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AES (Rijndael)

AES (Rijndael). Joan Daemen and Vincent Rijmen, “The Design of Rijndael, AES – The Advanced Encryption Standard”, Springer, 2002, ISBN 3-540-42580-2 FIPS Pub 197, Advanced Encryption Standard (AES), December 04, 2001 Rijndael : variable, AES : fixed. Vincent. AES- Requirements.

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AES (Rijndael)

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  1. AES (Rijndael) Joan Daemen and Vincent Rijmen, “The Design of Rijndael, AES – The Advanced Encryption Standard”, Springer, 2002, ISBN 3-540-42580-2 FIPS Pub 197, Advanced Encryption Standard (AES), December 04, 2001 Rijndael : variable, AES : fixed Vincent

  2. AES- Requirements. • Block cipher • 128-bit blocks • 128/192/256-bit keys • Worldwide-royalty free • More secure than Triple DES • More efficient than Triple DES

  3. AES Calendar • Jan. 2, 1997 : Announcement of intent to develop AES and request for comments • Sep. 12, 1997 : Formal call for candidate algorithms • Aug. 20-22, 1998 : First AES Candidate Conference and beginning of Round 1 evaluation (15 algorithms), Rome, Italy • Mar. 22-23, 1999 : Second AES Candidate Conference, NY, USA • Sep. 2000 : Final AES selection (Rijndael !) Apr. 2000 AES3 Jan. 1997 Call for algorithms Aug. 1998 AES1 15 algorithms Mar. 1999 AES2 Announce winner in Sep, 2000 5 algorithms selected

  4. AES Round1 algorithms • 15 algorithms are proposed at AES1 conference

  5. AES Round2 Algorithms • After AES2 conference, NIST selected the following 5 algorithms as the round 2 candidate algorithm.

  6. Security of AES Candidates

  7. Comparison(I) • Encryption speed analysis by NIST

  8. Comparison(II) • Java Implementation by A. Sterbenz (Graz Univ.)

  9. Comparison(III) • Smart Card Implementation by F. Sano (Toshiba) * : omit to check “weak” in the key schedule

  10. Comparison(IV) • CMOS ASIC Implementation by Ichikawa (Mitsubishi)

  11. Rijndael - Overview • Proposed by Joan Daemen, Vincent Rijmen(Belgium) • Design choices • Square type • Three distinct invertible uniform transformations(Layers) • Linear mixing layer : guarantee high diffusion • Non-linear layer : parallel application of S-boxes • Key addition layer : XOR the round key to the intermediate state • Initial key addition, final key addition • Representation of state and key • Rectangular array of bytes with 4 rows (square type) • Nb : number of column of the state (4~8) • Nk : number of column of the cipher key (4~8) • Nb is independent from Nk

  12. Key (Nk=4) State (Nb=6) Number of rounds (Nr) Rijndael - States

  13. Round transformation Output transformation Input whitening Output Input Mix-Column(MC) BS, SR, ARK Byte-wise substitution(BS) Shift-Low(SR) Bit-wise key addition Bit-wise key addition 44 byte array Rijndael - Encryption • Block size: 128 • Key size: 128/192/256 bit • Component Functions • ByteSubstitution(BS): S-box • ShiftRow(SR): CircularShift • MixColumn(MC): Linear(Branch number: 5) • AddRoundKey(ARK): • Omit MC in the last round.

  14. Properties • Substitution-Permutation Network (SPN) • (Invertible) Nonlinear Layer: Confusion • (Invertible) Linear Layer: Diffusion • Branch Number • Measure Diffusion Power of Linear Layer • Let F be a linear transformation on n words. • W(a): the number of nonzero words in a. • (F) = mina0 {W(a) + W(F(a))} • Rijndael: branch number =5

  15. Security Goals • K-secure • No shortcut attacks key-recover attack faster than key-exhaustive search • No symmetry property such as complementary in DES • No non-negligible classes of weak key as in IDEA • No Related-key attacks • Hermetic • No weakness found for the majority of block ciphers with same block and key length • Rijndael is k-secure and hermetic

  16. Component Functions(I) • ByteSubstitution • S(x)=x-1 in GF(28) with almost maximal nonlinearity over m(x) = x8 + x4 + x3 + x +1 • Shift Rows

  17. Component Functions(II) • Mixcolumn • AddRoundKey

  18. Rijndael: Pseudo-Code Rijndael(State,CipherKey) { KeyExpansion(CipherKey,ExpandedKey); AddRoundKey(State,ExpandedKey); For( i=1 ; i<Nr ; i++ ) Round(State,ExpandedKey + Nb*i); FinalRound(State,ExpandedKey + Nb*Nr); } Round(State,RoundKey) { ByteSub(State); ShiftRow(State); MixColumn(State); AddRoundKey(State,RoundKey); } FinalRound(State,RoundKey) { ByteSub(State); ShiftRow(State); AddRoundKey(State,RoundKey); }

  19. Mode of Operations

  20. Modeofoperation (I) • ECB (Electronic CodeBook) mode C P n n IF Ci = Cj, DK(Ci) = DK(Cj) K D K E n n P C i) Encryption ii) Decryption

  21. Mode of operation (II) • CBC (Cipher Block Chaining) P1 P2 Pl IV K IV : Initialization Vector E E K K E Ci = EK(Pi  Ci-1) Pi = DK(Ci)  Ci-1 C1 C2 Cl C1 C2 Cl - 2 block Error Prog. - self-sync - If |Pl|  |P|, Padding req’d K K D D D K IV P1 P2 Pl

  22. IV IV K K E m-bit E Pi Ci Ci Modeofoperation (III) • m-bit OFB (Output FeedBack) Ci = Pi  O(EK) Pi = Ci  O(EK) m-bit - No Error Prog. - Req’d external sync - Stream cipher - EK or DK Pi I) Encryption II) Decryption

  23. Modeofoperation (IV) • m-bit CFB (Cipher FeedBack) IV IV Ci = Pi  EK(Ci-1) Pi = Ci  EK(Ci-1) K E m-bit m-bit E K - Error prog. till an error disappears in the buffer - self-sync - EK or DK Pi Ci Pi Ci I) Encryption II) Decryption

  24. Mode of operation (V) • Counter mode ctr+m-1 ctr ctr+1 Ci = Pi  EK(Ti) Pi = Ci  EK(Ti) Ti = ctr+i -1 mod 2m |P|, |ctr|= m, Parallel computation K E E E K K Pm-1 P2 P1 C2 Cm-1 C1 ctr+1 ctr+m-1 ctr E K E K K E C2 C1 Cm-1 P2 Pm-1 P1

  25. Mode of Operation (VI) • CCM mode (Counter with CBC-MAC mode) • Ctr + CBC • Authenticated encryption by producing a MAC as a part of the encryption process

  26. Mode of operation - summary • Use of mode • ECB : key management, useless for file encryption • CBC : File encryption, useful for MAC • m-bit CFB : self-sync, impossible to use channel with low BER • m-bit OFB : external-sync. m= 1, 8 or n • Ctr : secret ctr, parallel computation • CCM : authenticated encryption • Performance Degradation/ Cost Tradeoff

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