Abstract:
An encryption device and method and decryption device and method which implement a bit-based encryption scheme and hardware design. The encryption device includes a random number generator, receiving a main key, determining a working key using at least one random number and outputting a working key, a model, receiving the main key, the working key and plain text to be encoded and generating at least two frequency counts. The encryption device further includes an encoder, which outputs encoded text based on the working key, the plain text and the at least two frequency counts. The encryption device and method and decryption device and method process encrypted text that is based upon a stream structure with an unlimited key length and may be compressed by 50%. The encoded text is changeable with different environments even for the same plain text and the same key. Operations of the hardware design are based on arithmetic additions and shifts, and not multiplications and divisions. As a result, the hardware design is simple and applicable to cryptography and e-commerce.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention is directed to encryption and decryption, and more particularly, to a variable size key cipher and method and device for utilizing variable size key cipher to perform encryption and decryption.  
       DESCRIPTION OF THE RELATED ART  
       [0002]     Traditionally, compression and cryptography have been considered distinct and separate technologies, which were developed and applied separately. However, they share a common goal of removing redundancy of an output, although they do so in different ways. Recognizing this common goal, Witten, Neal and Cleary (hereafter known as WNC) were the first to apply adaptive arithmetic coding to encryption. In particular, WNC made the following observations: 
        by re-coding messages, compression protects the messages from casual observers;     removing redundancy denies a cryptanalyst the leverage of exploiting the normal statistical regularities in natural language; and     adaptively taking advantage of the characteristics of the data being transmitted provides good compression performance.        
 
         [0006]     The properties identified in these three observations appear to offer the benefits of good compression as well as good security—the best of both worlds.  
         [0007]     The schematic flow of a conventional, general, arithmetic coding, model-based encryption scheme  10 , such as the WNC scheme, is illustrated in  FIG. 1 . As illustrated in  FIG. 1 , plain text  12  is input to both an encoder  14  and a model  16 . A key  18  is also input to the model  16 . The encoder  14  produces cipher text  20  based on the plain text  12  and an output of the model  16 . The model  16  provides, in any given context, a probability distribution for the next character. The simplest models are insensitive to context and give the same distribution regardless of the neighboring character. The model  16  should not assign zero probability to any symbol that actually occurs, otherwise the symbol cannot be coded because the upper and lower ends of its range coincide. For encoder  14 , a source symbol alphabet is chosen and each symbol is assigned a probability of occurrence. The interval range is usually 0 to 1 and each source symbol occupies a subinterval in the range according to its probability. The interval is successively subdivided as each new source symbol is read. Highly probable symbols reduce the interval by a smaller amount than less probable symbols. The cipher text  20  is represented by a value in the interval. Such a system is described in “Data Security in a Fixed-Model Arithmetic Coding Compression Algorithm” published in Computer &amp; Security, 11(1992), pp. 445-461.  
         [0008]     As the name arithmetic coding might suggest, the source symbols which make up the plain text  12  are encoded numerically. Each symbol does not necessarily translate into the same fixed code which makes up the cipher text  20  each time the symbol is encoded. An input source string, which may be a string of source symbols, is usually represented by an interval of real numbers between 0 and 1. The range of the interval may initially be defined by a value proportional to the probability of the symbol in question. The interval may be successively subdivided as each new source symbol is read from the plain text  12 . Highly probable symbols in the plain text  12  reduce the interval by a smaller amount than less probable symbols. As an analogy, the arithmetic coding, as illustrated in  FIG. 1 , is like using a flexible ruler to measure a symbol string.  
         [0009]     The WNC scheme is a byte-based arithmetic coding scheme for encryption that utilizes a frequency table without a random generator. Key features of the WNC scheme are a byte-based model and an initial frequency table as the key for encryption. In WNC, the working key and main key are the same.  
         [0010]     However, subsequent research by Bergen et al. in “Data Security in a Fixed-Model Arithmetic Coding Compression Algorithm”, Computer &amp; Security, pp. 445-461, 1992, has shown that there are security issues with the WNC scheme. In particular, the WNC implementation of a fixed model arithmetic-coding algorithm promotes easy analysis and therefore the possibility of easy and straightforward deciphering. This ease of analysis and deciphering is the direct result of repeating fixed sub-strings in the output, which characterize each particular symbol. The fixed nature of the WNC implementation permits relatively easy determination of both the ordering of symbols in the initial frequency table and the actual values of the symbol frequencies. As a result, it is difficult to design a secure model and key control for the WNC encryption scheme.  
       SUMMARY OF THE INVENTION  
       [0011]     The present invention solves the problems with conventional arithmetic coding techniques by providing an encryption device and method and a decryption device and method which are based on a bit-based arithmetic coding technique. The encryption device and method and the decryption device and method utilize frequency tables for value 0 and 1 and a random generator. The frequency tables includes working keys not main keys, as in conventional techniques. At the beginning of the encoding, a main key is input into an encoder. A model initializes the frequency table according to the main keys and a random bit to form a working key. The working key, which is changeable, is used as the probability to encode plain text. The model in the present invention update the probability according to the input text.  
         [0012]     More specifically, the present invention is directed to an encryption device, comprising a random number generator, receiving a main key, determining a working key using at least one random number and outputting the working key; a model, receiving the main key, the working key and plain text and generating at least two frequency counts; and an encoder, outputting cipher text, based on the working key, the plain text, and the at least two frequency counts.  
         [0013]     Further, the present invention is directed to a method of encrypting, comprising processing random bits and key bits to generate at least one frequency table; and encoding plain text using the at least one frequency table. Still further, the present invention is directed to a decryption device, comprising a model, receiving a main key, a working key and plain text and generating at least two frequency counts; a decoder, outputting plain text, based on the working key, the main key, the plain text, the at least two frequency counts, and a random number generator, receiving the plain text and determining the working key using at least one random number and outputting the working key to said model. Still further, the present invention is directed to a method of decrypting, comprising processing random bits and key bits to generate at least one frequency table; and decoding cipher text using the at least one frequency table.  
         [0014]     A bit-based encryption scheme and hardware design of the present invention produces a cipher that is based upon stream structure and with an unlimited key length. The cipher also has the advantage that it may compress plain text by at least 50%. The cipher is changeable with different environment even for the same plain text and the same key. Operations in the hardware design are based on arithmetic additions and shifts, no multiplication and divisions are included. Therefore, the hardware design is simple. The cipher, encoder, decoder and methods are applicable to cryptography and e-commerce. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]      FIG. 1  illustrates a conventional, general, arithmetic coding, model-based encryption scheme.  
         [0016]      FIG. 2  illustrates an exemplary schematic flow for encryption in one exemplary embodiment of the present invention.  
         [0017]      FIG. 3  illustrates a flowchart for encoding in one embodiment of the present invention; and  
         [0018]      FIG. 4  illustrates a model in more detail in one exemplary embodiment of the present invention.  
         [0019]      FIG. 5  illustrates the frequency table in one exemplary embodiment of the present invention.  
         [0020]      FIG. 6  illustrates an exemplary schematic flow of decryption in one exemplary embodiment of the present invention;  
         [0021]      FIG. 7  illustrates a flowchart for decoding in one embodiment of the present invention; and  
         [0022]      FIG. 8  illustrates a model in more detail in another exemplary embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0023]      FIG. 2  illustrates an exemplary schematic flow for encryption in one embodiment of the present invention. As illustrated in  FIG. 2 , plain text  12  is input to both an encoder  114  and a model  116 . A main key  118  is supplied to the model  116  and to a random generator  122 . The random generator  122  produces working keys from the main key  118  and random numbers generated within and the working keys are output to the encoder  114  and the model  116 . The model  116  provides to the encoder  114 , two frequency counts, for 0 and 1, respectively and the encoder  114  output is a compressed bit stream. The encoder  114  produces compressed information (i.e., cipher text  120 ), based on the plain text  12  and the working keys output from the random number generator  122 , and the frequency counts 0,1 from the model  116 .  
         [0024]     The encoder  114  may operate as follows. A message to be encoded is represented by an interval of real numbers between 0 and 1. As the message becomes longer, the interval needed to represent the message decreases and the number of bits needed to specify the interval increase. Successive symbols of the message reduce the size of the interval in accordance with the symbol probabilities generated by the model  116 . The more likely symbols reduce the range by less than the unlikely symbols and hence add fewer bits to the message.  
         [0025]     Initially, the interval assigned to a message is the entire interval [0,1)([0,1) denotes the half-open interval  0 ≦x&lt;1). As each symbol in the message is processed, the range is narrowed to that portion of the range allocated to the given symbol. For example, assume the alphabet is (a, b, c, d, e, f) and a fixed model is used with the probabilities shown in Table 1.  
                                                 TABLE 1                                   Symbol   Probability   Range                                        a   025   [0, 0.25)           b   0.25   [0.25, 0.5)           c   0.1   [0.5, 0.6)           d   0.1   [0.6, 0.7)           e   0.1   [0.7, 0.8)           f   0.2   [0.8, 1.0)                      
 
 Assume the message abc is transmitted. Initially, the encoder  114  (and an associated decoder which will be described later) knows that the range is [0,1). After receiving the first symbol a, the encoder  114  narrows the range to [0,0.25), the range that model  116  allocates to the symbol a. The second symbol b narrows the new range to the second one-fourth, [0.0625, 0.125)—the previous range was 0.25 units long and one-fourth of that is 0.0625. The next symbol c is allocated [0.5, 0.6), which when applied to [0.0625, 0.125) gives the smaller range [0.09375, 0.1). 
 
         [0026]     Suppose all the associated decoder knows about the message is the final range [0.9375, 0.1). The decoder can immediately deduce that the first character was a, since the range lies entirely within the space the model of Table 1 allocates for a. After this, the range is [0, 0.25). After seeing b [0.0625, 0.125) which entirely encloses the given range [0.09375, 0.1), the second character is b. Proceeding in this manner, the decoder can identify the whole message.  
         [0027]     In one exemplary embodiment, the encoder  114  is the encoder described in copending U.S. application Ser. No. 09/240,576 entitled “Multiplication-Free Arithmetic Coding” filed on Feb. 1, 1999, the entire contents of which are hereby incorporated by reference. An advantage of this encoder are that there is no multiplication and division operation involved, which makes the hardware design simple. This encoder is described below.  
         [0000]     Encoding  
         [0028]     Initially, two registers R and L, are set to 1 and an arbitrary number, respectively. The encoder  114  is supplied with three inputs, a first frequency count c 0  representing a fractional value of the probability of 0, a second frequency count c 1 , representing a fractional value of the probability 1, and a so-far encoded symbol i (either 0 or 1).  
         [0029]     The encoding steps performed by the encoder  114  can be summarized in pseudocode as: 
        1. If c 0 &gt;c 1 , exchange the values of c 0  and c 1 , and let i=!i.     2. While R≦c 1 , do 
            Output the most significant bit of L.     L=L&lt;&lt;=1, R=R&lt;&lt;=1.     If R&gt;˜L, then R=˜L+1.    
            3. If i=0, then R=c 0 ; else R=R−c 0 , L=L+c 0 . 
 
 Output L 
       
 
         [0036]     Note that some C Language notation is employed in the above pseudocode. ! represents logic complement, ˜represents binary complement, and &lt;&lt;=represents arithmetic shift left. From the description above, the present invention operates on the following assumption: for each iteration, R≈c 0 +c 1 . 
 
L:=L, R:=c 0 , i=0  (1) 
 
L:=L+c 0 , R:=R−c 0 , i=1  (2) 
 
         [0037]     In the present invention, initializing the two registers R and L to 1 and an arbitrary number, respectively, permits the first word in the output stream to denote a synchronous word for real time transmission applications. Further, step  1  is generally referred to as an exchange step, step  2  is referred to as an adjustment step, and step  3  is referred to as an encoding step. A magnitude step, which is required in conventional multiplication-free arithmetic coding techniques is not required in the present invention. In the present invention, the adjustment step is executed before the encoding step. In the adjustment step, executing the “while” loop when the value of register R is less than or equal to the value of the second frequency count and setting the value of register R equal to the binary complement of the value of register L plus one if the value of the register R is greater than the binary complement of the value of register R eliminates the need for a subsequent bit stuffing step.  
         [0038]     To summarize, the method of multiplication-free arithmetic coding of the present invention produces an encoded bit stream by receiving a symbol from an encoded string and two frequency counts, finding a most probable symbol and a least probable symbol; subjecting a first register to magnitude shift operations for outputting bits to the encoded bit stream and for approximating a contextual probability of each symbol in the encoded string, and encoding a next symbol in the encoded string based on the contextual probability.  
         [0039]      FIG. 3  includes the specific steps performed by the encoder  114  in the encoding process  20  in more detail. In particular, in step  22 , registers R and L are initialized to 1 and the sync word, respectively. The encoded bit stream, in this example, 11011100i, is input along with the initial values of registers R and L to the 0-order Markov model at step  24  to produce the frequency counts c 0  and c 1 . In step  26 , c 0  and c 1  are compared and if c 0  is greater than c 1 , c 0  and c 1  are exchanged and i is set to its logical complement at step  28 . If however, c 0  is not greater than c 1 , processing proceeds to step  30 , where it is determined whether the value in register R is greater than or equal to c 1 . If so, processing proceeds to step  32 , where the most significant bit of the L register is output, L and R are arithmetically left shifted, and if R is greater than the binary complement of L, then R is set to the binary complement of L plus one, and processing returns to step  30 . If the value of register R is not greater than equal to C 1 , then processing continues to step  34 . In step  34  it is determined whether i is equal to 0. If i is equal to 0, then the value of register R is set equal to C 0  at step  36  and if i is not equal to 0 then R is set to the previous value of R minus c 0  and L is set to the previous value of L plus c 0  in step  38 , thereby encoding the next bit in the bit stream. The process then repeats by inputting the next bit to the Markov model update at step  24 . The processing is continued until all bits of the input bit stream are encoded. Then, the value of register L is output as the encoded bit stream.  
         [0040]     Although the present invention is described utilizing a 0-order Markov model, any model, known to one ordinary skill in the art, could be utilized.  
         [0041]     As illustrated in  FIG. 4 , the model  116  includes a frequency table  130  (illustrated as RAMs  126 ) and a model controller  128 . The frequency counts contained in frequency table  130  represent the probabilities, such as the probabilities shown in Table 1. The plain text  12 , the main key  118  and the working keys are input to the model controller  128 . The random generator  122  generates one random bit per system clock. As illustrated in  FIG. 4 , the frequency table  130  may include two related terms that make it very difficult to trace all information saved in the frequency table  130  except the two related terms. The model  116  can use an address register r to record the closest t bits currently processed, the size of the frequency table  130  is 2 t . In one embodiment, the model  116  is a t-order Markov model and r looks like sliding windows of size t. Initially, the values in the frequency table  130  may be set to 1.  
         [0042]     The present invention may be described as a two phase cipher. The first phase processes random bits and key bits. In the first phase, the key size controls the random bit generator, so that controller  128  can obtain random bit string with the same size as the key. For each bit pair (one random bit, one key bit), controller  128  can perform the following: 
        1) according to a shift register in model controller  128 , get F 0  and F 1  from RAMs  126 ;     2) if the key bit is 0, add 1 to F 0 ; else add 1 to F 1 ;     3) pass the random bit and F 0 , F 1  to encoder  114 ;     4) if the random bit is 0, add 1 to F 0 ; else add 1 to F 1 ;     5) write F 0  and F 1  back to RAMs  126 ;     6) left shift the shift register in model controller  128 , and insert the current random bit into the last position of the shift register.        
 
         [0049]     In the first phase, the random bit is provided to encoder  114  (or decoder) via the model controller  128 . When the first phase is completed, a useful initial frequency table is obtained in RAMs  126 .  
         [0050]     In the second phase, the plain text  12  is encoded. In the second phase, the plain text  12  is input to the model controller  128  which executes the following actions for each input bit: 
        1) according to the shift register, get F 0  and F 1  from RAMs  126 ;     2) pass the plain text bit and F 0 , F 1  to encoder  114 ;     3) if the plain text bit is 0, add 1 to F 0 ; else add 1 to F 1 ;     4) write F 0  and F 1  back to RAMs  126 ;     5) left shift the shift register, and insert the current plain text bit into the last position of the shift register. Therefore, the plain text  12  also will pass to encoder  114  (or decoder) via the model controller  128 .        
 
         [0056]      FIG. 5  illustrates the frequency table  130  in one preferred embodiment of the present invention. As illustrated in  FIG. 5 , the frequency table  130  includes r entries for the frequency of 0 and r entries for the frequency of 1. The size of the frequency table  130  in one embodiment is 2 t . In one embodiment, t=15.  
         [0057]     The model controller  128  controls the read and writes of the RAMs  126  and the output of the frequency table  130  and source bit to the arithmetic coder  114 . The inputs to the encoder  114  include a text bit from the plain text  12 , a key bit from the main key  118 , a random bit from the random generator  122 , and two frequencies  136  from the RAMs  126 . The output of the model controller  128  to RAMs  126  is a read-enable signal  138 , a write-enable signal  140 , modified frequencies  142  for bits “0” and “1”, respectively and an address  144 . The outputs from the model controller  128  to the encoder  114  include a source bit  146  and a pair of frequency counts  148  for bits “0” and “1”. In one exemplary embodiment, the model  116  is implemented utilizing two clocks, a system clock and a RAM clock, in order to permit the model controller  128  to finish a read and write to the RAMs  126  in one system cycle.  
         [0058]     The interaction between the encoder  114  and the model  116  is as follows. Initially, r may be set to a fixed number; the current value of r is used to find two frequency counts respectively for 0 and 1 from the frequency table  130 . The two counts are then input to the encoder  114 . The current bit is encoded and the frequency count is updated at the location pointed to by r. Then, slide r to contain the current bit and repeat until all bits are encoded.  
         [0059]     As illustrated in the embodiment of  FIG. 4 , the frequency table  130  includes random access memories  126 . The two RAMs  126  represent the frequency tables for bits “0” and “1”, respectively. In one exemplary embodiment, there are a total of 64 k pairs of frequencies for bits “0” and “1”. As a result, the frequency may range from 1 to 255. The encoder  114  implements an arithmetic encoding algorithm, where its input signal is a one bit source signal and a pair of frequencies for bits “0” and “1”. For each time interval, the pair of frequencies are different and dependent on the input source bit. The output of the encoder  114  is the cipher-text  120  and an output valid bit  150 .  
         [0060]     The present invention may also use a key (any length of bit stream) to control the initial value in frequency table  130  and a random bit stream to control the values of r. The random bit stream may be generated by the random generator  122 . The key for encryption is termed the working key. To be more precise, if k 1 , k 2 , . . . , k n  is the bit stream for encryption key. An exemplary algorithm is as follows:  
         [0000]     Encryption  
         [0000]    
       
         
           
              Initialization: r=0. Let all items in frequency table  130  be 1, initialize the encoder  114 , j=1  
              Input: k 1 , k 2 , . . . k n    
              1. While j&lt;=n, do  
              Find the location pointed by r from the frequency table  130 .  
              If k j =1, add 1 to frequency  1  location; else add 1 to frequency  0  location.  
              Use the current frequency counts to encode one bit l from random generator  122 .  
              If l=1, add 1 to frequency  1  location; else, add 1 to frequency  0  location.  
              Left shift r, r=r| the random bit  
              2. Encode plain text  12  and update model  116  as follows:  
           
         
       
     
         [0070]     If current bit is 1, add 1 to frequency  1  location, else add 1 to frequency  0  location.  
         [0071]     Left shift r, r=r|the current bit  
         [0072]     It is noted that step  1  is used to generate the initial frequency table  130 , the frequency table  130  may depend on environment, since random generator  122  is used. Further, even if the same encryption key is used at different times, a different frequency table  130  will result. This indicates the cipher in the present invention is not one-to-one but is variable.  
         [0073]     In one preferred embodiment, VHDL language is used to describe the behavior model between the model controller  128  and the encoder  114  illustrated in  FIG. 4 . Exemplary VHDL is set forth below:  
                                   library IEEE ;       - use IEEE.std_logic_unsigned.all ;        use IEEE.std_logic_signed.all ;        use IEEE.std_logic_arith.all ;        use IEEE.std_logic_1164.all ;       entity cipher is        port (        key  : in std_logic ;        random : in std_logic ;        text  : in std_logic ;        end_of_key : in std_logic ;        end_of_text : in std_logic ;        data0_in : in std_logic_vector ( 7 downto 0 ) ;        data1_in : in std_logic_vector ( 7 downto 0 ) ;        sys_clock : in std_logic ;        mem_clock : in std_logic ;        data0_out : out std_logic_vector ( 7 downto 0 ) ;        data1_out : out std_logic_vector ( 7 downto 0 ) ;        addr  : buffer std_logic_vector (15 dowoto 0 ) ;        READ_ENABLE : out std_logic ;        WRITE_ENABLE: out std_logic ;        cipher_text : out std_logic ;        out_valid : out std_logic       ) ;       end cipher ;       architecture RTL of cipher is       signal encode_bit  : std_logic ;       signal encode_valid : std_logic :=‘0’;       signal c0,c1  : std_logic_vector ( 7 downto 0 ) ;       signal L   : std_logic_vector ( 31 downto 0 ) := “00000000000000000000000000000000”;       signal R,H   : std_logic_vector ( 31 downto 0 ) := “00000000000000000000000000000001”;       signal freq0  : std_logic_vector ( 7 downto 0) ;       signal freq1  : std_logic_vector ( 7 downto 0) ;       signal j   : std_logic;       begin       model_update : process        variable a,b : integer ;        variable counter : integer := −1 ;        begin         wait until mem_clock&#39;event and mem_clock=‘1’;         counter := ( counter + 1 ) mod 8 ;         case counter is          when 0 =&gt; READ_ENABLE &lt;= ‘1’ ;           WRITE_ENABLE &lt;= ‘0’ ;          if(end_of_key=‘0’) then            addr &lt;= SHL(addr,“01”) + key ;           else            addr &lt;= SHL(addr,“01”) + text ;           end if;        when 2 =&gt; if(end_of_key=‘0’) then           encode_bit &lt;= random ;           c0 &lt;= data0_in + not key;           c1 &lt;= data1_in + key;           a := conv_integer(data0_in) + conv_integer(not key) + conv_integer(not random);           b := conv_integer(data1_in) + conv_integer(key) + conv_integer(random);           else           encode_bit &lt;= text ;           c0 &lt;= data0_in;           c1 &lt;= data1_in;           a := conv_integer(data0_in) + conv_integer(not text);           b := conv_integer(data1_in) + conv_integer(text);           end if ;           if(end_of_text=‘0’) then           encode_valid &lt;= ‘1’ ;           else           encode_valid &lt;= ‘0’ ;           end if;           READ_ENABLE &lt;= ‘0’ ;           WRITE_ENABLE &lt;= ‘1’ ;           if(a&gt;16#FF# or b&gt;16#FF#) then           data0_out &lt;= shr(conv_std_logic_vector((a+1),8),“01”) ;           data1_out &lt;= shr(conv_std_logic_vector((b+1),8),“01”) ;           else           data0_out &lt;= conv_std_logic_vector(a,8) ;            data1_out &lt;= conv_std_logic_vector(b,8) ;           end if ;         when others =&gt; null ;         end case ;        end process ;        arith_coder : process         variable a,b,c : std_logic_vector (31 downto 0 ) ;         variable f0,f1 : std_logic_vector (7 downto 0 ) ;         variable k : std_logic ;         begin          wait until sys_clock=‘1’ and sys_clock&#39;event ;          if(encode_valid=‘1’) then           if(c0&gt;c1) then           freq0 &lt;= c1 ;           freq1 &lt;= c0 ;           j &lt;= not encode_bit ;           else           freq0 &lt;= c0 ;           freq1 &lt;= c1 ;           j &lt;= encode_bit ;           end if ;           f0 := freq0 ;           f1 := freq1 ;           k := j ;           while R&lt;=f1 loop           cipher_text &lt;= L(31) ;           out_valid &lt;= ‘1’ ;           a := shl(L,“01”) ;           b := shl(R,“01”) ;           c := not a ;          L &lt;= a;          if b&gt;a then           R &lt;= c + ‘1’ ;          else           R &lt;= b ;          end if ;          wait until mem_clock=‘1’ and mem_clock&#39;event ;          end loop;          out_valid &lt;= ‘0’ ;          if(k=‘0’) then          R &lt;= conv_std_logic_vector (conv_integer(f0),32);          else          R &lt;= R − f0 ;          L &lt;= L + f0 ;          end if ;         end if;         end process ;       end RTL ;                  
 
       EXAMPLE  
       [0074]     The parameters used for testing in this example are as follows: 
    L—Low end of the encoding interval: 32 bits, initially 0     H—High end of the encoding interval: 32 bits, initially 1     R—Range of the encoding interval: 32 bits, initially 1     V—Register for decoding bit stream     2 t —size of the frequency table  130 : 64K for both 0 and 1, t=15    
 
         [0080]     r—Address pointer register for table: 15 bits  
                             TABLE 2                           Plain text “AAAAAAAAAAAAAAAAAAAAAAAA”            Experiments   Keys   Cipher Text (HEX)               1   A   B9 50 C8 C9 1B F8 44 10       2   A   FA A1 91 91 3C 81 14 80       3   A   83 D3 C3 C7 28 1F 35       4   AbCD8910   56 DF B4 56 894867 9E 82 28 28 28               66 45 21 40       5   AbCD8910   B9 72 D9 5D A0 F1 62 68 99 7D 7D               70 98 EE F8                  
 
         [0081]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                   
               
               
                 Plain text “It is incredible for us” 
               
             
          
           
               
                 Experiments 
                 Keys 
                 Cipher Text (HEX) 
               
               
                   
               
               
                 1 
                 Zfg 
                 E7 95 CE 8C A3 B7 7E 1D 98 9E 1E 6F 0D 77 
               
               
                   
                   
                 32 14 C5 58 24 4b FF 40 69 43 1C 45 29 80 
               
               
                 2 
                 Zfg 
                 2B CF 08 FD 5F 54 87 E1 D9 89 E1 E6 F0 D7 
               
               
                   
                   
                 73 21 4C 55 82 44 BF F4 06 94 31 C4 52 98 
               
               
                 3 
                 123 
                 C4 99 9E F4 97 49 27 32 06 97 32 0A 0B 62 86 
               
               
                   
                   
                 25 13 CA 51 2E 44 BA 86 72 45 CA 95 27 00 
               
               
                 4 
                 123 
                 E5 3D C0 5C 82 58 12 EA 84 95 52 85 69 0D 77 
               
               
                   
                   
                 32 14 C5 58 24 4B FF 40 69 43 1C 45 29 80 
               
               
                   
               
             
          
         
       
     
         [0082]     From Tables 2 and 3 above, the following is apparent: 1) for the same plain text with the same key, different cipher text results, 2) the size of cipher text is changeable with different experiment parameters and different keys, and 3) for high correlative data the compression rate is high, but for less correlative date or a shorter string, the compression rate is also good.  
         [0083]     The technique of the present invention may be used for encryption if the values in the frequency table are used as the encryption key. One difference between the present invention and WNC is the model. The bit-based model of the present invention makes it extremely difficult to trace all the initial values using a technique such as the one described by Bergen/Hogan. The compressed bit stream or cipher text  120  may be decoded by a reverse process.  
         [0084]      FIG. 6  illustrates an exemplary schematic flow of decryption in one embodiment of the present invention. As illustrated in  FIG. 6 , the cipher text  120  is input to a decoder  124 . A main key  118  is input to the model  116  and to the decoder  124 . The output of random bit generator  152  is input to the model  116 . The output of the model  116  is input to the decoder  124 . The decoder  124  decodes the cipher text  120  to produce the plain text  12  which is fed back to the model  116 . The decoder  124  also passes an output to the random generator  152 . In one exemplary embodiment, the decoder  124  is the decoder described in copending U.S. application Ser. No. 09/240,576 entitled “Multiplication-Free Arithmetic Coding” filed on Feb. 1, 1999, the entire contents of which are hereby incorporated by reference. This decoder is described in more detail below.  
         [0085]     Decoding  
         [0086]     For decoding the R and L registers are again initialized and a third register V is utilized to store part of the decoding bit stream, and i denotes the output bit. If S is the decoding bit stream, which is generated by the encoding algorithm described above, the decoding steps performed by the decoder  124  are summarized in pseudocode as: 
        1. If c 0 &gt;c 1 , exchange the values of c 0  and c 1 , and let i=1; else i=0.     2. While R≦c 1 , do 
            L=L&lt;&lt;1, R=R&lt;&lt;1, V=V&lt;&lt;1.     V=V| next bit from S.     If R&gt;˜L, then R=˜L+1.    
            3. If c 0 &lt;V, then R=c 0 ; else R=R−c 0 , L=L+c 0 , and     i=!i        
 
         [0094]     To summarize, the method of the multiplication-free arithmetic coding to produce a decoded string receives bits from a decoded stream and two frequency counts, finds a most probable symbol and a least probable symbol, subjecting a first register to magnitude shift operations for inputting bits from the decoded bit stream and for approximating a contextual probability of each symbol in the decoded string, and decoding a next symbol to the decoded stream based on the contextual probability.  
         [0095]      FIG. 7  includes the specific steps performed by the decoder  124  in the decoding process  40  in more detail. In particular, in step  42 , the register R, L, and V are initialized. The values of registers R, L, and V and the string to be decoded are input to 0-Markov model at step  44  to produce frequency counts c 0  and c 1 . In step  46 , c 0  and c 1  are compared and if c 0  is greater than c 1 , c 0  and c 1  are exchanged and i is set to its logical complement at step  48 . If however, c 0  is not greater than c 1 , processing proceeds to step  50 , where it is determined whether the value of register R is greater than or equal to c 1 . If so, processing proceeds to step  52  where registers R, L, and V are all arithmetically left shifted, the next bit from the decoding bit stream S is added to register V, and if R is greater than the binary complement of L, then R is set to the binary complement of L plus one. Processing then returns to step  50 .  
         [0096]     If the value of register R is not greater than or equal to c 1 , then processing continues to step  54 . In step  54 , it is determined whether c 0  is less than V. If c 0  is less than V, then the value of register R is set equal to c 0  at step  56  and if c 0  is not less than V, then R is set to the previous value of R minus c 0 , L is set to the previous value of L plus c 0 , and i is set to its logic complement at step  58 , thereby decoding the next bit in the bit stream S. The process then repeats by inputting the next bit to the Markov model update at step  44 . The processing is continued until all bits of the decoding bit stream S are decoded.  
         [0097]     Again, although the present invention just described utilizing a 0-order Markov model, any model, known to one of ordinary skill in the art, could be utilized.  
         [0098]     Table 4, set forth below, illustrates a compression ratio comparison for files of varying types, between an encoder which implements multiplication, the prior art technique disclosed in U.S. Pat. No. 4,652,856, and the multiplication-free arithmetic coding of the present invention.  
                                                     TABLE 4                                   Encoder of the   U.S. Pat.               Multiplier   Present   No.       Source File   Size   Encoder   Invention   4,652,856                                C source   27620   37.5%   38.4%   39.9%       Chinese file   72596   43.3%   43.8%   44.9%       Scale image   262330   67.9%   68.8%   69.6%       EXE file   54645   74.3%   74.6%   75.6%       Mixed data   417192   67.2%   68.0%   68.9%                  
 
         [0099]     As illustrated in Table 4, the present invention achieves a compression ratio better than prior art multiplication-free arithmetic techniques. Table 4 also illustrates that the multiplication encoder usually provides the best compression because each multiplication-free design utilizes some approximate value instead of practical probabilities, so there will usually some degradation in compression ratios utilizing multiplication-free arithmetic techniques. However, the present invention, as illustrated in Table 4, provides a low computationally complex and low cost hardware implementation, which still achieves compression ratios which are comparable to multiplication-base techniques.  
         [0100]     As illustrated in  FIG. 8 , the main key  118  is supplied to the model controller  128 . The model controller  128  controls the read and writes of the RAMs  126  and the output of the frequency table  130  and the source bit to the decoder  124 . The inputs to the decoder  124  include a text bit from the cipher text  120 , a key bit from the main key  118 , and a pair of frequency counts  148  for bits “0” and “1”. The output of the model controller  128  to RAMs  126  is a read enable signal  138 , a write enable signal  140 , modified frequencies  142  for bits “0” and “1”, respectively, and an address  144 . The RAMs  126  output two frequencies  136  to the model controller  128 . In one exemplary embodiment, the model  116  is implemented utilizing two clocks, a system clock and a RAM clock, in order to permit a model controller  128  to finish read and write to the RAMs  126  in one system cycle.  
         [0101]     The present invention may also be described as a two-phase decipher. In the first phase, random bits are decoded from cipher bits. In the first phase, the key size controls the decoder  124  so that the model controller  128  can receive random bit strings from the decoder  124  with the same size as the key. For each bit pair (one random bit and one key bit), decipher is performed by: 
        1) using a shift register in decoder  124 , to get F 0  and F 1  from RAMs  126 ;     2) if the key bit is 0, add 1 to F 0 ; add 1 to F 1 ;     3) pass F 0 , F 1  to decoder  124 ;     4) decoder  124  decodes random bit and send the random bit to model controller  128 ;     5) if the random bit is 0, the model controller  128  adds 1 to F 0 ; else adds 1 to F 1 ;     6) write F 0  and F 1  back into RAMs  126 ; and     7) shift the register left, and insert the current random bit into the last position of the shift register.        
 
         [0109]     When the first phase is completed, a useful initial frequency table is obtained in RAMs  126 .  
         [0110]     In the second phase, the plain text  12  is decoded. In the second phase, only one input, the cipher text  120 , is required and deciphering includes the following steps for each input bit: 
        1) according to the shift register, get F 0  and F 1  from RAMs  126 ;     2) pass F 0 , F 1  to the decoder  124 ;     3) decoder  124  decodes a plain text bit and sends the plain text bit to model controller  126 ;     4) if the plain text bit is 0, add 1 to F 0 ; else add 1 to F 1 ;     5) write F 0  and F 1  back into to RAMs  126 ; and     6) shift the register left, and insert the current plain text bit into the last portion of the shift register. Therefore, plain text  12  will be output from decoder  124 .        
 
         [0117]     To decode an encrypted message, the frequency table  130  may be constructed and the random bit stream in the cipher text  120  can be recovered before decoding begin(s). Decoding can also be defined in pseudocode as follows:  
         [0000]     Decryption  
         [0000]    
       
         
           
              1. While j&lt;=n, do  
              Find the location pointed by r from the frequency table  130 .  
              If k j =1, add 1 to frequency  1  location; else add 1 to frequency  0  location.  
              Use the current frequency counts to decode one random bit  1 .  
              If l=1, add 1 to frequency  1  location; else, add 1 to frequency  0  location.  
              Left shift r, r=r| the random bit  
              2. Decode cipher text  120  and update model as follows:  
           
         
       
     
         [0125]     If current bit is 1, add 1 to frequency  1  location, else add 1 to frequency  0  location.  
         [0126]     Left shift r, r=r| current bit.  
         [0127]     It is noted that the functional blocks in  FIGS. 1-3 ,  6  and  8  may be implemented in hardware and/or software. The hardware/software implementations may include a combination of processor(s) and article(s) of manufacture. The article(s) of manufacture may further include storage media and executable computer program(s). The executable computer program(s) may include the instructions to perform the described operations. The computer executable program(s) may also be provided as part of externally supplied propagated signal(s).  
         [0128]     The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.