147-89)

Latest version of cheatsheet distilled from this note.