可笑的煮饺子文化

从小到大，一直看着周围的中华儿女在饺子第一次煮沸后，往里续些凉水，再煮沸，再续凉水，再煮沸……这宗教仪式，一直持续到——用打左脸给右脸的基督徒的说法，是地狱成了冰窖；用具有高尚情操的无产阶级革命者的话说，是共产主义在全人类实现。

小时候，家里没有煤气灶、电灶、烤箱、电磁炉、微波炉等资产阶级人定胜天的玩意儿，有的是玉米秆、劈柴、烟煤无烟煤等纯天然无毒副作用的自然妈妈的恩赐。看着我的生物妈妈在烟熏火燎中用凉水一次次镇压想逃生的饺子，我那天假有邪的心灵充满了期待和欣喜。当然，我的嘴也配合地流着口水。

后来马齿渐长，不幸听了郭沫若《科学的春天》的呼唤和受了徐迟《哥德巴赫猜想》的蛊惑，上了物理的贼船。成为物理海盗的一个好处，是弄明白了妈妈为什么用凉水镇压饺子。懵懵懂懂中，小学文化的妈妈，在试图将水温控制在尽量接近沸点的水平。如果不加控制，水一旦自由沸腾起来，汤汁四溅，不但可能烫着人，饺子也可能蹦出来。蹦不出来的饺子，可能因为对流引起的剧烈振荡而皮开肉绽。

当然，控制水温的另一个办法，是控制热源。扬汤止沸不如釜底抽薪的道理，是几千年前老祖宗就懂得的。在三十多年前妈妈当时的生活条件下，填汤止沸要优于釜底抽薪。从燃烧的炉灶里抽玉米秆和劈柴，是很难操控、危险且不卫生的。烧煤的炉灶更是如此。无法或不方便控制热源，剩下的选择很简单——填凉水。

妈妈当然不是填汤止沸手法的发明者。她，就像我们的千千万万平凡的母亲一样，从她们的长辈那里不加质疑地继承了这个生活经验。千千万万这样的生活经验集合到一起，就是所谓的文化。

绝大部分人，都象我的母亲一样，不加质疑地继承了填汤止沸的煮饺子经验，不但自己机械地重复着，也机械地传给下一代。传着传着，就传到了煤气灶、电灶、电磁炉的时代——热源精细可控的时代。

于是，我看到了无数可笑的重复的场景：一个个拥有自然科学最高学位的中华儿女，在现代厨房电器的一堆旋钮按钮中，往沸腾的饺子锅里一次次地续着凉水，没想到只是将控制热量的旋钮稍稍向左扭扭，就可以达到同样的效果，也没有想到，完全可以把水温控制在沸点下一点，不用再去劳心。

煮饺子尚且如此，遍地中医信徒又有何惊奇？

该同情谁？该憎恨谁？战争，无论基于什么理由，都是灭绝人性的。

 def ^(otherArray)
  zip(otherArray).map { |pair| pair[0]^pair[1] }
 end
end

class Fixnum
 def xtime    # GF(2^8) mulitiplication by x
  t=(self<<1) & 0xFF
  t^=0x1B if self[7]==1
  t
 end

 def fm(v)    # GF(2^8) mulitiplication
  r=0
  xm=self
  0.upto(7) {|b| r^=xm if v[b]==1; xm=xm.xtime; }
  r
 end
end
  
  
class Rijndael
 S=[
  0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
  0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
  0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
  0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
  0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
  0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
  0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
  0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
  0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
  0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
  0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
  0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
  0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
  0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
  0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
  0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16
 ]

 I_S=[
  0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,
  0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,
  0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e,
  0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,
  0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,
  0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,
  0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,
  0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,
  0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,
  0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,
  0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,
  0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,
  0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,
  0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,
  0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,
  0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d
 ]
 
 I_MixColPloy=[0xE,0xB,0xD,0x9]
 T=S.map {|byte| [byte, byte, byte.fm(3), byte.fm(2)]}
 I_T=I_S.map {|byte| [byte.fm(0x9), byte.fm(0xD), byte.fm(0xB), byte.fm(0xE)]}

 Rcon=[[0x8d,0,0,0]]    # 8d.xtime=01
 1.upto(13) {|j| Rcon[j]=[Rcon[j-1][0].xtime,0,0,0]}

 def initialize(nb=4)
  raise "Illegal value for Nb." unless [4,6,8].include?(nb)
  @nb=nb
 end

 def load_ek(key)    # load encrypt key
  @ek=keyExpansion(key)
 end

 def load_dk(key)    # load decrypt key
  @dk=keyExpansion(key)
  @dk[@nb..-5].each {|word| word[0..3]=invMixColumn(word)}
 end

 def invMixColumn(word)
  (0..3).map {|i|
   I_MixColPloy.zip(word.rot(i)).map{|pair| pair[0].fm(pair[1])}.inject{|a,b| a^b}
  }
 end

 def keyExpansion(key)
  # key is byte array
  nk=[4,6,8].find {|i| i*4==key.size} or raise "Illegal key length."
  nr=[@nb, nk].max+6
  w=[]
  (0..nk-1).each {|i| w[i]=key[4*i,4] }
  (nk..@nb*(nr+1)-1).each { |i|
   temp=w[i-1]
   if i%nk==0
    temp = temp.rot.map{|byte| S[byte]} ^ Rcon[i/nk]
   elsif nk>6 && i%nk==4
    temp = temp.map{|byte| S[byte]}
   end
   w[i]=w[i-nk]^temp
  }
  w
 end

 def invKeyExpansion(key)
  w=keyExpansion(key)
  w[1,-1].each {|word| invMixColumn(word)}
  w
 end

 def cipher(plaintext)
  raise "Invalid length of input data." if plaintext.size!=@nb*4
  a=(0..@nb-1).map {|j| plaintext[j*4,4]}  # map plaintext onto state
  nr=@ek.size/4-1
  a^=@ek[0,4]         # add round key
  1.upto(nr) { |round|
   k=@ek[round*4,4]
   e=[]
   0.upto(3) { |j|
    if round!=nr
     e[j]= T[a[j][0]].rot(3) ^ T[a[(j+1)%4][1]].rot(2) ^ T[a[(j+2)%4][2]].rot(1) ^ T[a[(j+3)%4][3]]
    else
     e[j]= [ S[a[j][0]], S[a[(j+1)%4][1]], S[a[(j+2)%4][2]], S[a[(j+3)%4][3]] ]
    end
   }
   a=e^k
  }
  a.flatten
 end

 def i_cipher(ciphertext)
  raise "Invalid length of input data." if ciphertext.size!=@nb*4
  a=(0..@nb-1).map {|j| ciphertext[j*4,4]}  # map ciphertext onto state
  nr=@dk.size/4-1
  k=@dk[nr*4,4]
  a^=k         # add round key
  (nr-1).downto(0) { |round|
   k=@dk[round*4,4]
   e=[]
   0.upto(3) { |j|
    if round!=0
     e[j]= I_T[a[j][0]].rot(3) ^ I_T[a[(j-1)%4][1]].rot(2) ^ I_T[a[(j-2)%4][2]].rot(1) ^ I_T[a[(j-3)%4][3]]
    else
     e[j]= [ I_S[a[j][0]], I_S[a[(j-1)%4][1]], I_S[a[(j-2)%4][2]], I_S[a[(j-3)%4][3]] ]
    end
   }
   a=e^k
  }
  a.flatten
 end
end

AES=Rijndael.new(4)   # Nb in AES is 4

# Example Vectors (FIPS-197 Appendix C)

plaintext=[0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77, 0x88, 0x99, 0xaa, 0xbb, 0xcc, 0xdd, 0xee, 0xff]
key=[0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f]
AES.load_ek key
AES.load_dk key
ciphertext = AES.cipher plaintext
output = AES.i_cipher ciphertext
output==plaintext
key=[0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17]
AES.load_ek key
AES.load_dk key
ciphertext = AES.cipher plaintext
output = AES.i_cipher ciphertext
output==plaintext
key=[0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f]
AES.load_ek key
AES.load_dk key
ciphertext = AES.cipher plaintext
output = AES.i_cipher ciphertext
output==plaintext

在“5.2.1 The Round Transformation”中：
c[j,0] = b[j,0]
c[j,1]  b[j-C1,1]
c[j,2]  b[j-C2,2]
c[j,3]  b[j-C3,3]

应为:
c[j,0] = b[j,0]
c[j,1]  b[j+C1,1]
c[j,2]  b[j+C2,2]
c[j,3]  b[j+C3,3]

害得我查了半天错