Abstract:
The present invention provides encryption schemes and apparatus, which are more efficient than the existing single pass authenticated encryption schemes, while providing the same level of security. The initial vectors, which are an essential part of these schemes, are chosen in an incremental and safe fashion. This also leads to an incremental method for generating the pair-wise differentially uniform sequences or XOR-universal sequences which are another essential part of such schemes. The incrementality of the generation of these sequences extends to even across different plain-text messages being encrypted, leading to substantial savings in time to encrypt. A further step of encryption is shown to be redundant and leads to savings over earlier schemes. Another embodiment describes splitting the plain-text blocks into two sets, and using the block-cipher in encrypt mode on one set and the block-cipher in decrypt mode on the other set, leading to beneficial hardware solutions.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of Invention 
         [0002]    This invention relates to a method and apparatus for cryptographically transforming an input message into an output message while assuring message integrity. 
         [0003]    Cryptographic systems are known in the data processing art. In general, these systems operate by performing an encryption operation on a plain-text input message, using an encryption key, and a symmetric key block cipher, producing a cipher-text message. The encrypted message may then be sent over an unreliable and insecure channel to a receiver who shares the secret key. The receiver of the encrypted message performs a corresponding decryption operation, using the same key to recover the plain-text block. Because the same key is used by both the sender and receiver of the message, the process is referred to as a “symmetric key” process. 
         [0004]    There is a related issue of message integrity. To elaborate, although the receiver of the cipher-text message can decrypt the cipher-text, the receiver is not assured that the cipher-text was not accidentally or maliciously altered during transmission. To ensure message integrity, the cipher-text message comes accompanied with a message authentication code (MAC). This MAC is generated by the sender from the cipher-text using a cryptographic hash function. 
         [0005]    Recently, various one-pass authenticated encryption schemes have been proposed, including IACBC, IAPM, which are described in the U.S. Pat. Nos. 7,093,126 and 6,963,976. These schemes provide both encryption and message integrity. Further variants of these schemes are described in the scheme OCB in U.S. Pat. No. 7,046,802. 
         [0006]    However, these schemes require an extra step in their mechanism, which can be 10 to 100% more computationally expensive. Further, these schemes fail to utilize the hardware and software optimizations possible to the full extent. 
       SUMMARY OF THE INVENTION 
       [0007]    An object of the present invention is to provide improved encryption schemes and apparatus, which securely generate a cipher-text, which in itself contains checks for assuring message integrity. 
         [0008]    Another object of this invention is to provide encryption and decryption schemes and apparatus which generate a cipher-text with message integrity in a single pass with less additional computational cost, while retaining at least the same level of security, as schemes based on a MAC, and other authenticated encryption schemes. 
         [0009]    These and other objects are attained with encryption/decryption methods and apparatus of the present invention. The methods and apparatus use a predetermined block cipher, which supports encryption and decryption of a fixed block size. The methods and apparatus also use a key for the block cipher, which is usually kept secret. 
         [0010]    An embodiment of a method comprises the steps of encrypting a plain-text message using a user supplied safe initial vector by dividing the plain-text message into a multitude of plain-text blocks and encrypting the plain-text blocks using the safe initial vector and the block cipher to form a multitude of cipher-text blocks. A single pass technique is used in this process to embed a message integrity check in the cipher-text block, again using the safe initial vector. The method further comprises the steps of decrypting the cipher-text blocks using the block cipher and the same key to reform the plain-text blocks, and testing the message integrity check in the cipher-text blocks to test the integrity of the reformed plain-text blocks. 
         [0011]    It is often advantageous to employ embodiments in which the message integrity check is embedded in the cipher-text blocks by using a safe initial vector, expanding this safe initial vector to generate a set of pseudo random numbers, which may be dependent, but are pair-wise differentially uniform in the sense to be defined below, and using the set of pseudo random numbers to embed the message integrity check in the cipher-text blocks as the cipher-text blocks are being formed. In these embodiments, during the decryption process, the safe initial vector and the set of pseudo random numbers are obtained from the cipher-text blocks, and as the cipher-text blocks are decrypted, these set of pseudo random numbers are used to reform the plain-text blocks from the cipher-text blocks. Also, the testing step advantageously includes the step of applying a predetermined test to the re-formed plain-text blocks to test the integrity of the re-formed plain-text blocks. 
         [0012]    In another embodiment, the message integrity check is embedded in the cipher-text blocks and a partial-block tag. In such an embodiment, the re-formed plain-text blocks are tested against the tag using a predetermined test, which may include another encryption or decryption step. 
         [0013]    In another embodiment, the method comprises the steps of encrypting a plain-text message using a user supplied initial vector (IV) by dividing the plain-text message into a multitude of plain-text blocks and encrypting the plain-text blocks by dividing them into two sets; and using the block cipher in encrypt mode on one set and the block cipher in decrypt mode on the other set to form a multitude of cipher-text blocks. The method further comprises the step of decrypting the cipher-text blocks by dividing them into corresponding two sets; and using the block cipher in encrypt mode on respective one set and block cipher in decrypt mode on the respective other set to reform the plain-text blocks. The message integrity checks are embedded as in earlier described embodiments. 
         [0014]    When encrypting a sequence of t plain-text messages, each of length up to len[i] blocks, with index i ranging from 1 to t, a sequence of n-bit numbers (or initial vectors) IV 1 ,IV 2 , . . . IV t  is called safe if for all message indices i, i 1 , ranging from 1 to t, with i different from i 1 , and numbers j ranging from 0 to len[i]+1, and j 1  ranging from 0 to len[i 1 ]+1, it is the case that IV i+j is not equal to IVi+j1.    
         [0015]    In one embodiment the initial vectors for each message can be chosen randomly and independently, and with extremely high probability the initial vectors so chosen will be safe by above definition. 
         [0016]    In another embodiment, for the first message to be encrypted using the same secret key, the initial vector can be set to 1. In other words, IV 1  can be initialized to 1. Inductively, from then on, the IV of the next message can be set to IV of the previous message plus the length of the previous message in integer blocks plus two. This makes the method to generate safe initial vectors incremental. 
         [0017]    A sequence of n-bit random numbers S 1 ,S 2 , . . . ,S m  is called pair-wise differentially uniform if each S i  is uniformly distributed, and for every i, i 1 , i not equal to i 1 , and i,i 1  ranging from 1 to m, and for every n bit constant c, the probability that the n-bit exclusive-or of S i  and S i1  is same as c is at most two to the power negative n. Such sequences are also called XOR-universal in the cryptography literature. 
         [0018]    Further benefits and advantages of the invention will become apparent from a consideration of the following detailed description, given with reference to the accompanying drawings, which specify and show example embodiments of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0019]      FIG. 1  generally illustrates a prior art encryption/decryption procedure; 
           [0020]      FIG. 2  shows a prior art encryption mechanism; 
           [0021]      FIG. 3  shows a prior art decryption mechanism; 
           [0022]      FIG. 4  illustrates a prior art encryption process that also guarantees message integrity; 
           [0023]      FIG. 5  is a flow chart showing how the generator of  FIG. 4  operates; 
           [0024]      FIG. 6  generally illustrates an example of a prior art decryption process; 
           [0025]      FIG. 7  shows the operation of a prior art decryption process in more detail; 
           [0026]      FIG. 8  illustrates a prior art parallelizable encryption mechanism; 
           [0027]      FIG. 9  shows a prior art apparatus for encryption with message integrity; 
           [0028]      FIG. 10  depicts a prior art apparatus for decryption; 
           [0029]      FIG. 11  illustrates an encryption process embodying the present invention; 
           [0030]      FIG. 12  describes a procedure for generating a safe initial vector; 
           [0031]      FIG. 13  is a flow chart showing the operation of a pair-wise differentially uniforms sequence generator according to an embodiment of the present invention; 
           [0032]      FIG. 14  illustrates an alternate encryption process embodying this invention; 
           [0033]      FIG. 15  is a flow chart showing how the generator of  FIG. 14  operates; 
           [0034]      FIG. 16  shows an apparatus for encryption with message integrity using the generator of  FIG. 14 ; 
           [0035]      FIG. 17  shows a method for authenticated encryption that uses both an encryptor and a decryptor. 
           [0036]      FIG. 18  illustrates an alternate authenticated encryption process. 
           [0037]      FIG. 19  describes a further alternate embodiment of the present invention, which reduces the size of the output message; and 
           [0038]      FIG. 20  describes the operation of the checksum and R combiner of  FIG. 19 . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0039]    In this specification and the drawings, a plain-text message is denoted by “P”, and a cipher-text message is denoted by “C”. The length of the plain-text and cipher-text are measured in blocks, where a block is the number of bits of input/output of a block cipher used in this construction. This number called block size will be designated n. Thus, if the plain-text P is of length m blocks, then the individual blocks of this message are designated P 1 ,P 2 , . . . ,P m . Similarly, the cipher-text blocks are designated C 1 ,C 2 , . . . ,C m . 
         [0040]    Further still, we will be referring to several applications of the encryption procedure using the same key. Thus, for example, the same key may be used to encrypt plain text messages P 1 , P 2 , . . . ,P t . The index of the message will be placed in the superscript, whereas the index of the block number in a particular message will be placed in the subscript. 
         [0041]      FIGS. 1-3  generally illustrate an encryption/decryption procedure of the type referred to as cipher block chaining (CBC). In this process, a sending party encrypts a plain-text message of a constant size, e.g. n=128 bits for AES, using a block cipher  101 , and the encrypted message is sent over an insecure or non-secure communication medium  102  to a receiving party. This latter party uses the same block cipher in decrypt mode  103  to decipher the message. Note that both parties have access to the same secret key K. 
         [0042]      FIGS. 2 and 3  respectively show the encryption and decryption mechanisms for messages of size multiple of the block-size of the underlying block-cipher. With reference to  FIG. 2 , mechanism  200  includes a series of cipher blocks  101  as in  FIG. 1 . Each cipher block is provided with the same key K. The first block  101   a  is also provided with a random number r that is n bits long. Each of the successive cipher blocks in the chain is provided with a respective one block (i.e. n bits) of the plain text and with the output of the previous block in the chain. Advantageously, for each of the cipher blocks after the first one, an exclusive or function is applied to the two text blocks applied to the cipher block. Each of the cipher blocks  101   a - 101   m  outputs a respective one block of the cipher-text. 
         [0043]    With reference to  FIG. 3 , a mechanism  300  for decrypting long cipher-text blocks generated by  200 , includes a series, or chain, of cipher blocks  103  in decrypt mode. Each block is provided with the same key K and with a respective one of the cipher-text blocks (each of n bits). For the first block  103   a  in chain  103 , an exclusive or operation is applied to the output of the block and the first cipher-text block. For the other blocks in chain  103 , an exclusive or operation is applied to the output of the block and the input of the previous block. The exclusive or operations performed on the outputs of the cipher blocks produce the original plain-text blocks. 
         [0044]      FIGS. 4-10  illustrate an encryption/decryption process, which also guarantees message integrity, which is prior art. Generally, the encryption process includes three steps. The first step is the randomness generation and its expansion. The second step is the further expansion of the randomness, and the third step is the actual encryption of the plain text using the above-generated randomness to produce the cipher-text. 
         [0045]    More specifically, in the first step, a random number r is generated. The randomness r may be generated by any of the well-known techniques to generate randomness. This number r is applied to the block cipher  101  with key K 2  to produce a pseudo random number R. The number R could also be obtained by any other well-known means of expanding randomness. 
         [0046]    This number R is fed into a pair-wise differentially uniform sequence generator  402 . This generator, using a process discussed below, outputs a series of S values, S 0 ,S 1 ,S 2 , . . . Sm, each of which is also n bits long. 
         [0047]      FIG. 5  is a flow chart  500  showing how generator  402  works. 
         [0048]    This generator may work as a well-known Linear Feedback Shift Register (LFSR). First a primitive polynomial g(x) representing the Galois Field GF(2̂n) is chosen. Such polynomials are well known and published in literature. Let g stand for the n-bit number representing g(x)−x̂n. At step  501 , a variable i is set equal to 0, and S 0  is set equal to R; and then at step  502 , i is compared to m. If i is greater than m, then the routine exits. Otherwise, the routine proceeds to  503 ,  504 ,  505 . At step  503 , the variable Si is copied into a temporary variable t. At step  504 , t is left shifted by 1 bit. At step  505 , it is checked if there was a carry produced from the previous shift operation. If so, the quantity g and t are combined by a bit-by-bit exclusive or operation to produce the new t. If there was no carry produced, then t is left intact. At step  507 , variable Si+1 is set to t and I is incremented by 1, and the routine returns to step  502 . An important advantage of this process is that the expansion does not require any cryptographic operations, like block cipher invocations. 
         [0049]    With reference again to  FIG. 4 , after r and the S values are generated, the blocks of plain-text P 1 -Pm are encrypted to obtain the cipher-text blocks C 0 -Cm+1. A series of m+2 cipher blocks  101  are used to do this. Each of the cipher blocks is provided with the key K 1 . The first block  101   a  is also provided with the random number r. Each of the following cipher blocks, except the last one  101   n , is provided with a combination of a respective one of the plain-text blocks and the output of the preceding cipher block. In particular, this combination is the result of the exclusive-or operation performed on the two inputs, on a bit location by bit location basis. The last cipher block  101   n  in the series is provided with the combination of (i) the output of the previous block, and (ii) the result of a series of exclusive or operations performed on the sequence of plain-text blocks P 1 ,P 2 , . . . Pm. This combination is the result of the exclusive or operation performed on the two inputs. 
         [0050]    The output of the first cipher block  101   a  is the first block of cipher-text C 0 . The other blocks of cipher-text, C 1 -Cm, are obtained by performing the exclusive or operation, on a bit location by bit location basis, on the output of each cipher block and a respective one of the S values. Specifically, S 1 -Sm, are applied to the outputs of blocks  101   b  through  101   m  respectively, while S 0  is applied to the output of the last block  101   n.    
         [0051]      FIG. 6  generally illustrates an example of a decryption process. In this process, the cipher-text blocks are applied to decryption  601 , which outputs the plain-text blocks. Then these plain-text blocks are used to determine if Pm+1 is equal to the result obtained by applying the exclusive or function, on a bit location by bit location basis, to the sequence of the plain-text blocks P 1 , . . . Pm. The message passes or fails the integrity test if Pm+1 is, respectively, equal or not equal to this result. 
         [0052]      FIG. 7  illustrates the operation of an example of a decryption  601  in greater detail. As shown in this figure, the decryption includes a series of cipher blocks  103  in decrypt or inverse mode. Each of the cipher blocks is provided with a key K, and with a respective one of the cipher-text blocks C 0 , . . . Cm+1. Each of these blocks, except the first one  103   a , is also provided with a respective one of the S values. In particular, blocks  103   b  through  103   m  are provided with S 1  through Sm respectively, and the last cipher block  103   m +1 is provided with S 0 . The exclusive or operation is performed on the C and S values provided to each cipher block. 
         [0053]    The output of the first cipher block  103   a  is the random number r. For each of the cipher blocks  103   b - 103   m +1, the exclusive or function is applied to the output of the block and the input to the previous block to obtain a respective one of the plain-text blocks P 1 -Pm. 
         [0054]    The pseudo code below is an alternative way to generate the pair-wise differentially uniform random sequence S 0 ,S 1 , . . . Sm. Again, this alternative way uses a primitive polynomial g(x), and arithmetic in a Galois Field. 
         [0000]    
       
         
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 C01 
                 W(0) = R; S(0) = W(0); 
               
               
                 C02 
                 for i = 1 to m−1 do 
               
             
          
           
               
                 C03 
                 j=i+1; 
               
               
                 C04 
                 if (j is a power of 2) 
               
             
          
           
               
                 C05 
                 W(i) = W(i−1) &lt;&lt;1 /* left shift K(i−1) by 1 bit) */ 
               
               
                 C06 
                 if (most significant bit of W(i−1) is 1) then W(i) = W(i) 
               
             
          
           
               
                   
                 xor g 
               
             
          
           
               
                 C07 
                 endif 
               
               
                 C08 
                 S(i) =0 
               
               
                 C09 
                 for k = 0 to n−1 do 
               
             
          
           
               
                 C10 
                 if (least significant bit of j is 1) then S(i) = S(i) xor 
               
             
          
           
               
                   
                 W(k) 
               
             
          
           
               
                 C11 
                 j = j &gt;&gt;1 /* right shift j by 1 bit */ 
               
             
          
           
               
                 C12 
                 end for 
               
             
          
           
               
                 C13 
                 end for 
               
               
                   
               
             
          
         
       
     
         [0055]    There is yet another well-known technique for generating the pair-wise differentially uniform random sequence S 0 ,S 1 , . . . ,Sm. Once again, it uses a primitive polynomial g(x). Below is the pseudo code for generating the sequence using the well know Gray code: 
         [0000]    
       
         
               
               
             
               
               
             
               
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
               
               
             
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 D01 
                 W(0)=R; S(0) = W(0) 
               
               
                 D02 
                 for i=1 to m−1 do 
               
             
          
           
               
                 D03 
                 j=i+1 
               
               
                 D04 
                 k=0 
               
               
                 D05 
                 While ( (j&amp;1) == 0) do 
               
             
          
           
               
                 D06 
                 k= k+1; j = j&gt;&gt;1; 
                 /*increment k and right shift j */ 
               
             
          
           
               
                 D07 
                 end while 
                 /* finds the index of the least 
               
             
          
           
               
                   
                 significant ON bit in (i+1) */ 
               
             
          
           
               
                 D08 
                 if (j xor 1) == 0) 
                 /* (i+1) is a power of 2 */ 
               
             
          
           
               
                 D09 
                 W(k) = W(k−1) &lt;&lt;1 
                 /* left shift W(k−1) by 1 bit*/ 
               
             
          
           
               
                 D11 
                 if (most significant bit of W(k−1) is 1) then W(k) = W(k) 
               
             
          
           
               
                   
                 xor g 
               
             
          
           
               
                 D12 
                 end if 
               
               
                 D13 
                 S(i) = S(i−1) xor W(k) 
               
               
                 D14 
                 end for 
               
               
                   
               
             
          
         
       
     
         [0056]    There are many other ways to generate such pair-wise differentially uniform sequence. As long as the sequence satisfies the pair-wise differentially uniform property it can be embedded as explained above to guarantee an encryption scheme with message integrity. 
         [0057]      FIG. 8  illustrates a parallelizable encryption mechanism  800 . In this mechanism, each of the blocks is provided with the key K 1 . The first block  101   a  is also provided with the random number r. Each of the following cipher blocks, except the last one, is provided with a combination of a respective one of the plain-text blocks and a respective one of the S values. Specifically, this combination is the result of the exclusive or operation performed on the two inputs, on a bit location by bit location basis. The last cipher block  101   n  in the series is provided with the combination of (i) Sm and (ii) the result of a series of exclusive or operations performed on the sequence of plain-text blocks P 1 ,P 2 , . . . ,Pm. This combination is the result of exclusive or operation performed on the two inputs. 
         [0058]    As with the system in  FIG. 4 , the output of the first cipher block  101   a  of mechanism  800  is the first blocks of cipher-text C 0 . The other blocks of cipher-text C 1 -Cm are obtained by performing the exclusive or operation, on a bit location by bit location basis, on the output of each cipher block and a respective one of the S values. Specifically S 1 -Sm are applied to the outputs of blocks  101   b - 101   m  respectively, while S 0  is applied to the output of the last cipher block in the series. 
         [0059]      FIG. 9  shows an apparatus for encryption with message integrity. The apparatus shown includes a Randomness Generator  901  to generate a first random number; a Randomness Transformer  902  to transform said first random number into a first pseudo random number; a Pairwise Additively Uniform Sequence Generator  903  to further expand a randomness of said first random number and/or said first pseudo random number into a set of pair-wise differentially-uniform pseudo random numbers; an Encryptor  905  to divide said plain-text message into a plurality of plain-text blocks, and to encrypt said plain-text blocks to form a plurality of cipher-text blocks; a Checksum Generator  908  to combine said plurality of plain-text blocks into at least one check sum; and an Integrity Extractor and Checker  907  to employ said set of pair-wise differentially-uniform pseudo random numbers, together with said first random number and/or said first pseudo random number, to embed a message integrity check in said cipher-text blocks. 
         [0060]      FIG. 10  shows an apparatus for decryption. The apparatus shown includes a Decryptor  1005  to divide said cipher-text message  1006  into a plurality of cipher-text blocks, and to decrypt said cipher-text blocks in forming a plurality of plain-text blocks; a Randomness Transformer  1002  to transform at least one of said plain-text blocks into a first pseudo random number; a Pairwise Additively Uniform Sequence Generator  1003  to further expand at least one of said plain-text blocks and/or said first pseudo random number into a set of pair-wise differentially-uniform pseudo random numbers; a Checksum Generator  1008  to combine said first pseudo random number, and/or said set of pair-wise differentially-uniform pseudo random numbers, and/or said at least one plain-text block to form at least two check sums and to form a plurality of output blocks; and an Integrity Extractor and Checker  1007  to compare said at least two check sums in declaring success of a message integrity check. 
         [0061]    So far, we have described methods known in prior art for authenticated encryption, i.e. encryption with message integrity in a single pass. Some of the methods described were also parallelizable. 
         [0062]      FIG. 11  describes the present invention, which can be compared with prior art  FIG. 8 . Instead of using block cipher  101   x  to expand randomness r into new randomness R, the present invention does not require a block cipher. Instead, a Safe IV (or initial vector) generator is used to generate r in such a fashion that there is no need to convert r to R before applying  402 , the pair-wise differentially uniform sequence generator. The pair-wise differentially uniform sequence generator in  FIG. 11  is now labeled  1102 , as it uses the process  1300  described below in connection with  FIG. 13 , instead of the process  500  of  FIG. 5 . As will be clear later, there is a change in process  1300  from process  500 . As we will show in various embodiments, the use of the safe IV generator eliminates the need for the costly step of block cipher  101   x . Even though it may seem that step  101   x , which is a block cipher invocation is identical in cost to step  101   a  to  101   n , which are also block cipher invocations, one must note that the steps  101   a  to  101   n  can be performed in parallel, whereas  101   x  must be performed before any of the  101   a  to  101   n  steps can be performed. Further, there are applications where there are at most one or two steps  101 , i.e. m=0 or 1. 
         [0063]      FIG. 12  describes an embodiment of safe IV generator. For the first message to be encrypted using the secret key, the initial vector is set to 1, and a variable count is also set to 1. Thereafter, the initial vector for the next message is computed to be initial vector of the previous message plus the length of the previous message in blocks plus two. As is clear, from  FIG. 12 , this implementation saves tremendously over using a block cipher as done in prior art. 
         [0064]      FIG. 13  describes how the new pair-wise differentially uniform sequence generator  1300  is implemented. It can be contrasted with process  500 . Note that the only change is in the first step, i.e.  1301 , where instead of using R as in  501 , S 0  is set to r multiplied by the key k 2  in Galois Field GF(2̂n). This multiplication step can be rather expensive, and we see in the next embodiment, how this step can also be removed. 
         [0065]      FIG. 14  describes another embodiment of the current invention, where the step of generating the safe IV, and the step of generating the pair-wise differentially uniform sequence are combined into one step  1401 . The overall advantage of this combination is that it generates both the initial vector r and the pair-wise differentially uniform sequence incrementally, even across different messages. It is called stateful as it maintains a state from one message encryption to the next. 
         [0066]      FIG. 15  is a flow chart  1500  showing how generator  1401  works. This generator works as a well-known Linear Feedback Shift Register (LFSR) as in  FIG. 5 , except that it is incremental over all messages. As in generator  500 , first a primitive polynomial g(x) representing the Galois Field GF(2̂n) is chosen. Let g stand for the n-bit number representing g(x)−x̂n. Steps  1502  to  1507  are identical to steps  502  to  507 . These steps multiply the current S value Si represented as a polynomial by x in the field GF(2̂n). The novel parts include the steps  1508  to  1512 . The initial vector to be output is maintained in variable r, which is set to 1 for the first message ever to be encrypted using the current secret key. 
         [0067]    Also, for the first message, S 0  is initialized in step  1510  to the second secret key k 2 . If this plain-text message is not the first message, then S 0  is initialized to variable “prev”, which is the previous message&#39;s computed values S[m+1]. After the sequence S 0  to S[m+1] is computed, as checked by step  1502 , in step  1511 , the initial vector r and the sequence S is output. Thereafter in step  1512 , r is incremented to its current value plus the length m of the current message plus 2, and saved in r to be used for the next message. Also, the variable “prev” is set to the just computed S[m+1]. 
         [0068]    An important advantage of the current invention also comes from formally proving that the safe initial vector scheme and the incremental generator  1500  scheme are as secure as prior art for authenticated encryption. 
         [0069]    The secret value k 2 , which is an additional key apart from the key k 1  used in  101   a  to  101   n  in  FIG. 14 , can actually be generated from key k 1  itself by encrypting a constant, e.g. zero, with key k 1  and the given block cipher  101 . It can be proven that this way of generating k 2  from k 1  is secure. 
         [0070]      FIG. 16  shows an apparatus for encryption with message integrity with the advanced incremental differentially uniform sequence generator  1401 . The apparatus includes an Encryptor  1603  to divide said plain-text message  1602  into a plurality of plain-text blocks, and to encrypt said plain-text blocks to form a plurality of cipher-text blocks  1604 ; a Checksum Generator  1606  to combine said plurality of plain-text blocks into at least one check sum; and an Integrity Extractor and Checker  1605  to employ said set of pair-wise differentially-uniform pseudo random numbers to embed a message integrity check in said cipher-text blocks. 
         [0071]      FIG. 17  describes a novel method for authenticated encryption in that it uses both the encryptor  101  and decryptor  103  while encrypting a long message. In contrast, in the prior art, e.g. see  FIGS. 4 and 8 , while encrypting a long message, the same encryptor  101  was used on all message blocks. Similarly, while decrypting a long message in the prior art (see  FIG. 7 ) the same decryptor  103  was used on all blocks. An important aspect of the method described in  FIG. 17  is that while encrypting a long message, the said plain-text blocks (as in  FIG. 8 ) can be divided into two sets; on the first set, the encryptor  101  can be employed, and on the second set, decryptor  103  can be employed. This has the advantage that most hardware solutions have both an engine for  101  and for  103 , and by this invention one can double the throughput. 
         [0072]      FIG. 18  describes the alternate embodiment of this invention, as it incorporates the invention described in  FIG. 14  as well. Note that decryptor  103  is used on some blocks, whereas encryptor  101  is used on other blocks. An important aspect of this invention is that it comes with a proof that by doing so, there is no impact on the security of the scheme. 
         [0073]      FIG. 19  describes an alternate embodiment of authenticated encryption, which reduces the size of the output message by one block. This may be advantageous in situations where the output must be stored in a storage device, and which has limited storage space. This figure should be compared with  FIG. 8  (prior art). An important distinction is that there is no output block C 0 , and the input to encryptor  101   n  is different. The value r, which was previously output as C 0 , is now incorporated into C[m+1] by means of checksum &amp; r combiner  1901 . Note that, there is no post-whitening by S 0  to the output of  101   n  (compare with  FIG. 8 ). This is important as S 0  depends on r, and if the decrypting process does not have access to r, it cannot compute S 0 . However, it can be proven that this scheme is as secure as authenticated encryption schemes in the prior art. 
         [0074]      FIG. 20  describes the checksum &amp; r combiner. First an n-bit checksum is computed from the said plaintext-blocks (as in  FIG. 8 ). For example, while using AES with 128 bits, n=128. 
         [0075]    Next, the checksum is truncated to be n/2 bits, i.e. 64 bits in the case of AES example. Next, this embodiment assumes that r itself can be represented unambiguously by only n/2 bits. Hence, the truncated checksum and r are concatenated to produce n bits. 
         [0076]    The present invention can be realized in hardware, software, or a combination of hardware and software. The present invention can be realized in a centralized fashion in one computer system, or in a distributed fashion where different elements are spread across several interconnected computer systems. Any kind of computer system—or other apparatus adapted for carrying out the methods described herein—is suitable. A typical combination of hardware and software could be a general-purpose computer system with a computer program that, when loaded and executed, controls the computer system such that it carries out the methods described herein. The present invention can also be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein, and which—when loaded in a computer system—is able to carry out these methods. 
         [0077]    Computer program means or computer program in the present context include any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after conversion to another language, code or notation and/or reproduction in a different material form. 
         [0078]    Other beneficial results can be realized by applying the disclosed invention in a different manner or modifying the invention in ways known to those familiar with the art. 
         [0079]    While it is apparent that the invention herein disclosed is well calculated to fulfill the objects stated above, it will be appreciated that numerous modifications and embodiments may be devised by those skilled in the art, and it is intended that the appended claims cover all such modifications and embodiments as fall within the true spirit and scope of the present invention.