1. Cryptography and Network Security Chapter 5 Advanced Encryption Standard Fourth Edition by William Stallings Lecture slides by Lawrie Brown

2. 對稱式加密系統之代表 1970 年代中期由 IBM 公司所發展 美國國家標準局公佈為資料加密標準的一種區塊 加密法 (Block Cipher) DES 屬於區塊加密法，而區塊加密法就是對一定 大小的明文或密文來做加密或解密動作 每次加密解密的區塊大小均為 64 位元 (Bits) 傳統的加解密法： DES DES (Data Encryption Standard)

3. 就一般資料而言，資料通常大於 64 位元。只要將明 / 密文中每 64 位元當作一個區塊加以切割，再將每個 區塊做加密或解密即可。 最後一個區塊大小可能小於 64 位元，此時就要將此 區塊附加 “0” 位元，直到區塊大小成為 64 位元為止。 56 DES 所用加密或解密金鑰也是 64 位元大小。但其中 有 8 個位元是用來做錯誤更正，真正的金鑰有效長度 只有 56 位元。 傳統的加解密法： DES DES (Data Encryption Standard)

4. EEE3 ：用三把不同秘密金鑰（即金鑰長度為 168 位元） 並以加密 - 加密 - 加密依序處理產生密文。 EDE3 ：用三把不同秘密金鑰，並以加密 - 解密 - 加密依序處理產生密 文。 EEE2 ：用二把不同秘密金鑰（即金鑰長度為 112 位元）任選二個 DES 金鑰設為相同（例如，第一個及第二個 DES 金鑰相同，但與第三個 DES 金鑰不同），並以加密 - 加密 - 加密依序處理產生密文。 EDE2 ：用二把不同秘密金鑰（即金鑰長度為 112 位元）第一個 DES 金 鑰與第三個 DES 金鑰相同，但與第二個 DES 金鑰不同，並以加密 - 解 密 - 加密依序處理產生密文。 傳統的加解密法： DES Triple DES

5. 傳統的加解密法： DES Triple DES

6. 傳統的加解密法： DES Triple DES

7. 就目前科技而言，現有之 DES 密碼系統所使用之金鑰 長度過短 ( 僅 56 位元 ) ，其安全性已遭受質疑，為提高 其安全性，便有了 Triple-DES 的構想。 隨著電腦技技的發展，可預見未來 Triple-DES 的加密 演算法也勢必淘汰，有鑑於此，美國國家標準技術 局 (NIST) 於 1997 年元月二日開始著手計劃公開徵求新 一代加密標準 ( 簡稱 AES) 。 傳統的加解密法： AES

8. Advanced Encryption Standard (AES) AES 為新一代 NIST/FIPS 的加密標準 NIST 於 1998 年開始 15 個 AES 候選演算法之技術分析 1999 年選出五個候選演算法 :MARS, RC6, Rijndael, Serpent, Twofish NIST 於 2000 年選定 Rijndael 為新一代的加密標準 傳統的加解密法： AES

9. Origins  clear a replacement for DES was needed have theoretical attacks that can break it have theoretical attacks that can break it have demonstrated exhaustive key search attacks have demonstrated exhaustive key search attacks  can use Triple-DES – but slow, has small blocks  US NIST issued call for ciphers in 1997  15 candidates accepted in Jun 98  5 were shortlisted in Aug-99  Rijndael was selected as the AES in Oct-2000  issued as FIPS PUB 197 standard in Nov-2001

10. AES Requirements  private key symmetric block cipher  128-bit data, 128/192/256-bit keys  stronger & faster than Triple-DES  active life of 20-30 years (+ archival use)  provide full specification & design details  both C & Java implementations  NIST have released all submissions & unclassified analyses

11. AES Evaluation Criteria  initial criteria: security – effort for practical cryptanalysis security – effort for practical cryptanalysis cost – in terms of computational efficiency cost – in terms of computational efficiency algorithm & implementation characteristics algorithm & implementation characteristics  final criteria general security general security ease of software & hardware implementation ease of software & hardware implementation implementation attacks implementation attacks flexibility (in en/decrypt, keying, other factors) flexibility (in en/decrypt, keying, other factors)

12. AES Shortlist  after testing and evaluation, shortlist in Aug-99: MARS (IBM) - complex, fast, high security margin MARS (IBM) - complex, fast, high security margin RC6 (USA) - v. simple, v. fast, low security margin RC6 (USA) - v. simple, v. fast, low security margin Rijndael (Belgium) - clean, fast, good security margin Rijndael (Belgium) - clean, fast, good security margin Serpent (Euro) - slow, clean, v. high security margin Serpent (Euro) - slow, clean, v. high security margin Twofish (USA) - complex, v. fast, high security margin Twofish (USA) - complex, v. fast, high security margin  then subject to further analysis & comment  saw contrast between algorithms with few complex rounds verses many simple rounds few complex rounds verses many simple rounds which refined existing ciphers verses new proposals which refined existing ciphers verses new proposals

13. The AES Cipher - Rijndael  designed by Rijmen-Daemen in Belgium  has 128/192/256 bit keys, 128 bit data  an iterative cipher processes data as block of 4 columns of 4 bytes processes data as block of 4 columns of 4 bytes operates on entire data block in every round operates on entire data block in every round  designed to be: resistant against known attacks resistant against known attacks speed and code compactness on many CPUs speed and code compactness on many CPUs design simplicity design simplicity

14. Rijndael  data block of 4 columns of 4 bytes is state  key is expanded to array of words  has 9/11/13 rounds in which state undergoes: byte substitution (1 S-box used on every byte) byte substitution (1 S-box used on every byte) shift rows (permute bytes between groups/columns) shift rows (permute bytes between groups/columns) mix columns (subs using matrix multipy of groups) mix columns (subs using matrix multipy of groups) add round key (XOR state with key material) add round key (XOR state with key material) view as alternating XOR key & scramble data bytes view as alternating XOR key & scramble data bytes  initial XOR key material & incomplete last round  with fast XOR & table lookup implementation

15. Rijndael

16. Byte Substitution  a simple substitution of each byte  uses one table of 16x16 bytes containing a permutation of all 256 8-bit values  each byte of state is replaced by byte indexed by row (left 4-bits) & column (right 4-bits) eg. byte {95} is replaced by byte in row 9 column 5 eg. byte {95} is replaced by byte in row 9 column 5 which has value {2A} which has value {2A}  S-box constructed using defined transformation of values in GF(2 8 )  designed to be resistant to all known attacks

17. Byte Substitution

18. Shift Rows  a circular byte shift in each each 1 st row is unchanged 1 st row is unchanged 2 nd row does 1 byte circular shift to left 2 nd row does 1 byte circular shift to left 3rd row does 2 byte circular shift to left 3rd row does 2 byte circular shift to left 4th row does 3 byte circular shift to left 4th row does 3 byte circular shift to left  decrypt inverts using shifts to right  since state is processed by columns, this step permutes bytes between the columns

19. Shift Rows

20. Mix Columns  each column is processed separately  each byte is replaced by a value dependent on all 4 bytes in the column  effectively a matrix multiplication in GF(2 8 ) using prime poly m(x) =x 8 +x 4 +x 3 +x+1

21. Mix Columns

22.  can express each col as 4 equations to derive each new byte in col to derive each new byte in col  decryption requires use of inverse matrix with larger coefficients, hence a little harder with larger coefficients, hence a little harder  have an alternate characterisation each column a 4-term polynomial each column a 4-term polynomial with coefficients in GF(2 8 ) with coefficients in GF(2 8 ) and polynomials multiplied modulo (x 4 +1) and polynomials multiplied modulo (x 4 +1)

23. Add Round Key  XOR state with 128-bits of the round key  again processed by column (though effectively a series of byte operations)  inverse for decryption identical since XOR own inverse, with reversed keys since XOR own inverse, with reversed keys  designed to be as simple as possible a form of Vernam cipher on expanded key a form of Vernam cipher on expanded key requires other stages for complexity / security requires other stages for complexity / security

24. Add Round Key

25. AES Round

26. AES Key Expansion  takes 128-bit (16-byte) key and expands into array of 44/52/60 32-bit words  start by copying key into first 4 words  then loop creating words that depend on values in previous & 4 places back in 3 of 4 cases just XOR these together in 3 of 4 cases just XOR these together 1 st word in 4 has rotate + S-box + XOR round constant on previous, before XOR 4 th back 1 st word in 4 has rotate + S-box + XOR round constant on previous, before XOR 4 th back

27. AES Key Expansion

28. Key Expansion Rationale  designed to resist known attacks  design criteria included knowing part key insufficient to find many more knowing part key insufficient to find many more invertible transformation invertible transformation fast on wide range of CPU’s fast on wide range of CPU’s use round constants to break symmetry use round constants to break symmetry diffuse key bits into round keys diffuse key bits into round keys enough non-linearity to hinder analysis enough non-linearity to hinder analysis simplicity of description simplicity of description

29. AES Decryption  AES decryption is not identical to encryption since steps done in reverse  but can define an equivalent inverse cipher with steps as for encryption but using inverses of each step but using inverses of each step with a different key schedule with a different key schedule  works since result is unchanged when swap byte substitution & shift rows swap byte substitution & shift rows swap mix columns & add (tweaked) round key swap mix columns & add (tweaked) round key

30. AES Decryption

31. Implementation Aspects  can efficiently implement on 8-bit CPU byte substitution works on bytes using a table of 256 entries byte substitution works on bytes using a table of 256 entries shift rows is simple byte shift shift rows is simple byte shift add round key works on byte XOR’s add round key works on byte XOR’s mix columns requires matrix multiply in GF(2 8 ) which works on byte values, can be simplified to use table lookups & byte XOR’s mix columns requires matrix multiply in GF(2 8 ) which works on byte values, can be simplified to use table lookups & byte XOR’s

32. Implementation Aspects  can efficiently implement on 32-bit CPU redefine steps to use 32-bit words redefine steps to use 32-bit words can precompute 4 tables of 256-words can precompute 4 tables of 256-words then each column in each round can be computed using 4 table lookups + 4 XORs then each column in each round can be computed using 4 table lookups + 4 XORs at a cost of 4Kb to store tables at a cost of 4Kb to store tables  designers believe this very efficient implementation was a key factor in its selection as the AES cipher

33. Summary  have considered: the AES selection process the AES selection process the details of Rijndael – the AES cipher the details of Rijndael – the AES cipher looked at the steps in each round looked at the steps in each round the key expansion the key expansion implementation aspects implementation aspects