Abstract:
An encryption and authentication technique that achieves enhanced integrity verification through assured error-propagation using a multistage sequence of pseudorandom permutations. The present invention generates intermediate data-dependent cryptographic variables at each stage, which are systematically combined into feedback loops. The encryption technique also generates an authentication tag without any further steps that is N times longer than the block size where N is the number of pseudorandom permutations used in the encipherment of each block. The authentication tag provides a unique mapping to the plaintext for any number of plaintext blocks that is less than or equal to N. In addition to being a stand alone encryption algorithm, the disclosed technique is applicable to any mode that uses pseudorandom permutations such as, key dependent lookup tables, S-Boxes, and block ciphers such as RC5, TEA, and AES.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present invention claims priority from U.S. provisional patent application No. 60/595,720, filed on Sep. 13, 2005, the entire contents of which are incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to the technical field of data communication and storage. Specifically, the invention relates to cryptographic methods and systems that allow for both the encryption and authentication of information through the use of a generic pseudorandom permutation. 
     BACKGROUND OF THE INVENTION 
     Data encryption methods provide privacy of the encrypted information over insecure communication channels. Encryption methods alone, however, lack manipulation detection abilities to ensure the integrity or authenticity of the information. Data authentication methods are required to detect when the received message was altered by an adversary during communication. 
     Many known algorithms provide authentication separate from privacy. One of the most well known methods for providing data authentication generates an authentication tag or Message Authentication Code (MAC) through the use of a key-dependent one-way hash function. A one-way hash function is designed such that it is comparatively easy to compute but almost impossible to reverse. Because the length of the authentication tag is usually fixed and shorter than the length of the initial message, the authentication tag cannot ensure a one-to-one mapping of messages to authentication tags. The length of the authentication tag, however, is designed to be long enough to thwart brute force attacks. 
     In the method for exchanging a message with an authentication tag, the sender initiates the exchange by generating an authentication tag from the authentic message using a shared key. The sender then transfers the message and authentication tag to the receiver. At the receiving end, the receiver must generate an authentication tag from the received message using the shared key as well. The receiver then compares his or her generated authentication tag with the received authentication tag. If the two tags match, then the receiver can be assured that the message has not been modified during transmission and that it was sent by someone who knows the secret key. 
     The use of an authentication tag or MAC consumes time on the receiving end, because it requires the receiver to generate a MAC for comparison. When combined with a data encryption method, the receiver must decrypt the message and generate an authentication tag before the received information can be used. This conventional approach requires two passes over the same message on both the sending and receiving end often with the same basic algorithm. Furthermore, this conventional approach often requires the use of separate keys for each function. The use of two separate functions uses excessive processing power, memory, and time. 
     In applications focused on minimizing latency such as Supervisory Control and Data Acquisition (SCADA) networks, Remote Frequency Identification (RFID), and other real-time data exchange systems, received information must be used immediately making it impossible to use a separate MAC for data authentication. The devices used in such applications present further restrictions on processing power, code space, and memory. These applications highlight the need for methods that provide message integrity integrated with strong cryptographic privacy to minimize the latency and overhead imposed by separate conventional methods. 
     In response to the disadvantages of the conventional approaches, various methods have been suggested. Based on a new proof in error detection, the SCADA community including the AGA12 committee suggested assured error-propagation as a means for providing integrity without the need for a traditional MAC. Various methods exist that include error-propagation to provide some level of integrity. Depending on the level of error-propagation, a one-bit modification to the transmitted ciphertext results in some amount of randomization of subsequent bits in order to provide enhanced manipulation detection. One such method, Propagating Cipher Block Chaining (PCBC) was designed to fully propagate a one-bit modification to all subsequent bits. Since its design, however, PCBC mode has been found to be vulnerable to some straight-forward attacks. For example, switching two ciphertext blocks leaves the rest of the message unchanged. 
     Andrew Wright et al. recently proposed another solution, AES PE-mode for use in SCADA networks that was designed based on the error detection proof to assure at least six bits of randomization following a one-bit manipulation (viz., A. K. Wright, J. A. Kinast, and J. McCarty. Low-Latency Cryptographic Protection for SCADA Communications. In: Proc. 2nd Int. Conf. on Applied Cryptography and Network Security, ACNS 2004). While PE-mode lacks the straight-forward vulnerabilities of PCBC, PE-mode imposes a great deal of latency and overhead, because it is essentially a cascade cipher of two AES encryption modes. In addition to encrypting the message twice, PE-mode is designed to be used with a separate message authentication algorithm such as a CBC-MAC. The drawbacks of PCBC and PE-mode illuminate the need for an error-propagating encryption algorithm that is both fast and small and does not require further steps to achieve integrity. 
     SUMMARY 
     The defined invention provides methods and systems for efficiently integrating integrity and strong encryption through assured error-propagation and an automatically generated authentication tag. The present invention is designed to work with considerably low levels of needed code space, processing resources, memory, and latency requirements. Briefly, the present invention consists of a multi-stage encryption system, wherein a plaintext chunk is passed through a sequence of pseudorandom permutations. The system generates intermediate data-dependent cryptographic variables at each stage, which are systematically combined into feedback loops to produce assured error-propagation. At the conclusion of encryption, the invention generates a cryptographic hash using the final data-dependent cryptographic variables. 
     The invention in question can be implemented in numerous ways including as a method, a system, a process, a device, a stand-alone cryptographic algorithm, or a mode of an existing cryptographic algorithm. Several inventive embodiments of the present invention are described below. 
     In one embodiment of the present invention, a method for multi-stage data encryption and authentication is defined wherein each stage is a pseudorandom permutation. The method comprises the steps of: receiving plaintext data, partitioning the plaintext into equal size plaintext blocks, passing the each plaintext block through a sequence of pseudorandom permutations, modifying the states of the pseudorandom permutations for the next block based on each current block&#39;s intermediate stage cryptographic variables each of which is the output of one stage in the sequence, and generating ciphertext from the output of each plaintext block&#39;s final stage. It should be noted that pseudorandom permutations are usually considered stateless. The present invention creates what will be referred to as states by storing variables that are used to modify the input to each pseudorandom permutation. Since the state of these variables directly affects the output of each pseudorandom permutation, the permutations can be seen as having states. 
     In one further aspect of the present invention, the implementation of each pseudorandom permutation can be achieved by one or multiple of the following: generating shifted permutation tables also known as S-Boxes, using existing cryptographic algorithms, including but not limited to AES, RC5, TEA, IDEA, TWOFISH, or electronically implementing classical rotors. 
     In one further aspect of the present invention, the modification of the states of each pseudorandom permutation is accomplished by following the pattern which will be referred to as the “312 rule”. The pattern outlines the following steps:
         a. The state of the first pseudorandom permutation is modified by the output of the next to the last pseudorandom permutation.   b. The states of the middle pseudorandom permutations are modified by the output of previous pseudorandom permutation.   c. The state of the last pseudorandom permutation is modified by both the state and output of the first pseudorandom permutation.       

     In one further aspect of the present invention, the method generates an authentication tag using the final plaintext block&#39;s state variables. The generation of the authentication tag is accomplished by either concatenating the final state variables or masking the final state variables by combining them with the initial permutation states before concatenation. 
     In one further aspect of the present invention, the method includes the step of initializing the beginning state variables. The initialization process is conducted by encrypting an nonce using a non-initialized version of the defined method and using the generated ciphertext and authentication tag as the beginning variables. 
     In one further aspect of the present invention, an internal counter is used to further modify the states of the pseudorandom permutations. The addition of a counter, designed to eliminate short cycles, is performed by storing a N counter variables where N is the number of pseudorandom permutation stages, incrementing the counter variables in an odometric fashion, and modifying each pseudorandom permutation state by the associated counter variable. 
     In one further aspect of the present invention, the number of needed pseudorandom permutations is reduced by substituting the inverse of pseudorandom permutations in use for some number of other pseudorandom permutations. For example, in a 4-stage method with pseudorandom permutations ABCD, the number of pseudorandom permutations required could be reduced by using the permutations ABA −1 B −1  where A −1  and B −1  are the inverses of A and B respectively. 
     In one further aspect of the present invention, the number of needed pseudorandom permutations can be reduced on one side of the communications channel by supplying only pseudorandom permutations on one side while the other side has both pseudorandom and inverse pseudorandom permutations. For example the server side can have both ABCD and A −1 B −1 C −1 D −1  permutations while the client side can have only ABCD permutations. Communication from the server to the client is accomplished by first decrypting the plaintext message (has the same effect as encrypting). The client can then recover the message by encrypting the ciphertext (has the same effect as decrypting). Communication from the client to the server is done in the normal fashion i.e. client encrypts message, server decrypts message. 
     In one further embodiment of the present invention, a data decryption method that is the inverse of the multi-stage data encryption and authentication method is defined. The method comprises the steps of: receiving ciphertext data, partitioning the ciphertext into equal size ciphertext blocks, passing each block through a sequence of pseudorandom permutations where each permutation is an inverse of the permutations used in the encryption method, modifying the states of the pseudorandom permutations for the next block based on each current block&#39;s intermediate stage cryptographic variables, and generating plaintext from the output of each ciphertext block&#39;s final stage. The decryption method passes each ciphertext block backwards through the sequence in the encryption method. It should be noted that the chosen embodiment of the decryption method should match those in the chosen embodiment of the encryption method. For example, if the chosen embodiment of the encryption method uses RC5 as the pseudorandom permutation, generates an authentication tag, and utilizes counters, the chosen embodiment of the decryption method should also use RC5, generate an authentication tag, and use counters. 
     In one further embodiment of the present invention, a method for performing an integrity check is defined. The method consists of the steps of: performing the encryption method defined in order to generate ciphertext and an authentication tag, performing the decryption method defined on said ciphertext in order to generate plaintext and a second authentication tag, and comparing the two authentication tags for equality. It can be assured with high probability that the ciphertext was not modified after encryption if the two authentication tags are equal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention and for further features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a first flowchart in accordance with a preferred embodiment of the present invention; 
         FIG. 2  is a second flowchart in accordance with a preferred embodiment of the present invention; 
         FIG. 3  illustrates an encryption system in accordance with a preferred embodiment of the present invention; 
         FIG. 4  illustrates a decryption system in accordance with a preferred embodiment of the present invention; 
         FIG. 5  illustrates initializing variables using a nonce in accordance with a preferred embodiment of the present invention; 
         FIG. 6  illustrates generating an authentication tag from final state variables in accordance with a preferred embodiment of the present invention; 
         FIG. 7  illustrates generating a masked authentication tag from a combination of the initial and final state variables in accordance with a preferred embodiment of the present invention; 
         FIG. 8  illustrates decrypting and verifying the integrity of the message using a received authentication tag in accordance with a preferred embodiment of the present invention; 
         FIG. 9  illustrates the encryption method from  FIG. 3  with the addition of counters, in accordance with a preferred embodiment of the present invention; 
         FIG. 10  illustrates the decryption method from  FIG. 4  with the addition of counters, in accordance with a preferred embodiment of the present invention; and 
         FIG. 11  illustrates incrementing counters in accordance with a preferred embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIGS. 1 and 2  represent two versions of the flow chart explaining the steps of encryption for the present invention.  FIG. 1  was the original diagram as can be found in the provisional patent of the present invention. While maintaining the essential core of the invention,  FIG. 2  is the revised encryption diagram with a more clear representation and the elimination of unneeded steps. Before explaining the details of the revised diagram, it is good to note the difference between the two diagrams. 
     The original diagram uses the term Variable Exchange Table (VET) which is now referred to as the more generally used and understood term, pseudorandom permutation. Furthermore, what was originally denoted as a VET Setting (VS) is now referred to as a state variable (SV), and the Output of a VET is now referred to as an intermediate cryptographic variable (CV). The terms have been modified for ease of understanding. 
       FIG. 1  contains all of the same steps as the revised diagram except the generation of the authentication tag  270  and the initialization of the state variables  500 . At the time of submission of the provisional patent, the cryptographic strength of the present invention was still undetermined. In order to compensate for the uncertainty, additional steps  115 ,  120 , and  150  were added to the encryption method to facilitate the combination of the output of the final pseudorandom permutation with an AES keystream through an exclusive or (XOR) function to produce ciphertext. Said additional steps were thought to further protect the ciphertext from attacks. Further consideration and evaluation have eliminated the need for said additional steps, and therefore they have been removed from the revised diagram. Note that corresponding steps in the two diagrams have been numbered the same (ex  125  corresponds to  225 ). 
       FIG. 2  illustrates the steps involved in an encryption embodiment of the present invention. From the start, a key and counter are loaded  200  in order to initialize the pseudorandom permutations if necessary  205  and  210 . The next step initializes the state variables and counters with an nonce  500  which is described in further detail in  FIG. 5 . Once the plaintext is acquired  225 , the first plaintext block is combined with the initialized state variables and stepped through a series of four pseudorandom permutations  230 - 245  resulting in the first ciphertext block  255 . Before the next plaintext block can be encrypted, the state variables are updated using the intermediate cryptographic variables  260 . This cycle continues  265  and  225  for all plaintext blocks. Optionally, the final state variables can be combined to form an authentication tag  270 . The details of the embodied encryption method are described to a greater extent in the next diagram. 
       FIG. 3  represents an encryption embodiment of the present invention wherein m plaintext blocks P i    301  are each passed through a sequence of four pseudorandom permutations  303  resulting in m ciphertext blocks  304 . In this embodiment each of the four permutations  303  are keyed with different keys k 1 , k 2 , k 3 , and k 4 . The embodied method includes the step of initializing the state variables  302  by passing an nonce  310  through a randomization function  500  that is discussed in detail below. Once the state variables are initialized, the first plaintext block P 1    301   a  is combined with the initial state variable SV 1   0    302   a  through modular 2 n  addition where n is the size of a plaintext block. The result of said combination is passed into the first pseudorandom permutation F k1    303   a  producing an intermediate cryptographic variable CV 12   1  (the cryptographic variable between the first pseudorandom permutation Fk 1    303   a  and the second Fk 2    303   b ) which will be fed forward to encrypt the next plaintext block P 2    301   b . Continuing with the encryption of P 1    301   a , CV 12   1  is combined with the second initialized state variable SV 2   0    302   b  through modular 2 n  addition and passed into the second pseudorandom permutation F k2    303   b  resulting in CV 23   1 . The encryption continues to follow the same pattern for the two remaining pseudorandom permutations F k3    303   c  and F k4    303   d  where the result of F k4    303   d  is the first ciphertext block C 1    304   a.    
     For the encryption of the next plaintext block P 2    301   b , the state variables  305  must be updated using a feedback mechanism as will be described. The first state variable SV 1   1    305   a  produced following the encryption of the first plaintext block P 1    301   a  is generated by combining the previous state variable SV 1   0    302   a  with the output from the previous block&#39;s third permutation CV 34   1  through modular 2 n  addition where n is the size of a plaintext block. The second state variable SV 2   1    305   b  is generated by combining the previous state variable SV 2   0    302   b  with the output from the previous block&#39;s first permutation CV 12   1  through modular 2 n  addition. Similarly, the third state variable SV 3   1    305   c  is generated by combining the previous state variable SV 3   0    302   c  with the output from the previous block&#39;s second permutation CV 23   1  through modular 2 n  addition. The fourth state variable SV 4   1    305   d  is generated by combining the previous state variable SV 4   0    302   d  with the output from the previous block&#39;s first permutation CV 12   1  and the current block&#39;s first state variable SV 1    305   a , through modular 2 n  addition. It should be noted that the calculation of SV 1    305   a  should occur before the calculation of SV 4   1    305   d . Furthermore, while the described embodiment of the present invention stores the state variables SV 1 , SV 2 , SV 3 , and SV 4 , derived embodiments could entail the same spirit of the present embodiments without actually storing the state variables. The step of storing state variables is disclosed in the present invention for ease of understanding. 
     The encryption of all further plaintext blocks P 2    301   b  through P m    301   c  are conducted in the same manner as the encryption of P 1    301   a . For example, the second plaintext block P 2    301   b  is conducted in the same manner as the encryption of the first plaintext block P 1    301   a  substituting the updated state variables  305  for the previous state variables  302 . 
       FIG. 4  represents a decryption embodiment of the present invention wherein m ciphertext blocks C i    404  are each passed through a sequence of four inverse pseudorandom permutations F K   −1    403  resulting in m plaintext blocks P i    401 . In this embodiment each of the four inverse permutations F K   −1    403  are keyed with the same keys used in the encryption in  FIG. 3 . The embodied method includes the step of initializing the state variables  402  by passing an nonce  410  through a randomization function  500  that is discussed in detail below. Once the state variables  402  are initialized, the first ciphertext block C 1    404   a  is passed into the first inverse pseudorandom permutation F k4   −1    403   d . The result of said inverse pseudorandom permutation F k4   −1    403   d  is combined with the initial state variable SV 4   0    402   d  through modular 2 n  subtraction where n is the size of a ciphertext block producing an intermediate cryptographic variable CV 34   1  (the cryptographic variable between F k3   −1    403   c  and F k4   −1    403   d ) which will be fed forward to decrypt the next ciphertext block C 2    404   b . Continuing with the decryption of C 1    404   a , CV 34   1  is passed into the second inverse psuedorandorandom permutation F k3   −1    403   c . The result of said inverse permutation F k3   −1    403   c  is combined with SV 3   0  using modular 2 n  subtraction producing CV 23   1 . The decryption continues to follow the same pattern for the two remaining inverse pseudorandom permutations F k2   −1    403   b  and F k1   −1    403   a  where the result of F k1   −1    403   a  is combined with SV 1   0    402   a  using modular 2 n  subtraction to produce the first plaintext block P 1    401   a.    
     For the decryption of the next ciphertext block C 2    404   b , the state variables  405  must be updated using a feedback mechanism as will be described. The state variable SV 1   1    405   a , produced following the decryption of the first ciphertext block C 1    404   a , is generated by combining the previous state variable SV 1   0    402   a  with the input from the previous block&#39;s second inverse permutation CV 34   1  through modular 2 n  addition where n is the size of a ciphertext block. The second state variable SV 2   1    405   b  is the output of the previous block&#39;s third inverse permutation F k2   −1    403   b . Similarly, the state variable SV 3   1    405   c  is the output of the previous block&#39;s second inverse permutation F k3   −1    403   c . The state variable SV 4   1    405   d  is generated by combining the previous state variable SV 4   0    402   d  with the input from the previous block&#39;s fourth inverse permutation CV 12   1  and the current block&#39;s state variable SV 1   1    405   a , through modular 2 n  addition. It should be noted that the calculation of SV 1   1    405   a  should occur before the calculation of SV 4   1    405   d . Furthermore, while the described embodiment of the present invention stores the state variables SV 1 , SV 2 , SV 3 , and SV 4 , derived embodiments could entail the same spirit of the present embodiments without actually storing the state variables. The step of storing state variables is disclosed in the present invention for ease of understanding. 
     The decryption of all further ciphertext blocks C 2    404   b  through C m    404   c  are conducted in the same manner as the decryption of C 1    404   a . For example, the second ciphertext block C 2    404   b  is conducted in the same manner as the decryption of the first ciphertext block C 1    404   a  substituting the updated state variables  405  for the previous state variables  402 . 
       FIG. 5  illustrates the function of generating initial values by randomizing a nonce as used in  FIGS. 3 ,  4 ,  9 , and  10 . The purpose said function is to initialize the state variables and counters to unique and unpredictable values. The nonce or input to the function may be a random number, an incrementing counter, or any value as long as it has not been used before in the context of a given key(s). It should be noted that the nonce need not be secret. The initialization function parses a unique value into m blocks N i    501  and passes each block through a sequence of m pseudorandom permutations  503  resulting in values that are used in the initial setup of both the encryption and decryption methods. Padding may be necessary in order to facilitate equal sized blocks. The number of blocks m and the number of pseudorandom permutations m must always be the same. In the present embodiment of the initialization function, m is equal to 4. The randomization function keys each of the four permutations F K    503  with different keys k 1 , k 2 , k 3 , and k 4 . The embodied method includes the step of initializing the state variables  502  to a constant such as zero. Once the state variables  502  are initialized, the first block N 1    501   a  is combined with the initial state variable SV 1   n1    502   a  through modular 2 n  addition where n is the size of a block. The result of said combination is passed into the first pseudorandom permutation F k1    503   a  producing an intermediate cryptographic variable CV 12   1  (the cryptographic variable between the first pseudorandom permutation F k1    503   a  and the second F k2    503   b ) which will be fed forward to encrypt the next block N 2    501   b . Continuing with the randomization function of N 1    501   a , CV 12   1  is combined with the second initialized state variable SV 2   n1    502   b  through modular 2 n  addition and passed into the second pseudorandom permutation F k2    503   b  resulting in CV 23   1 . The randomization continues to follow the same pattern for the two remaining pseudorandom permutations F k3    503   c  and F k4    503   d  where the result of F k4    503   d  is the first CTR value CTR 1   0    504   a . It should be noted that some embodiments may not use the generated CTR  504  values. 
     For the next block N 2    501   b , the state variables  505  must be updated using a feedback mechanism as will be described. The first state variable SV 1   n2    505   a  produced following the randomization of the first block N 1    501   a  is generated by combining the previous state variable SV 1   n1    502   a  with the output from the previous block&#39;s third permutation CV 34   1  through modular 2 n  addition where n is the size of a block. The second state variable SV 2   n2    505   b  is generated by combining the previous state variable SV 2   n1    502   b  with the output from the previous block&#39;s first permutation CV 12   1  through modular 2 n  addition. Similarly, the third state variable SV 3   n2    505   c  is generated by combining the previous state variable SV 3   n1    502   c  with the output from the previous block&#39;s second permutation CV 23   1  through modular 2 n  addition. The fourth state variable SV 4   n2    505   d  is generated by combining the previous state variable SV 4   n1    502   d  with the output from the previous block&#39;s first permutation CV 12   1  and the current block&#39;s first state variable SV 1   n2    505   a , through modular 2 n  addition. It should be noted that the calculation of SV 1   n2    505   a  should occur before the calculation of SV 4   n2    505   d . Furthermore, while the described embodiment of the present invention stores the state variables SV 1 , SV 2 , SV 3 , and SV 4 , derived embodiments could entail the same spirit of the present embodiments without actually storing the state variables. The step of storing state variables is disclosed in the present invention for ease of understanding. 
     The randomization of all further plaintext blocks N 2    501   b  through N 4    501   d  are conducted in the same manner as the randomization of N 1    501   a . For example, the second plaintext block N 2    501   b  is conducted in the same manner as the randomization of the first plaintext block N 1    501   a  substituting the updated state variables  505  for the previous state variables  502 . After the four blocks  501  are each randomized, the resulting state variables SV 1   0 , SV 2   0 , SV 3   0 , and SV 4   0    508  can be used as initial state variables for  FIGS. 3 ,  4 ,  9 ,  10 . Similarly, the resulting randomized values, CTR 1   0 , CTR 2   0 , CTR 3   0 , and CTR 4   0    504  can be used as initial counters for FIGS.  9 , 10 . 
       FIG. 6  presents an elevated look at the method for generating an authentication tag from the results of the previously described encryption embodiment. The diagram includes an abbreviated version of the encryption method  300  in which each sequence of pseudorandom permutations is depicted in a single encryption function E i    601 . The final encryption function E m    601   c  produces four final state variables  602  which are concatenated to form an authentication tag  603 . As explained previously, an authentication tag is used to provide an integrity check on encrypted data. 
       FIG. 7  represents an alternative embodiment of the method for generating an authentication tag from the results of the encryption embodiment. As in  FIG. 6 , the diagram includes an abbreviated version of the encryption method  300 . In this alternative embodiment, each final state variable  702  is combined with its corresponding initial state variable  701  through an XOR function  703  before being concatenated to form the authentication tag  704 . This alternative embodiment masks the final state variables from being openly accessible to an attacker and may serve to increase the cryptographic strength of the present invention. 
       FIG. 8  represents an embodied method for performing an integrity check of a message after decryption. The diagram includes an abbreviated version of the decryption method  400  in which each sequence of inverse pseudorandom permutations is depicted in a single decryption function D i    802 . The received message includes a previously generated authentication tag AT  805  in addition to the ciphertext  801 . Said authentication tag was previously generated during encryption as is depicted in  FIG. 6 . The final decryption function D m    802   c  produces four final state variables  803  which are concatenated to form an authentication tag AT′  804 . The received authentication tag AT  805  identifies the original message that was encrypted, while the newly generated authentication tag AT′  804  identifies the received message. With the two authentication tags, an integrity check  806  is performed as follows. If the two authentication tags are not equal, the message was modified between its encryption and decryption and should be rejected. Conversely, if the authentication tags are equal, it can be assured with high probability that the message has not been tampered with and can be accepted. It should be noted that an integrity check could also be performed using a previously generated authentication tag as in  FIG. 7 . The method for generating an authentication tag during decryption would match the encryption method in  FIG. 7  followed by an integrity check as in the present figure. 
       FIG. 9  represents a further aspect the present invention wherein counters are added. In the same manner as the embodiment in  FIG. 3 , m plaintext blocks P i    901  are each passed through a sequence of four pseudorandom permutations F k    903  resulting in m ciphertext blocks C i    904 . Each of the four permutations F k    903  are keyed with different keys k 1 , k 2 , k 3 , and k 4 . The embodied method includes the step of initializing the state variables  902  and counters  906  by passing a nonce  900  through a randomization function  500  that has been previously defined. Once the state variables and counters are initialized, the first plaintext block P 1    301   a  is combined with the initial state variable SV 1   0    902   a  through modular 2 n  addition where n is the size of a plaintext block. The result of said combination is passed into the first pseudorandom permutation F k1    903   a  producing an intermediate cryptographic variable CV 12   1  (the cryptographic variable between the first pseudorandom permutation F k1    903   a  and the second F k2    903   b ) which will be fed forward to encrypt the next plaintext block P 2    901   b . Continuing with the encryption of P 1    901   a , CV 12   1  is combined with the second initialized state variable SV 2   0    902   b  through modular 2 n  addition and passed into the second pseudorandom permutation F k2    903   b  resulting in CV 23   1 . The encryption continues to follow the same pattern for the two remaining pseudorandom permutations F k3    903   c  and F k4    903   d  where the result of F k4    903   d  is the first ciphertext block C 1    904   a.    
     For the encryption of the next plaintext block P 2    901   b , the state variables  905  must be updated using counters and a feedback mechanism as will be described. The first state variable SV 1   1    905   a  produced following the encryption of the first plaintext block P 1    901   a  is generated by combining the previous state variable SV 1   0    902   a  with the output from the previous block&#39;s third permutation CV 34   1  and a counter CTR 1   0    906   a  through modular 2 n  addition where n is the size of a plaintext block. The second state variable SV 2   1    905   b  is generated by combining the previous state variable SV 2   0    902   b  with the output from the previous block&#39;s first permutation CV 12   1  and a counter CTR 2   0    906   b  through modular 2 n  addition. Similarly, the third state variable SV 3   1    905   c  is generated by combining the previous state variable SV 3   0    902   c  with the output from the previous block&#39;s second permutation CV 23   1  and a counter CTR 3   0    906   c  through modular 2 n  addition. The fourth state variable SV 4   1    905   d  is generated by combining the previous state variable SV 4   0    902   d  with the output from the previous block&#39;s first permutation CV 12   1  and the current block&#39;s first state variable SV 1   1    905   a  and a counter CTR 4   0    906   d  through modular 2 n  addition. The counters  906  are then incremented using function  1100 . It should be noted that the calculation of SV 1   1    905   a  should occur before the calculation of SV 4   1    905   d . Furthermore, while the described embodiment of the present invention stores the state variables SV 1 , SV 2 , SV 3 , and SV 4 , derived embodiments could entail the same spirit of the present embodiments without actually storing the state variables. The step of storing state variables is disclosed in the present invention for ease of understanding. 
     The encryption of all further plaintext blocks P 2    901   b  through P m    901   c  are conducted in the same manner as the encryption of P 1    901   a . For example, the second plaintext block P 2    901   b  is conducted in the same manner as the encryption of the first plaintext block P 1    901   a  substituting the updated state variables  905  for the previous state variables  902 . 
       FIG. 10  represents a decryption embodiment of the present invention wherein m ciphertext blocks C i    1004  are each passed through a sequence of four inverse pseudorandom permutations  1003  resulting in m plaintext blocks P i    1001 . In this embodiment each of the four inverse permutations  1003  are keyed with the same keys used in the encryption in  FIG. 9 . The embodied method includes the step of initializing the state variables  1002  and initial counters  1006  by passing a nonce  1000  through a randomization function  500  that has been previously defined. Once the state variables and counters are initialized, the first ciphertext block C 1    1004   a  is passed into the first inverse pseudorandom permutation F k4   −1    1003   d . The result of said inverse pseudorandom permutation F k4   −1    1003   d  is combined with the initial state variable SV 4   0    1002   d  through modular 2 n  subtraction where n is the size of a ciphertext block producing an intermediate cryptographic variable CV 34   1  (the cryptographic variable between F k3   −1    1003   c  and F k4   −1    1003   d ) which will be fed forward to decrypt the next ciphertext block C 2    1004   b . Continuing with the decryption of C 1    1004   a , CV 34   1  is passed into the second inverse psuedorandorandom permutation F k3   −1    1003   c . The result of said inverse permutation F k3   −1    1003   c  is combined with SV 3   0  using modular 2 n  subtraction producing CV 23   1 . The decryption continues to follow the same pattern for the two remaining inverse pseudorandom permutations F k2   −1    1003   b  and F k1   −1    1003   a  where the result of F k1   −1    1003   a  is combined with SV 1   0    1002   a  using modular 2 n  subtraction to produce the first plaintext block P 1    1001   a.    
     For the decryption of the next ciphertext block C 2    1004   b , the state variables  1005  must be updated using a feedback mechanism as will be described. The state variable SV 1   1    1005   a  produced following the decryption of the first ciphertext block C 1    1004   a  is generated by combining the previous state variable SV 1   0    1002   a  with the input from the previous block&#39;s second inverse permutation CV 34   1  and a counter CTR 1   0    1006   a  through modular 2 n  addition where n is the size of a ciphertext block. The second state variable SV 2   1    1005   b  is the output from the previous block&#39;s third inverse permutation F k2   −1    1003   b  and a counter CTR 2   0    1006   b  through modular 2 n  addition. Similarly, the state variable SV 3   1    1005   c  is the output from the previous block&#39;s second pseudorandom permutation F k3   −1    1003   c  and a counter CTR 3   0    1006   c  through modular 2 n  addition. The state variable SV 4   1    1005   d  is generated by combining the previous state variable SV 4   0    1002   d  with the input from the previous blocks fourth inverse permutation CV 12   1  and the current block&#39;s state variable SV 1    1005   a  and a counter CTR 4   0    1006   a  through modular 2 n  addition. The counters  1006  are then incremented using function  1100 . It should be noted that the calculation of SV 1   1    1005   a  should occur before the calculation of SV 4   1    1005   d . Furthermore, while the described embodiment of the present invention stores the state variables SV 1 , SV 2 , SV 3 , and SV 4 , derived embodiments could entail the same spirit of the present embodiments without actually storing the state variables. The step of storing state variables is disclosed in the present invention for ease of understanding. 
     The decryption of all further ciphertext blocks C 2    1004   b  through C m    1004   c  are conducted in the same manner as the decryption of C 1    1004   a . For example, the second ciphertext block C 2    1004   b  is conducted in the same manner as the decryption of the first ciphertext block C 1    1004   a  substituting the updated state variables  1005  for the previous state variables  1002 . 
       FIG. 11  represents an embodied method for modifying the counters from one block encipherment to the next. The method takes as input four counters CTR 1   i  through CRT 4   i  and produces four counters CTR 1   i+1  through CRT 4   i+1 . The steps taken in the embodied method model a typical mileage odometer from an automobile where CTR 1  is the lowest order of magnitude and CTR 4  is the highest order of magnitude. The embodied method always begins by incrementing the lowest order counter CTR 1   1105  through modular 2 n  addition where n is the size of the counter in bits. If CTR 1  has reset itself and is equal to zero  1110 , the embodied method continues to increment CTR 2   1115  in the same manner as CTR 1 . If CTR 1  is not zero  1110 , the method exits  1140   a  and the resulting counters are stored for use in encrypting or decrypting the next block. Each subsequent counter is incremented in the same manner as long as all lower order counters are equal to zero. 
     In one embodiment of the present invention, a method for encrypting a plaintext message comprises receiving at least one plaintext message, wherein the plaintext message forms at least one plaintext block, encrypting said plaintext block by applying 2 or more pseudorandom permutations to each block, and modifying an input to each said pseudorandom permutation by at least one state variable which is modified for each plaintext block by at least one of previously generated permutation outputs, previously generated permutation inputs, ciphertext, and plaintext. The method comprises generating at least one ciphertext block from the output of each plaintext block&#39;s final pseudorandom permutation, partitioning the plaintext message into a plurality of equal size plaintext blocks, padding the plaintext message to facilitate the equal sized plaintext blocks, wherein the modification of the state variables comprises at least one of: modifying the state variable for a first pseudorandom permutation by an output of a next to the last pseudorandom permutation from the previous block, modifying the state variable for a final permutation by an output of the first pseudorandom permutation from the previous block and the state variable for the first pseudorandom permutation from the current block, and modifying the state variables for all other pseudorandom permutations by an output of the preceding pseudorandom permutation from the previous block, wherein the state variables are modified using at least one of modular 2 n  addition and modular 2 n  subtraction wherein n represents the size of a block, and wherein the state variables are modified using a bitwise exclusive or (XOR). 
     The method comprises initializing the state variables before encrypting the first plaintext block by randomizing a nonce and padding the nonce in order to facilitate the initialization of the state variables, wherein the initialized state variables are unique from other initialized state variables in a context of a session key, wherein the number of pseudorandom permutations determines the number of state variables, wherein the pseudorandom permutations are at least one of: block ciphers, keyed substitution tables, S-Boxes, and rotors, wherein each pseudorandom permutation is keyed by at least one different key, wherein each pseudorandom permutation is keyed by a same key, wherein a portion of the pseudorandom permutations may be substituted for the inverses of a remaining portion of the pseudorandom permutations, and wherein the pseudorandom permutations and inverse pseudorandom permutations may be arranged in any order. 
     The method comprises generating an authentication tag from a combination of the state variables, wherein the generation consists of concatenating the resulting state variables after the encryption of the final plaintext block, wherein the generation consists of concatenating the resulting state variables after the encryption of a chosen plaintext block, wherein the generation consists of concatenating the resulting state variables after the encryption of the final plaintext block, concatenating the initial state variables, and combining the two sets of concatenated variables through an exclusive or (XOR), comprises attaching the authentication tag to a ciphertext message, wherein the number of state variables determines the size of the authentication tag, and comprises modifying the input to a pseudorandom permutation by at least one counter, and initializing the counters before encrypting the first plaintext block by randomizing a nonce. 
     In another embodiment of the present invention, an apparatus for encrypting a plaintext message comprises logic to form at least one nonce block from at least one nonce, memory to store at least one state variable, an initializer to set the at least one state variable to at least one initial value, wherein the logic is coupled to the memory and to the initializer, wherein the logic includes at least two pseudorandom permutations to sequentially randomize each nonce block, wherein the logic combines the at least one state variable with inputs to the pseudorandom permutations, and wherein the logic generates the at least one state variable of a current nonce block from at least one of: state variables of a previous nonce block, outputs from the previous nonce block&#39;s pseudorandom permutations, and inputs to the previous nonce block&#39;s pseudorandom permutations, wherein the memory stores outputs of final pseudorandom permutations as initial values to use in an encryption or decryption, wherein the memory stores final state variables as initial values for use in an encryption or decryption, wherein the logic adds at least one bit of padding to the nonce to generate equal sized nonce blocks, wherein the number of pseudorandom permutations is equal to the number of nonce blocks and the number of state variables, wherein the pseudorandom permutations are at least one of: block ciphers, keyed substitution tables, S-Boxes, and rotors, wherein a portion of the pseudorandom permutations may be substituted for inverses of a remaining portion of the pseudorandom permutations. 
     In a further embodiment of the present invention, a computer readable medium comprising instructions for: receiving at least one plaintext message, wherein the plaintext message forms at least one plaintext block, encrypting said plaintext block by applying 2 or more pseudorandom permutations to each block, modifying an input to the pseudorandom permutations by at least one state variable, modifying the at least one state variable after each plaintext block is encrypted for use in encrypting a next plaintext block, modifying the at least one state variable for a first pseudorandom permutation by an output of a next to last pseudorandom permutation from a previous block, modifying the at least one state variable for a final permutation by an output of the first pseudorandom permutation from the previous block and the at least one state variable for the first pseudorandom permutation from the current block, and modifying the at least one state variable for all other pseudorandom permutations by an output of a preceding pseudorandom permutation from the previous block. 
     The computer readable medium comprises instructions for initializing the at least one state variable before encrypting a first plaintext block by randomizing a nonce, modifying the input to a pseudorandom permutation by an internal counter, generating an authentication tag from a combination of the state variables, generating at least one ciphertext block from an output of each plaintext block&#39;s final pseudorandom permutation, wherein the pseudorandom permutations are at least one of: block ciphers, keyed substitution tables, S-Boxes, and rotors. 
     Although an exemplary embodiment of the system of the present invention has been illustrated in the accompanied drawings and described in the foregoing detailed description, it will be understood that the invention is not limited to the embodiments disclosed, but is capable of numerous rearrangements, modifications, and substitutions without departing from the spirit of the invention as set forth and defined by the following claims. For example, the capabilities of the invention can be performed fully and/or partially by one or more of the elements. Also, these capabilities may be performed in the current manner or in a distributed manner and on, or via, any device able to provide and/or receive information. Further, although depicted in a particular manner, various modules or blocks may be repositioned without departing from the scope of the current invention. Still further, although depicted in a particular manner, a greater or lesser number of modules and connections can be utilized with the present invention in order to accomplish the present invention, to provide additional known features to the present invention, and/or to make the present invention more efficient. Also, the information sent between various modules can be sent between the modules via at least one of a wireless source, and a wired source and via plurality of protocols.