Cheat Sheet

Public Key Cryptography - ComputerphileComputerphile · public-key cryptography in plain words, 6 min

Elliptic Curves - ComputerphileComputerphile · what elliptic curves are and why crypto uses them, 9 min

AES Rijndael Cipher explained as a Flash animationAppliedGo · AES round animation for quick revision, 4 min

Foundations Search on YouTube

Security model Search on YouTube

Item	One line
Security dimensions	Security attack (action), security mechanism (detect, prevent, recover), security service (counters attacks)
Passive attacks	Eavesdropping, traffic analysis — read, no change
Active attacks	Masquerade, replay, modification of messages, denial of service
Five security services	Authentication (peer entity / data origin), Access control, Confidentiality, Integrity, Non-repudiation — AACIN
Specific mechanisms	Encipherment, digital signature, access control, data integrity, authentication exchange, traffic padding, routing control, notarization
Network model, 4 tasks	Design algorithm, generate key material, distribute and share the secrets, specify the protocol

Classical ciphers Search on YouTube

Cipher	Rule to remember
Caesar	Replace each letter 3 places down: $C = (P+3) \bmod 26$
Monoalphabetic	Any permutation; key space $26!$ ; broken by frequency analysis
Playfair	5x5 keyword matrix, I/J share a cell, encrypt a digram at a time. Rules: filler X for repeats, same row → right, same column → below, else rectangle corners
Vigenère	$C_i = (P_i + K_i) \bmod 26$ with the keyword repeated; key length hides it imperfectly (repeated patterns leak)
Autokey	Key = keyword prefixed to the plaintext (Vigenère's idea); still period-1 frequencies once the key becomes plaintext
One-time pad	$C = (P+K) \bmod 26$ , $K$ truly random as long as $P$ , used once. Unbreakable; unusable because of key distribution
Rail fence	Write diagonally on r rails, read off row by row
Row transposition	Key = column order; read the matrix column by column. Transposition keeps the letter frequencies
Product / rotor	Multiple stages (confusion + diffusion); rotor machines rotate wirings every key press

Symmetric ciphers Search on YouTube

S-DES and DES Search on YouTube

	s-DES	DES
Block	8-bit plaintext	64-bit
Key	10-bit key	64-bit key carrying 8 parity bits, real key 56 bits ( $2^{56} = 7.2\times10^{16}$ )
Subkeys	Two 8-bit: P10, split 5+5, LS-1, P8 = $K_1$ ; LS-2, P8 = $K_2$	16 x 48-bit: PC-1 (56 bits), shifts in halves, PC-2 (48 bits)
Pipeline	IP, $f_{K_1}$ , SW, $f_{K_2}$ , IP $^{-1}$	IP, 16 Feistel rounds, 32-bit swap, IP $^{-1}$
$f_K$	$f_K(L,R) = (L \oplus F(R, SK),\ R)$ ; F = E/P (4→8), XOR subkey, S0+S1 (4→2 each), P4	Round function on Li,Ri: expansion E (32→48), XOR $K_i$ , 8 S-boxes (6→4 each, 32 bits), permutation P
Decryption	Same functions, same order, keys swapped	Same pipeline with $K_1..K_{16}$ reversed

S-box rule both scales: leading and trailing bit give the row, the middle two give the column.

AES layers Search on YouTube

Item	One line
Parameters	128-bit block (4x4 byte state), keys 128/192/256, rounds 10/12/14 (key 10 words, round key expands)
Round (nr-1 times)	SubBytes → ShiftRows → MixColumns → AddRoundKey
Final round	SubBytes → ShiftRows → AddRoundKey (no MixColumns)
SubBytes	S-box: multiplicative inverse in GF $2^8$ , then affine transform; byte-wise confusion
ShiftRows	Row r rotates left r bytes
MixColumns	Column mixes; diffusion over 4 bytes
AddRoundKey	XOR the round key; the only layer that uses the key
Decryption	Invert each layer (InvSubBytes, InvShiftRows, InvMixColumns), key schedule reversed

GF(2^8) arithmetic Search on YouTube

GF $2^8$ = bytes with irreducible polynomial $m(x) = x^8 + x^4 + x^3 + x + 1$ = 0x11B; arithmetic is polynomial mod $m(x)$ , addition and subtraction are both XOR.
Multiply by 02 (xtime): shift left; if the MSB was 1, XOR with 0x1b.
Examples: $02 \cdot 63 = C6$ (MSB 0, shift only). $02 \cdot 87 = 15$ (MSB 1: $0E \oplus 1B = 15$ ). $03 \cdot x = (02 \cdot x) \oplus x$ .
MixColumns per column, with input $b_0..b_3$ :

$\begin{aligned} c_0 &= 02b_0 \oplus 03b_1 \oplus 01b_2 \oplus 01b_3 \\ c_1 &= 01b_0 \oplus 02b_1 \oplus 03b_2 \oplus 01b_3 \\ c_2 &= 01b_0 \oplus 01b_1 \oplus 02b_2 \oplus 03b_3 \\ c_3 &= 03b_0 \oplus 01b_1 \oplus 01b_2 \oplus 02b_3 \end{aligned}$

Matrix is circulant with the row $02\ 03\ 01\ 01$ . Multiply by 03 = XOR of xtime (02) and the identity (01).

Modes of operation Search on YouTube

Mode	Formula	Notes
ECB	$C_i = E_K[P_i]$	Simple, parallel; repeated plaintext blocks give repeated ciphertext blocks; do not use for long messages
CBC	$C_i = E_K[P_i \oplus C_{i-1}]$ , $C_0 = IV$	Chained; needs full blocks; sequential; error hits 2 blocks
CFB	$C_i = P_i \oplus E_K[C_{i-1}]$ , $C_0 = IV$	Stream mode (s bits); uses only the encryption function; errors spread over several blocks
OFB	$O_i = E_K[O_{i-1}]$ , $O_0 = IV$ ; $C_i = P_i \oplus O_i$	Keystream independent of the message; bit errors stay put; never reuse the IV
CTR	$O_i = E_K[\mathrm{CNT}_i]$ ; $C_i = P_i \oplus O_i$	Parallel, random access, preprocessing for both O and C

Hooks: Every Code Breaker Crashes One Counter (mode order). Errors: ECB one, CBC two, CFB several, OFB/CTR clean.

Public-key ciphers Search on YouTube

RSA, DH and ECC Search on YouTube

Item	Formula
RSA setup	$n = pq$ , $\phi(n) = (p-1)(q-1)$ , $e$ with $\gcd(e,\phi(n))=1$ , $d \equiv e^{-1} \pmod{\phi(n)}$
RSA encrypt / decrypt	$C = M^{e} \bmod n$ ; $M = C^{d} \bmod n$ ; keys $PU=\{e,n\}$ , $PR=\{d,n\}$
RSA check	$M^{ed} \equiv M \bmod n$ (Euler: $ed = 1 + k\phi(n)$ )
DH setup	Public: prime $q$ , primitive root $a$ . Private: $x_A < q$ . Public key: $y_A = a^{x_A} \bmod q$
DH shared key	$K = y_B^{x_A} \bmod q = y_A^{x_B} \bmod q = a^{x_A x_B} \bmod q$
DH example	$q=353$ , $a=3$ , $x_A=97$ , $x_B=233$ : $y_A = 40$ , $y_B = 248$ , $K = 160$
ECC setup	Curve $E_q(a,b)$ , point $G$ of order $n$ ; private $n_A < n$ , public $P_A = n_A G$
ECC DH	$K = n_A P_B = n_B P_A = n_A n_B G$
ECC encrypt	$C_m = \{kG,\ P_m + kP_b\}$ ; decrypt: subtract $n_b(kG)$
ECC sizes	ECC $n$ = symmetric key x2 = RSA modulus x2: 112/160/224/256/384/512 ↔ 512/1024/2048/3072/7680/15360

RSA attacks: brute force, mathematical (factor $n$ / find $\phi(n)$ / find $d$ ), timing (defences: constant time, random delays, blinding), chosen ciphertext (OAEP).

Integrity and signatures Search on YouTube

Hash and SHA-1 Search on YouTube

Item	One line
6 properties	Any input size; fixed output; fast; one-way; weak collision (given $x$ , no $y\ne x$ with $H(y)=H(x)$ ); strong collision (no pair at all). 1-5 weak, 1-6 strong
Uses	MIC, MAC (keyed hash), signatures, passwords, integrity anchors $C = H(S_{AB}\Vert M)$
Birthday attack	Find a pair with equal hashes; effort $\approx 2^{n/2}$ for an $n$ -bit digest. SHA-1 160 bits → $2^{80}$ ; brute force preimage $2^{160}$
SHA-1 padding	Pad with 1 bit + zeros to length $\equiv 448 \bmod 512$ , append 64-bit length, message is a multiple of 512 bits
SHA-1 buffer	$A=67452301$ , $B=EFCDAB89$ , $C=98BADCFE$ , $D=10325476$ , $E=C3D2E1F0$
SHA-1 rounds	4 rounds x 20 steps; $K_t$ : 5A827999 / 6ED9EBA1 / 8F1BBCDC / CA62C1D6
Round functions	$f_1 = (B\wedge C) \vee (\neg B \wedge D)$ , $f_2 = B \oplus C \oplus D$ , $f_3 = (B\wedge C)\vee(B\wedge D)\vee(C\wedge D)$ , $f_4 = B \oplus C \oplus D$
Output	$CV_{q+1} = SUM_{32}(CV_q, ABCDE_q)$ , $MD = CV_L$ ; SHA-1 160-bit digest, phased out after 2005

DSA Search on YouTube

Group	Formula
Global	$q$ = 160-bit prime, $p$ prime with $2^{L-1} < p < 2^L$ , $L$ = 512..1024 multiple of 64, and $q \mid (p-1)$
Generator	$g = h^{(p-1)/q} \bmod p > 1$
Keys	$0 < x < q$ private; $y = g^{x} \bmod p$ public
Sign (random $k$ , $0<k<q$ , use once)	$r = (g^{k} \bmod p) \bmod q$ ; $s = k^{-1}(H(M) + xr) \bmod q$ ; signature $(r,s)$ , 320 bits total
Verify	$w = s^{-1} \bmod q$ ; $u_1 = H(M)w \bmod q$ ; $u_2 = rw \bmod q$ ; $v = [(g^{u_1} y^{u_2}) \bmod p] \bmod q$ ; accept iff $v = r$

Same-key-two-signatures reveals $x$ : never reuse $k$ (ElGamal behaves the same).

HMAC Search on YouTube

$\text{HMAC}_K(M) = H\big(K^+ \oplus\ \text{opad}\ \Vert\ H(K^+ \oplus\ \text{ipad} \ \Vert\ M)\big)$

ipad = 3636..., opad = 5C5C..., key padded to the block size. Two-pass order: inner with ipad, outer with opad. Design objectives: use existing hash functions, cheap, easy to swap, keep performance, simple, sound interaction mechanics with hash behaviour.

Keys and authentication Search on YouTube

Key management Search on YouTube

Item	One line
Hierarchy	Master key (KDC only) → session key per connection
Symmetric via KDC	One master per party; KDC issues session keys; nonce + timestamps stop replays
Public-key distribution	Announcement, publicly available directory, public-key authority, public-key certificates
Certificate	Binds subject to public key, signed by CA; CA-only modification, anyone reads it
X.509 fields	V, SN, AI, issuer X.500 name, TA (validity period), subject X.500 name, subject public-key info, issuer/subject unique ID (v2+), extensions (v3), signature
Chain	CAs form a hierarchy: forward certificates to clients, backward to parents. User checks the issuer's certificate with a higher CA until a trusted one
Revocation	CRL: compromised key, no longer certified by CA, CA certificate compromised

User authentication Search on YouTube

Item	One line
Means K-P-I-D	Knows (password, PIN), Possesses (token, smartcard), Is (static biometrics: fingerprint, retina), Does (dynamic: voice, signature). Combine card + PIN; all have issues
Replay defences	Sequence numbers (impractical), timestamps (need synced clocks), challenge/response nonce (number used once, $f(N) \ne N$ )
One-way (email)	Header stays clear, body protected and sender authenticated inside the message
Needham-Schroeder	KDC exchange with nonces $N_1$ , $N_2$ ; flaw: a replayed old ticket with a compromised session key is accepted. Fix: add timestamps (Denning)

Kerberos v4 Search on YouTube

Kerberos v4 uses DES and symmetric keys only. The exchange has four steps:

$C \to AS$ : $ID_C \Vert ID_{tgs} \Vert TS_1$ (once per logon).
$AS \to C$ : $E(K_C,[K_{c,tgs} \Vert ID_{tgs} \Vert TS_2 \Vert Lifetime_2 \Vert Ticket_{tgs}])$ — $K_C$ comes from the password.
$C \to TGS$ : $ID_V \Vert Ticket_{tgs} \Vert Authenticator_C$ (once per service type); Authenticator carries $TS_3$ against replays.
$C \to V$ : $Ticket_V \Vert Authenticator_C$ ; for mutual authentication $V \to C$ : $E(K_{c,v},[TS_5 + 1])$ .

Network security Search on YouTube

PGP message format Search on YouTube

Outer chain: ZIP → E(K_s) → R64 (radix-64 armour). Three content components, learn K-Sig-M:

Component	Fields
Session key component	Key ID of recipient's $PU_b$ ; session key $K_s$ , both inside $E(PU_b, \cdot)$
Signature	Timestamp; Key ID of sender's $PU_a$ ; leading two octets of the digest; message digest, inside $E(PR_a,\cdot)$
Message	Filename; timestamp; data (compressed by ZIP, encrypted by $E(K_s,\cdot)$ )

SSL/TLS Search on YouTube

Thing	One line
Architecture	Record protocol (confidentiality + integrity) under handshake, change cipher spec, alert, heartbeat
Record format	Content type, major, minor, compressed length (8/8/8/16 bits); fragment $2^{14} = 16384$ B; MAC 0/16/20 B via HMAC; total $\le 2^{14}+2048$
Handshake, 4 phases	1: client_hello / server_hello (version, session ID, cipher suite, compression, randoms). 2: certificate, server_key_exchange, certificate_request, server_hello_done. 3: certificate, client_key_exchange, certificate_verify. 4: change_cipher_spec + finished both ways
Change cipher spec	1 message, 1 byte, value 1: pending state → current state
Alert	2 bytes: level (warning 1, fatal 2) + code. Fatal kills the connection
Master secret	48 bytes: PRF(pre_master_secret, "master secret", ClientHello.random $\Vert$ ServerHello.random); pre_master via RSA (48 B encrypted with server PU) or DH
Heartbeat	heartbeat_request / response, set at Phase 1; proves liveness, keeps firewalls from idling out
TLS versions	SSL 2.0 1995, SSL 3.0 1996, TLS 1.0 RFC 2246 1999, 1.1 RFC 4346 2006, 1.2 RFC 5246 2008, 1.3 RFC 8446 2018

IPSec Search on YouTube

Item	One line
RFCs	4301 architecture, 4302 AH, 4303 ESP, 4306 IKEv2
Services	Access control, connectionless integrity, data origin authentication, replay rejection, confidentiality, limited traffic flow confidentiality
Mode compare	Transport: payload protection, host-to-host, outer IP header visible. Tunnel: whole packet encrypted under a new IP header, VPNs, gateways
SA	Logical one-way connection: algorithms, keys, lifetime; identified by SPI + IP destination + security protocol identifier; stored in the SAD
ESP layout	SPI, seq no, IV (optional), payload, TFC padding, padding 0-255, pad length, next header — encrypted; ICV after encryption, not encrypted
AH vs ESP	AH authenticates all but mutable IP fields, no encryption (protocol 51); ESP encrypts + optional auth (protocol 50)
Anti-replay	Seq counter from 0, +1 per packet, limit $2^{32}-1$ ; receiver window $(N-W+1) \dots N$
Bundles	Transport adjacency or iterated tunneling; ESP+auth, inner ESP + outer AH, inner transport + outer ESP
IKEv2	Negotiate SA parameters, authenticate endpoints, derive keys, rekey before lifetimes expire

Model: attacks → mechanisms → services (AACIN); the network model needs algorithm, keys, distribution, protocol.
Classical: substitution ciphers die to frequency analysis (Caesar, Playfair, Vigenère, autokey), OTP is unbreakable, transposition keeps frequencies, product ciphers stack confusion and diffusion.
s-DES: 8/10 bits, P10-LS1-P8 then LS2-P8, $f_K$ with E/P, S0/S1, P4. DES: 64-bit block, 56-bit key, 16 Feistel rounds with 48-bit subkeys, S-boxes 6→4. AES: 128-bit state, 10/12/14 rounds, SubBytes-ShiftRows-MixColumns-AddRoundKey, final round without MixColumns, GF $2^8$ arithmetic mod 0x11B and xtime with 0x1b.
Modes: ECB, CBC, CFB, OFB, CTR — formulas above, error behaviour and parallelism hooks.
Asymmetric: RSA $M^e \bmod n$ over factoring; DH $a^{x_A x_B} \bmod q$ ( $q=353$ example lands $K=160$ ); ECC point arithmetic, $K = n_A n_B G$ , far smaller keys.
Signatures and integrity: hash 6 properties, SHA-1 4x20 steps with fixed $K_t$ and magic buffer; DSA $(r,s)$ with $v = r$ ; HMAC double-hash with ipad/opad.
Distribution and users: key hierarchy, X.509 fields and CA chains with CRLs, K-P-I-D authentication. Kerberos AS/TGS/V four steps with tickets and authenticators. PGP K-Sig-M inside R64.
Network security: TLS record + 4-phase handshake + 48-byte master secret through the PRF. IPSec AH (51, integrity only) vs ESP (50, encryption), transport/tunnel modes. SPI+destination+protocol SAs, $2^{32}-1$ replay ceiling, IKEv2 keys.

FoundationsSearch on YouTubeBookmarkSaved

Security modelSearch on YouTubeBookmarkSaved

Classical ciphersSearch on YouTubeBookmarkSaved

Symmetric ciphersSearch on YouTubeBookmarkSaved

S-DES and DESSearch on YouTubeBookmarkSaved

AES layersSearch on YouTubeBookmarkSaved

GF(2^8) arithmeticSearch on YouTubeBookmarkSaved

Modes of operationSearch on YouTubeBookmarkSaved

Public-key ciphersSearch on YouTubeBookmarkSaved

RSA, DH and ECCSearch on YouTubeBookmarkSaved

Integrity and signaturesSearch on YouTubeBookmarkSaved

Hash and SHA-1Search on YouTubeBookmarkSaved

DSASearch on YouTubeBookmarkSaved

HMACSearch on YouTubeBookmarkSaved

Keys and authenticationSearch on YouTubeBookmarkSaved

Key managementSearch on YouTubeBookmarkSaved

User authenticationSearch on YouTubeBookmarkSaved

Kerberos v4Search on YouTubeBookmarkSaved

Network securitySearch on YouTubeBookmarkSaved

PGP message formatSearch on YouTubeBookmarkSaved

SSL/TLSSearch on YouTubeBookmarkSaved

IPSecSearch on YouTubeBookmarkSaved

On this page