Block ciphers

Product’ = permutation + substitution. • Iterated cipher = many rounds – Key schedule– schedule: • Key K is used to construct Nr round keys (subkeys) K1, …, KNr. – Round function g: • stater = g(stater-1, Kr). • state0 = x.

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Block ciphers

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Product ciphers

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The Data Encryption Standard

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History of DES

¢ May 1973, the National Institute of Standards and Technology (NIST) published a

solicitation for cryptosystems

¢ The Data Encryption Standard (DES), first

version in 1975, developed by IBM, then

became the standard in 1977

¢ DES was used for 20 years until AES appeared

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DES—S boxes

For each S box: 6 bits > 4 bits An S box is a 4x16 array:

*6 bits (b,b,b,b,b;b,) are divided into 2-bit (b,b,) row number, °4-bit (b,b,b,b;) column number, the output is the value

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DES— computation of key schedule

K (64 bits) Actual key is 64 bits, of which 56 bits are

TT key and 8 bits are parity-check, in the

(PC-1 |} ? positions 8,16,24, , 64

(28 bits) ~y—~ (28 bits)

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Analysis of DES

¢ The decryption of DES 1s the exact same as the encryption, but with the 16 sub-keys reversed ¢ Problem is that key length is too short

— Easy to be broken by exhaustive key search, e.g., “DES challenge III” finds the DES key in 22 hours, 15

minutes, in 1999

— Easy to be broken by differential cryptanalysis and

linear cryptanalysis

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DES modes of operation

¢ 4 different modes of DES operation:

— Electronic Codebook mode (ECB)

¢ Naive use of DES: each 64-bit block encrypted to 64-bit cipher block

 Y=y) Y; Ơ, = DES,(x,) DES; (x,) DES; (x,)

— Cipher Block Chaining mode (CBC)

¢ Define y,=IV, (initialization vector), then y=DES,(y;., © x;) — Output Feedback mode (OFB)

¢ A synchronous stream cipher:

— Z=IV, z=DES,(Z;1), y=x, P Z;

— Cipher Feedback mode (CFB)

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Properties of four DES modes

¢ ECB: identical plaintext blocks to get identical ciphertext blocks

¢ ECB and OFB: any change in block x, only affects cipher block y,, not other In some situation such as unreliable communication channel, this is a good property E.g., OFB is used to encrypt satellite transmissions

¢ CBC and CFB: if a block x, is changed, the cipher block y; and all subsequent blocks are changed This property is good for authentication E.g., these two modes can be used to generate Message Authentication Code (MAC)

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Triple DES Plaintext

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Advanced Encryption Standard (AES)

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Advanced Encryption Standard (AES)

Intended to replace DES Block length is 128 bits

Key length is 128, or 192, or 256 bits

Iterated cipher: Nr=10/12/14 rounds for key length 128/192/256 respectively

Of course, very secure No better known attack other than exhaustive key search

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History of AES

¢ In 1997, NIST needed an advanced

encryption standard (AES) to replace DES ¢ From 1998 to 2000, many cryptosystem

candidates submitted The final 5 ones

were: MARS, RC6, Rijndael, Serpent, and Twofish

° In 2000, Rijndael was selected for the AES

Then become the standard in 2001

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Advanced Encryption Standard (AES)

A private key encryption scheme

An US Federal Information Processing Standard (FIPS) PUB 197 http://csrc.nist.gov/publications/fips/fips197/fips- 197.pdf) AES has a fixed block size of 128 bits and a key size of 128, 192 or 256 bits

Each block passes through certain number of

rounds of operations, depending on the key length

Each round contains four transformations,

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AES—brief description

Given a plaintext x (length 128 bits), initialize State to be x, and perform an operation ADDROUNDKEY, which 1s x-

ors the RoundKey with State

For each of first Nr-1 rounds, perform a substitution operation called SUBBYTES on State using an S-box;

perform a permutation SHIFTROWS on State; perform an operation MIXCOLUMNS on State; and perform

ADDROUNDKEY on State

(Final round) perform SUBBYTES; perform

SHIFTROWS; and perform ADDROUNDKEY, all are on

State

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AES States ¢ Transition of input (message) bytes,

input bytes State array oniput bytes ig | ig | ïs | ?nạ Soo | Sor | Soa | So3 OHfa | O1f4 | OMfs |OHft3

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SubBytes Transformation, s.| |S„.|s Š-Box ttal %„ | #a2|s “99 | “01 0.2) "634." 040 01 03 — | + 5 $ t2 | Ÿt3 Shy F + | địa ` r.c ` c —— ’ i § 5 q Sy $5 2 5 $ í 5 1 $5 ` 55 3 Sep'| Say | Say] Sis Hig | Mag: | Sen | Sa

S-box was derived from the calculations of

binary polynomials based on some mathematical theories

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MixColumns Transformation, MixColumns ()

A lookup table, derived from the calculations of binary

polynomials based on some mathematical theories, is available

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AddRoundKey Transformation, l=round* 4

¡1s a subkey originated from a key seed via

a deterministic key expansion algorithm

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AES Decryption

¢ Each transformation 1s invertible,

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Criteria for the selection of a cryptosystem 1) Security 2) Cost (speed and memory requirements) — Software — Hardware — Smart card

3) Algorithm and implementation characteristics ¢ Riyndael was chosen for AES with the

combination of all criteria

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The end