Method and apparatus for variable-overhead cached encryption

A digital encryption structure allows the varying of the computational overhead by selectively reusing, according to the desired level of security, a pseudorandom encoding sequence at the transmitter end and by storing and reusing pseudorandom decoding sequences, associated with one or more transmitters at the receiver end. A public initialization vector is combined with a secret key to produce a deterministic sequence from a pseudorandom number generator. This pseudorandom sequence in turn, is used to convert plaintext to ciphertext. The sequence may be selectively reused by storing the sequence to a transmitter memory cache and iteratively reading the sequence from memory according to a counter which controls the level of security of the encryption system. The ciphertext is decrypted on the receiver end by invertibly combining the ciphertext with the same pseudorandom sequence used by the transmitter to originally encode the plaintext. The pseudorandom sequence is independently generated by the receiver end using the original key and initialization vector used in the transmitter end. Once generated in the receiver, the pseudorandom sequence is stored in a receiver cache for reuse with each iterative use of the stored transmitter pseudorandom sequence.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to data encryption, and more particularly to a 
method and apparatus for varying the computational overhead associated 
with encrypting and decrypting digital data signals by selectively 
reusing, according to the desired level of security, a pseudorandom 
encoding sequence at the transmitter end and by storing and reusing 
pseudorandom decoding sequences at the receiver end. 
2. Description of the Background Art 
Data encryption is a function that ensures the privacy of a digital 
communication by preventing an unauthorized receiver from understanding 
the contents of a transmitted message. A conventional "symmetric key" 
cryptosystem is generally illustrated in FIG. 1(a). A transmitter 
transforms a plaintext message into ciphertext using an invertible 
encryption transformation. This transformation is a function of the 
plaintext input message and a secret key which is shared by both the 
transmitter and the receiver. The ciphertext is then transmitted over an 
unsecured public channel and the intended receiver of the message, also in 
possession of the secret key, applies the inverse transformation to 
decrypt the ciphertext and recover the original plaintext message. The 
secret key is communicated to a plurality of authorized users through a 
secure channel (for example, a secure Key Exchange Algorithm may be 
employed) and the key effectively dictates a specific encryption 
transformation from a family of cryptographic transformations. In general, 
any station in possession of the secret key may encrypt or decrypt 
messages. 
A conventional cryptosystem can be said to exhibit "unconditional security" 
if the secret key is as long as the ciphertext message, each key is used 
only once, and all keys are equally likely. However, since most systems 
can be expected to transmit a large number of messages, the problem of 
distributing the key information becomes formidable. Most practical 
cryptosystems have short keys compared to the length of a message. The 
lessened security resulting from short keys is compensated for by relying 
on the complexity of the way that the key is combined with the data. 
A particular example of a conventional cryptosystem, hereafter referred to 
as an electronic codebook, is generally illustrated in FIG. 1(b). The 
electronic codebook involves the use of a secret key that is shared by 
both the transmitter and the receiver. The transmitter utilizes the key to 
generate a deterministic, apparently random sequence of binary digits 
using a Pseudorandom Number (PN) generator. An essential feature of the PN 
generator is that with a specific key input, a unique PN sequence of 
arbitrary length may be generated. The PN sequence is then combined with 
the binary representation of the plaintext message to be encrypted to 
produce a sequence of ciphertext. The combination of the PN sequence and 
the plaintext must be accomplished using an invertible function. An 
invertible function is one that has a known inverse such that when the 
inverse function is applied to the ciphertext the original plaintext can 
be extracted. For example, two's complement addition or bit-wise 
exclusive-OR (XOR) are two widely used invertible functions, although 
other functions can be employed. 
Decoding of the encrypted ciphertext may be performed by the receiver using 
a method identical to that used by the transmitter. Ciphertext is received 
from the transmitter and combined using a logical XOR gate, with a 
pseudorandom sequence generated by a PN generator identical to that used 
in the transmitter. The essence of the electronic codebook system is that 
an encryption key is used to generate a pseudorandom sequence in the 
transmitter side, and the identical sequence is then generated in the 
receiver when the same encryption key is applied to the receiver PN 
generator. The XOR gate in the receiver provides the inverse function of 
the XOR gate in the transmitter so that logical combination of the 
ciphertext and the PN sequence in the receiver produces the same plaintext 
that was originally encoded by the transmitter. 
One drawback of the prior art system described is that the overhead of 
generating PN sequences is quite high, particularly relative to the 
overhead of applying the combination function. In practice, it is typical 
to generate and combine the PN sequence with a plaintext message of 
arbitrary length one character at a time, as needed. The characters of the 
PN sequence are discarded after a single use, so there is no opportunity 
to spread the cost of computing the sequence over several messages. The 
rate at which messages can be encrypted and decrypted is therefore limited 
by the speed at which the PN sequence can be produced. What is needed is a 
method for storing and reusing PN sequences in order to increase the 
transmission rate of messages through the cryptosystem. 
Another drawback of the prior art system is that the receiver's PN 
generator may lose synchronization with that of the transmitter under some 
circumstances, necessitating additional recovery procedures in order for 
the plaintext to be recovered. For example, if the next character emitted 
by the PN generator is a function of the initial key input as well as the 
number of characters that have been previously emitted, and if the message 
is being communicated from the transmitter to the receiver in several 
fragments or packets, and if any packets are lost or received out of 
order, then it will first be necessary for the receiver to receive and 
arrange all the fragments in the proper order before decoding of the 
message can be accomplished. It is therefore desirable that a high speed 
cryptosystem exhibit the property of self-synchronization between 
transmitter and receiver such that no additional recovery procedures are 
required to decode messages. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, an apparatus and method are 
described for variable overhead cached encryption and decryption. A 
transmitter unit is used for encoding or encrypting data and a separate 
authorized receiver decodes or decrypts the data. Both the transmitter and 
receiver share a common secret key that has been communicated through some 
separate channel. The transmitter combines the secret key (which serves as 
a constant base value) with an Initialization Vector (IV), using an XOR 
operation to produce a temporal key. This temporal key is then used as an 
input to a pseudorandom number (PN) generator to produce a unique PN 
sequence of binary digits, for each new temporal key entered. The 
generated PN sequence is equal in length to the longest anticipated 
message fragment. The initialization vector together with its 
corresponding PN sequence is then stored in a cache and the PN sequence is 
iteratively reused, as determined by a counter, to encrypt one or more 
plaintext messages. The counter is initialized to a maximum count value 
whenever a new PN sequence is generated, and the counter tracks reuse of 
the PN sequence to encrypt the number of messages specified by the maximum 
count value. When the maximum count value specifies that the PN sequence 
is to be used only once, the security afforded by the present invention 
will be high, but a new PN sequence must be generated for each message 
sequence transmitted and so the computational overhead will also be high. 
If the maximum count value specifies a maximum count value greater than 
one, the PN sequence stored in the cache will be reused to encrypt the 
maximum count number of message sequences. The resulting ciphertext 
messages will be more vulnerable to statistical cryptoanalytic attack as 
the maximum count value increases. The PN sequence from the cache is 
combined with the plaintext data to be transmitted using an invertible 
combination function. An exclusive-OR (XOR) function is used in the 
preferred embodiment to produce a ciphertext message. The unencrypted 
initialization vector is then concatenated with the ciphertext, and 
together, both are exported by the transmitter to the receiver for 
decrypting. As each plaintext message is encrypted and exported, the value 
of the counter is decremented. If the value of the counter goes to zero 
then a new initialization vector is selected and the above steps are 
repeated for subsequent messages. A new initialization vector should be 
chosen with equal probability from the set of all possible initialization 
vectors since this has the desirable result of selecting a large number of 
different encoding sequences over the life of the secret key. 
The encoded communication is imported by the receiver and the 
initialization vector portion is extracted. The receiver's cache of 
previously received initialization vectors is searched using the imported 
initialization vector as a search key to determine whether an entry exists 
for it in the cache. If the initialization vector has been previously 
received and stored, then the corresponding PN sequence has already been 
computed and stored and is available for decoding the imported ciphertext 
without having to regenerate the PN sequence. If the imported 
initialization vector is not found in the cache, then the associated PN 
sequence is not available and the receiver then combines the 
initialization vector with the secret key to produce a temporal key and 
corresponding PN sequence identical to the sequence used by the 
transmitter to encode the data. This PN sequence is then combined with the 
ciphertext, using an XOR gate, to recover the original plaintext from the 
ciphertext. The initialization vector and corresponding newly generated PN 
sequence are then stored in the receiver cache, to be available for 
comparison with subsequently received initialization vectors. Utilization 
of this cache can greatly reduce the overhead associated with generating 
PN sequences, particularly when higher count values are used by a given 
transmitter.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The encryption-decryption system of the present invention consists of a 
unique combination of digital functional blocks, all of which are 
separately conventional and well understood in the art. The system is 
preferably implemented on a general purpose computer using programmed 
instructions; however, the discussion which follows teaches the invention 
in terms of functional blocks which may be readily implemented using 
conventional discrete or integrated digital circuitry. The preferred 
implementation is described with reference to FIGS. 4 and 5 below. 
Referring now to FIG. 2, a transmitter 10 is shown for encrypting plaintext 
data 32 into ciphertext 28. Plaintext data 32 is digital information which 
may be readily understood by both a sender and a receiver and may also be 
readily understood by other unauthorized third parties having access to 
the communications channel. The function of transmitter 10 is to encode or 
encrypt the plaintext data 32 in such a way that the information is usable 
only to a receiver having a bona fide access to the data. A central 
feature of transmitter 10 is a key 12 which is secret as to third parties 
but shared between the transmitter and a receiver 20 (shown in FIG. 3) of 
data 32. As discussed with reference to FIG. 1(a), key 12 would ideally be 
infinite in length and would be unique as to every message communicated 
between the transmitter 10 and the receiver 20. In practice, however, key 
12 is relayed only periodically between the transmitter 10 and the 
receiver 20 and during the periods between the relay of the key, the key 
is used repetitively to encrypt plaintext data 32 from transmitter 10 
before transmission to receiver 20. 
An initialization vector (IV) 14 is produced by IV generator 29 and 
utilized by the transmitter 10 and receiver 20 to extend the usability of 
the key 12. The key 12 is a relatively expensive component to generate and 
maintain. The key 12 must be randomly generated and must be securely 
transmitted between transmitter 10 and receiver 20 in a secure channel 
which is separate from the communication system through which ciphertext 
28 is transmitted. Consequently, even though the security of the key 12 
diminishes with each successive use, efficiency demands that maximum 
utilization of the key occurs. One way of extending the utilization of the 
key 12 is to combine the key with a local key such as the initialization 
vector 14. IV generator 29 generates a random sequence having the same 
length as key 12. Generator 29 repeats the same IV sequence until reset 25 
signals that a new sequence is to be generated. Initialization vector 14 
is combined with key 12 using a conventional exclusive-OR (XOR) gate 16 to 
produce a temporal key 17. Various other logical functions can be 
equivalently used in place of XOR gate 16 to mask the identity of the key. 
This logical function need not be invertible. The XOR function is applied 
bitwise and is defined by a logical "0" whenever all inputs are the same, 
and a logical "1" otherwise. Initialization vector 14 is transmitted to 
receiver 20 as part of the communication sequence containing the 
ciphertext output 28. Information transmitted from transmitter 10 to 
receiver 20 includes a block of ciphertext 28 concatenated with 
initialization vector 14. In essence, the initialization vector 14 becomes 
public in that it is transmitted in an unencrypted format and may be more 
easily appropriated by third parties. However, since initialization vector 
14 is always encoded with key 12 to produce temporal key 17, the value 
knowing of this initialization vector is limited. Since the initialization 
vector 14 is merely a component of temporal key 17, it would be difficult 
to determine the value of the temporal key knowing only the value of the 
initalization vector. 
Temporal key 17 acts as a seed to a Pseudorandom Number (PN) generator 18. 
PN generator 18 is a deterministic machine, conventional in the art, and 
characterized by the fact that given a specific input or seed value, a 
unique and repeatable output sequence of arbitrary length can be 
generated. This output sequence from PN generator 18 is referred to in 
FIG. 2 as a temporal sequence 23 and is equal in length to the longest 
anticipated plaintext data 32. Once generated, the temporal sequence 23, 
is then stored in cache 22, a conventional memory register. The contents 
of cache 22 is then written as a PN sequence to XOR gate 26. XOR gate 26 
is similar in construction to XOR gate 16 and is used to combine the PN 
sequence 24 with the plaintext data 32 to produce ciphertext 28. 
An additional feature of the present invention is counter 21, which 
controls the generation of new initialization vectors 14 and thereby the 
security level of the encryption system. Cache 22 contains the temporal 
sequence 23 produced by the PN generator 18 in response to the input 
combination of the initialization vector 14 and the key 12. In the 
preferred embodiment, cache 22 is designed to contain one or more temporal 
sequences 23 arranged as a function of initialization vectors 14. For a 
specific initialization vector 14, a corresponding temporal sequence 23 
will be stored. A further discussion of the implementation of cache 22 can 
be found with reference to the discussion of FIGS. 4(a) and 4(b) below. 
Counter 21 selectively resets IV generator 29, enabling the iterative 
reuse of a specific initialization vector 14 and corresponding temporal 
sequence 23 in order to improve the efficiency of the transmitter 10. The 
counter 21 is operated by initially loading a maximum count signal 19 into 
the counter 21. As each new data sequence 32 is present, a decrement 
signal 27 instructs counter 21 to decrement. When counter 21 decrements to 
zero, then a new initialization vector 14 is subsequently utilized by XOR 
16 in generating a new temporal key 17. With each sequence of plaintext 
data 32 combined in XOR gate 26, a PN sequence 24 of identical length is 
read from cache 22 by XOR 26. With each new plaintext date 32 sequence, 
the decrement signal 27 reduces the counter 21 contents by one. The 
encrypting process proceeds in XOR gate 26, reading PN sequences 24 and 
decrementing counter 21 until the counter 21 contents reaches zero causing 
the IV generator 29 to reset. Resetting the IV generator 29 results in the 
generation of a new initialization vector 14. Counter 21 has been 
described with respect to FIG. 2 as a plaintext data 32 sequence counter, 
decrementing with each sequence processed. Counter 21 equivalently 
implements a timer or clock function, resetting the IV generator 29 after 
a period of time set by Max Count 21. In this way, initialization vector 
14 extends the usability of the key 12 by making the corresponding PN 
sequence 24 more difficult to determine. Use of counter 21 and cache 22 
serve the purpose of reducing the costly overhead associated with 
generating PN sequences 24 by reusing the sequences generated and stored 
in the cache 22. The counter 21 enables variability of the overall 
security of the transmitter 10 and receiver 20 by providing a selection of 
the number of times each specific temporal sequence 23 is used in the 
encoding of data. In the preferred embodiment, the counter 21, reset 25, 
maximum count 19, and decrement 27 signals are implemented in the central 
processing unit of a conventional general purpose computer. 
Referring now to FIG. 3, a receiver 20 is shown in which a ciphertext 28 is 
decoded to produce an unencrypted plaintext data 66 which is identical to 
the plaintext data 32 sequence of transmitter 10. As the communication 
sequence containing an initialization vector 14 and a block of ciphertext 
28 is imported by receiver 20, the initialization vector 14 is stripped 
off and applied to cache 48 and to XOR gate 42. Other functions may be 
equivalently substituted in place of XOR gate 42; however, gate 16 and 
gate 42 must be identical. Initialization vector 14 is then compared in 
cache 48 with other initialization vectors stored in cache 48 to determine 
whether the specific initialization vector 14 has previously been received 
and stored. If the specific initialization vector 14 is found to be stored 
in cache 48, then the PN sequence associated with that initialization 
vector is written to an XOR gate 64, and the stored PN sequence is used to 
decode the imported ciphertext 28. When a match of the received 
initialization vector 14 is made to a stored initialization vector in 
cache 48, read cache signal 52 instructs multiplexer 58 to route the 
stored sequence 56 output to the XOR gate 64. From the viewpoint of the 
XOR gate 64, the PN sequence stored in cache 48 becomes the selected 
sequence and is delivered through multiplexer 58 via the stored sequence 
56 output of the cache. 
If a determination is made that the initialization vector 14 has not been 
previously received, then the read cache signal 52 of cache 48 signals 
multiplexer 58 to connect the PN generator 44 to the XOR gate 64. In this 
event, initialization vector 14 is used in producing a temporal key 38 
input to PN generator 44 to generate a new PN sequence 46 identical to the 
corresponding PN sequence 23 used in the encoding of the ciphertext 28 by 
the transmitter 10. The read cache signal 52 is then inverted and used to 
enable the output of the PN generator 44. Just as in the case with the 
transmitter 10, initialization vector 14 is combined with key 12 in XOR 
gate 42 to produce a temporal key 38. It should be noted that this 
temporal key 38 is identical to the corresponding temporal key 17 produced 
in the transmitter 10 by the XOR gate 16 combination of key 12 and 
initialization vector 14. PN generator 44 receives temporal key 38 to 
produce a PN sequence 46, which is then connected via multiplexer 58 to 
XOR gate 64 as a selected sequence 62. In order to improve the efficiency 
of future decoding of ciphertext 28 utilizing this specific initialization 
vector 14, the PN sequence associated with the initialization vector is 
then stored in cache 48 together with its corresponding initialization 
vector. When the next block of ciphertext 28 is received using the same 
initialization vector 14, the PN sequence 46 need not be regenerated by PN 
generator 44, but rather may be read from cache 48 as a stored sequence 
56. It should further be noted that the imported initialization vector 14 
has a dual purpose: it is used both as a component of the temporal key 17 
for generating PN sequence 46 and as an input to cache 48 for the purpose 
of determining whether there exists a stored sequence 56 corresponding to 
the imported initialization vector 14. The XOR gate 64 combines the 
selected sequence 62 with ciphertext 28 to produce plaintext data 66 which 
is identical in content to the corresponding plaintext data 32 originally 
encoded in transmitter 10. 
An important benefit of the encryption system of the present invention is 
that the transmitter 10 and receiver 20 are self-synchronizing. That is, 
assuming the key is shared, everything needed to decode a block of 
transmitted data is contained within the message. Knowledge of prior 
messages or sequences is not required. 
Referring now to FIG. 4(a), a diagram is shown of a general purpose 
computer 40 used for the preferred implementation of the encryption system 
shown in FIGS. 2 and 3. The preferred implementation of the present 
invention consists of programmed instructions implemented on an Apple 
Macintosh.RTM. computer, manufactured by Apple Computer, Inc. of 
Cupertino, Calif. The general method steps, described below, can be 
equivalently implemented on any general purpose computer and many other 
programmable processor-based systems. The general purpose computer 40 
consists of a CPU 31 attached to a number of processing components. CPU 31 
contains a keyboard 37 and a CRT 35 through which a user can interact with 
CPU 31. The CPU 31 is connected to a communication port 33 for interfacing 
with other processors and communication devices, such as modems and area 
networks. CPU 31 further comprises a data bus 45 for connecting various 
memories, including program memory 39, cache memory 60, counter memory 43, 
and mass storage 41. Program memory 39 contains operating instructions for 
directing the control of CPU 31. Cache 60 contains high speed temporary 
memory for use by CPU 31 in executing the encryption and decryption 
program instructions of the present invention. Also attached to data bus 
45 is mass storage 41 which contains stored data, utilized by CPU 31 in 
executing program instructions from program memory 39. 
Referring also to FIGS. 2 and 3, the XOR gates 16, 26, 42 and 64 are 
implemented by CPU 31 using Boolean arithmetic; counter 21 is implemented 
using counter memory 43; and the caches 22 and 48 are implemented using 
cache 60 memory. PN generator 18 and 44 are implemented by the CPU 31 
using a conventional pseudorandom number generator algorithm. Computer 
system 40 can implement the encryption system in a number of ways. A first 
computer system can act as a transmitter 10 and export ciphertext to a 
second computer system via the communication port 33. In this operation 
mode, the first computer acts as transmitter 10 while the second computer 
acts as receiver 20. This first mode of operation provides for a secure 
transmission of sensitive data. 
In an alternative operating mode, a single computer system 40 acts as both 
a transmitter 10 and as a receiver 20, storing ciphertext to mass storage 
41 and later retrieving the stored ciphertext for decoding and use. The 
purpose of this second mode of operation is to allow for the secure 
storage of sensitive data. 
Referring now to FIG. 4(b), a memory map of cache 60 is shown in which a 
list of initialization vectors 72 are paired with corresponding sequences 
74. The entry "IV 1" has a corresponding "Sequence 1", "IV 2" has a 
corresponding "Sequence 2", and "IV n" has a corresponding "Sequence n". 
Cache 60 memory provides a functional implementation of cache 22 in FIG. 
2, when computer system 40 is operating as a transmitter 10, and provides 
an implementation of cache 48 in FIG. 3, when the computer system is 
operating as a receiver 20. The counter 21 output in transmitter 10 is 
implemented as a CPU 31 function in which the CPU reads and decrements the 
contents of counter memory 43 each time a PN sequence is utilized to 
encode a sequence of plaintext data 32. 
Referring now to FIG. 5, a flow chart is shown outlining the programmed 
instruction steps which are executed by the general purpose computer 40, 
acting in the mode of a transmitter 10 (FIG. 2) in encrypting plaintext 
data to produce the ciphertext 28 of the present invention. Step 61 is the 
entry point for the encrypting instructions of FIG. 5. If step 63 
determines that the routine variables have not been initialized, CPU 31 
initializes the routine variables in step 65 by setting the packet count 
to Max Count generating an Initialization Vector (IV), and setting the PN 
Sequence to the value NewSeq(IV XOR Secret Key). The variable IV is equal 
to the initialization vector 14 and the variable Secret Key is a 
previously determined and stored value equal to key 12. The function 
"NewSeq()" is a conventional algorithm for pseudorandom number generation, 
using the values of IV and Secret Key as seed components. For example see 
Blahut, Richard, Digital Transmission of Information, Addison Wesley 
Publishing Company, 1990, p 497. The variable Packet Count represents the 
maximum number of times that a particular initialization vector can be 
used in the generation of a PN sequence 24. The maximum value (Max Count) 
for the variable packet count is equal to the maximum count signal 19. In 
step 67, packet count is decremented by one, and in step 71 the CPU 31 
tests whether Packet Count is equal to zero. If Packet Count is equal to 
zero, then the program returns to the initialization step in 65. In the 
event that packet count is not equal to zero, a Ciphertext sequence is 
calculated in step 73 using the formula: 
EQU Ciphertext[i]=PN Sequence[i]XOR Plaintext[i] 
where i is an indexing integer ranging from zero to one less than the 
length of the plaintext sequence in bits. It should be noted that in this 
preferred method, the length of the plaintext, PN, and ciphertext 
sequences are all of equal length. Following the calculation of the 
ciphertext sequence, data strings called "message.iv" and "message.data" 
are generated, in which message.iv is set equal to the initialization 
vector sequence and message.data is set equal to the ciphertext sequence. 
The routine exits 77 at which time CPU 31 transmits message.iv and message 
.data as a concatenated data string to communication port 33 or to mass 
storage 41 for transmission or storage. 
Referring now to FIG. 6, with the computer 40 acting in the mode of a 
receiver 20 (FIG. 3), the concatenated data string containing message.iv 
and message.data is received by CPU 31 in step 87, and the initialization 
vector and ciphertext sequences are separated. Using the initialization 
vector component (message.iv), a search 89 of cache 60 is made for an 
initialization vector matching the incoming message.iv. Since each 
initialization vector in cache 60 is matched to a PN sequence, locating a 
matching initialization vector to the incoming message.iv provides 
identification of the PN sequence used to encrypt the incoming 
message.data. If the message.iv can be matched 91 to a stored IV and PN 
sequence, the receiver 20 will not have to expend the overhead of creating 
a new PN sequence to decode the message.data sequence. If the sequence is 
found in the cache 60, then the plaintext data is determined 95 using the 
formula: 
EQU Plaintext[i]=PN Sequence[i]XOR Ciphertext[i] 
If the sequence is not found 91 in the cache 60, then CPU 31 generates 93 
the sequence using the same pseudorandom number generation routine used in 
step 65 of FIG. 5, wherein: 
EQU PN Sequence=NewSeq(IV XOR Secret Key) 
This PN Sequence is stored in cache 48 and then used in step 95 to recover 
the plaintext data 66. The routine exits in step 97. 
The invention has now been explained with reference to specific 
embodiments. Other embodiments will be apparent to those of ordinary skill 
in the art in light of this disclosure. For example, the invertible 
function described in the preferred embodiment is an XOR function. Other 
invertible functions are equivalently effective. Also the counter 21 is 
shown as a "preset with decrement-to-zero" function. Alternative 
up-counters and the CPU-implemented increment-and-compare functions are 
viewed as equivalents with respect to the present invention. Therefore, it 
is not intended that this invention be limited, except as indicated by the 
appended claims.