就目前科技而言.ppt

1、1-,1,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)。,一、傳統的加解密法：AES,1-,2, 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

2、, Rijndael, Serpent, Twofish NIST於2000年選定Rijndael為新一代的加密標準,一、傳統的加解密法：AES,1-,3,有限體GF(28),一個位元組( byte) b 是由8個bits b7 b6 b5 b4 b3 b2 b1 b0所組成的，我們可以將它視為一個係數為0或1的多項式如下: b7 x7+ b6 x6+ b5 x5+ b4 x4+ b3 x3+ b2 x2+ b1 x1+ b0 x0 Example: 16進位表示法57的2進位表示法為01010111，它所對應的多項式則為: x6+ x4+ x2+ x+1 .,1-,4,Example 1:

3、(x6+ x4+ x2+ x+1) +( x7+ x+1)= x7+ x6+ x4+ x2 . ”01010111”+”10000011”=”11010100”,Example 2: (x6+ x4+ x2+ x+1)( x7+ x+1) = x13 + x11 + x9 + x8 + x7 + x7 + x5 + x3 + x2 + x +x6 + x4 + x2 + x + 1 = x13+ x11+ x9+ x8+ x6+ x5+ x4+ x3+1 x13+ x11+ x9+ x8+ x6+ x5+ x4+ x3+1 modulo x8+ x4+ x3+ x+1 = x7 + x6 +

4、1,有限體GF(28)下之運算,1-,5,Multiplication by x,Multiply b(x) with the polynomial x: b7x8+b6x7+b5x6+b4x5+b3x4+b2x3+b1x2+b0 x If b7=0, the reduction is identity operation; if b7=1, m(x) must be subtracted (i.e. EXORed). That is, multiplication by x (02) can be implemented by a left shift and a conditional E

5、XOR with1B.,1-,6,Example,57 13 =FE 57 02=xtime(57)=AE 57 04=xtime(AE)=47 57 08=xtime(47)=8E 57 10=xtime(8E)=07 57 13 =57(010210) = 57AE07=FE,1-,7,Polynomials with coefficients in GF(28),Two polynomials over GF(28): a(y)=a3y3+a2y2+a1y+a0 b(y)=b3y3+b2y2+b1y+b0 Their product c(y)=c6y6+c5y5+c4y4+c3y3+c2

6、y2+c1y+c0 c0=a0 b0 c1=a1 b0 a0 b1 c2=a2 b0 a1 b1 a0 b2 c3=a3 b0 a2 b1 a1 b2+ a0 b3 c4=a3 b1 a2 b2 a1 b3 c5=a3 b2 a2 b3 c6=a3 b3,1-,8,Polynomials with coefficients in GF(28),By reducing c(y) modulo a polynomial of degree 4, the result can be reduced to a polynomial of degree below 4. M(y)=y4+1 and yi

7、 mod y4+1=yi mod 4.,1-,9,Polynomials with coefficients in GF(28),Product of a( y ) and b( y ): d( y ) = a( y ) b( y )= d3y3+d2y2+d1y+d0 d0 = a0 b0 a3 b1 a2 b2 a1 b3 d1 = a1 b0 a0 b1 a3 b2 a2 b3 d2 = a2 b0 a1 b1 a0 b2 a3 b3 d3 = a3 b0 a2 b1 a1 b2 a0 b3,1-,10,Polynomials with coefficients in GF(28),ci

8、rculant matrix:,1-,11,Rijndael 演算法,Rijndael是一個包含可變區塊長度和可變密鑰長度的區塊加密法,其區塊長度和密鑰長度可允許為128, 192或256 bits,運算回合數與區塊長度和密鑰長度之關係,1-,12,Example of The State and the Cipher Key,128bits之區塊長度表示法(Nb = 4),128bits之密鑰長度表示法(Nk = 4),1-,13,Round 函數,Round(State, RoundKey) ByteSub(State); ShiftRow(State); MixColumn(State)

9、; AddRoundkey(State, RoundKey); FinalRound(State, Roundkey) ByteSub(State); ShiftRow(State); AddRoundkey(State, RoundKey); ,1-,14,ByteSub 函數,1-,15,ShiftRow 函數,不同的區塊長度所須旋轉的大小,ShiftRow運算在狀態值表的情形 (Nb=4),1-,16,在MixColumn函數中，狀態值表的每一行是被視為在GF(28)中的多項式，並且乘上一個固定的多項式C(x)後再同餘於多項式y4+1，而其中C(y)=03y3+01y2+01y+02 我

10、們可將其表示矩陣乘法。令b(y)=c(y)a(y) b0 02 03 01 01 a0 b1 = 01 02 03 01 a1 b2 01 01 02 03 a2 b3 03 01 01 02 a3,MixColumn 函數,1-,17,子金匙加法函數(The Round Key Addition),(Nb = 4),1-,18,Key Expansion,(Nk 6) KeyExpansion(CipherKey , W) for( i =0 ; i Nk ; i+) Wi=CipherKeyi ; for( j= Nk ; j Nb*(Nr+1) ; j + = Nk ) W j =W j

11、 - Nk SubByte(Rotl(Wj-1) Rconj/ Nk ; for( i =1 ; i Nk ,1-,19,Key Expansion,(Nk 6) KeyExpansion(CipherKey , W) for( i =0 ; i Nk ; i+) Wi=CipherKeyi ; for( j= Nk ; j Nb*(Nr+1) ; j + = Nk ) W j =W j - Nk SubByte(Rotl(Wj-1) Rconj/ Nk ; for( i =1 ; i 4 ; i +) Wi+j = W i+j- Nk W i+j-1; Wj+4 = Wj+4- Nk Sub

12、Byte(Wj+3) for( i =5 ; i Nk ; i+) Wi+j = W i+j- Nk W i+j-1; ,1-,20,加密演算法,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 ); ,1-,21,InvCipher(byt

13、e in4 * Nb, byte out4 * Nb, word wNb * (Nr + 1) begin bytestate4,Nb;state = in AddRoundKey(state, w + Nr * Nb) for round = Nr - 1 step -1 to 1 InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w + round * Nb) InvMixColumns(state) end for InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w) out = state end,Pseudo Code for the Inverse Cipher,1-,22,AES的使用模式可參考DES的使用模式，有底下四種標準操作模式：,(1) 電子編碼模式（Electronic Codebook Mode, ECM） (2) 密文塊串連模式（Cipher Block Chaining, CBC） (3) 密文反饋模式（Cipher Feedback, CFB） (4) 輸出反饋模式（Output Feedback, OFB）