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In another aspect, the present invention relates to a system and method of the type described above for the provision of secret messaging between two participants who are unknown to one another, but are known to a specific contact point in the system in which both participants are communicating. In accordance with the system and method, each participant is connected to the system with an ES prior-secret relationship, and while they are unknown to one another, they communicate in secret as previously described above with their known contact point which then communicates also as described above with other known contact points until reaching the contact point that knows the intended recipient.

This contact point is then also communicated with as described above, and he finally communicates with the end-recipient. Thus, for example, if Alice wants to communicate with Bob, whom she does not have an ES prior-secret relationship, but she does have such a relationship with Point A in the network, and if she knows that Bob is at least also on the network, then she communicates in secret as described above with Point A, whom she instructs to find Bob.

Hence, Alice can communicate with Bob indirectly by utilizing this chain of existing ES prior-secret relationships. In so doing, each Point in the chain communicates Alice's message to the next Point in the chain using ES prior-secret relationships, until finally Point D communicates the message to Bob, with whom it has an existing ES prior-relationship.

In still another aspect, the present invention relates to a system and method of the type described above wherein, after a unique MK is created and exchanged, the system will encrypt the accompanying content using a variable portion, up to and including the entirety, of this unique MK in a manner that includes one of two different key expansion techniques, and at least one, and preferably two, different transposition processes.

In still another aspect, the present invention relates to a system and method of the type described above which is used only for communicating as a key exchange system to generate the next future message's new ES and the unique MK. Instead of using this method's encryption technique for the accompanying message content, another system is used to encrypt the accompanying message content. In some embodiments of this aspect of the invention, a predetermined accompanying content will be used to exchange a new ES for the next future message.

In another aspect, the present invention relates to a method for exchanging secure messages between two parties, comprising the steps of receiving a first sequence of characters, operating on the first sequence with a first algorithm at least twice in succession, thereby forming second and third sequences of characters, encrypting a message through the use of at least one of the second and third sequences, thereby forming an encrypted message, and sending the encrypted message, and preferably the second and third sequences, to a recipient.

In a further aspect, the present invention relates to a method for exchanging secure messages between three parties based on a first existing sequence of characters known to a first and second party and a second existing sequence, distinct from the first existing sequence, which is known to the second and third party. The method comprises the steps of generating a first encrypted message through the use of a first encryption key derived from the first sequence of characters, generating a second encrypted message from the first encrypted message through the use of a second encryption key derived from the second sequence of characters, and decrypting the second encrypted message through the use of a third encryption key derived from the second sequence of characters.

In another aspect, the present invention relates to a method for exchanging secure messages between two parties based on an existing sequence of characters, comprising the steps of operating on the existing sequence with a first algorithm at least two times, thereby forming first and second sequences of characters, encrypting a first message such that it can be decrypted using the first sequence, thereby forming a first encrypted message, and sending the first encrypted message and the second sequence to a recipient, wherein the recipient operates on the second sequence with the first algorithm to generate third and fourth sequences of characters.

In a further aspect, the present invention relates to a method for exchanging secure messages between two parties, comprising the steps of receiving an original sequence of characters; operating on the original sequence three consecutive times with a first equation, thereby forming first, second and third sequences of characters, respectively; operating on one of the first, second and third sequences with a second equation, thereby creating a fourth sequence of characters; and encrypting a message through the use of the fourth sequence of characters.

In still another aspect, the present invention relates to a method for exchanging encryption keys, comprising the steps of receiving from a sender a first message encrypted through the use of a first encryption key; decrypting the first message through the use of the first encryption key; operating on the first encryption key with an equation so as to produce a second encryption key; encrypting a second message through the use of the second encryption key, thereby creating a second encrypted message; and communicating the second encrypted message and the second encryption key to the sender.

In another aspect, the present invention relates to a method for exchanging encryption keys, comprising the steps of a providing an encryption key defined as a first sequence of characters; b operating on the key with a first equation so as to produce at least a second and third sequence of characters; c encrypting a message through the use of at least one of said second and third sequences of characters, thereby creating a first encrypted message; d communicating the first encrypted message and the second and third sequences of characters to a recipient; e redefining the encryption key as said second sequence of characters; and repeating steps a through e at least once.

In a further aspect, the present invention relates to a method for exchanging message keys between two parties based on an sequence of characters known to the parties, comprising the steps of operating on the existing sequence of characters with a first equation at least two times, thereby forming a first and second sequence of characters; creating a message containing first and second parts, wherein the first part of the message comprises the first and second sequence of characters, and wherein the second part of the message comprises a message text; encrypting the message, thereby forming a first encrypted message; and sending the first encrypted message to a recipient.

In another aspect, the present invention relates to a software program or set of programs which are disposed in a tangible medium, and which contain instructions suitable to carry out any of the above noted methods, or any portions thereof. In yet another aspect, the present invention relates to a system adapted to carry out any of the above noted methods, or any portions thereof. These and other aspects of the present invention are described in greater detail below.

In accordance with the present invention, a perfectly secure key exchange and authenticated messaging system and methodology is provided for encryption key distribution, management and message protection. The system and methodology overcome a number of infirmities in existing systems that are designed for secure messaging.

For convenience, the system of the present invention will frequently be referred to as the Krypt eXchange Protocol KXP , and components or portions of systems and methodologies in accordance with the present invention may be referred to by similar or derivative names, it being understood that the present invention is not limited in any way by any products or services that may be sold or marketed under that name or designation, either now or in the future.

The system of the present invention will typically include software components, which may be written in multiple programming languages for operation on a variety of computer operating systems or platforms. Hardware components may also be provided that may be built to facilitate the use and deployment of the system and methodology of the present invention in multiple electronic devices. In the preferred embodiment of the system of the present invention, a set of software referred to as a KXP Toolkit is used to provide a security layer to other software applications, business processes or electronic devices.

This security layer acts to secure communications between the user of the device, application or process and another user or an owner of the content within the device, application or process. The KXP Toolkit preferably requires that all communicating participants have a single, original Existing Shared Secret that is in a Base 10 or Base 16 number format and preferably of at least digits or characters in length.

These ES numbers will preferably have been initially distributed to each participant outside the scope of the KXP using existing distribution and registration processes such as exists for the initial distribution of a credit card and its ES, which is typically the account number. Along with the ES, an OpenID number or character string is provided that associates any secure communication to the ES and owning participant. If desired, the format of such OpenID can be application, device or process dependent.

As explained in greater detail below, the KXP process allows for the secure exchange of future encryption keys based on existing encryption keys or an ES, even if the existing encryption keys or ES has been compromised. Hence, additional security can be imparted to the system by requiring that the first communication between parties, prior to the exchange of any substantive message, is a key exchange to establish a new ES that can be used in the exchange of the first substantive message.

Additional security can also be imparted to the system by requiring periodic or random key exchanges between parties, even if the parties are not actively exchanging substantive messages, since this makes derivation of any particular key set by a third party significantly more resource intensive.

In order to understand the KXP as a process for key exchange and encryption, a few system fundamentals functions or primitives of one particular embodiment of the system are provided:. The end result? The following exemplary embodiment of the KXP illustrates the logic process of the system. The KXP has delivered a secure, authenticated key exchange, secure communications that even if discovered retains the sanctity of the original secret, and a capability to communicate new secrets at will.

The KXP system provides all of this, in a performance-enhancing single asymmetric transmission. The KXP is a compact, single transmission system that is performance enhanced by the simple formulas and is future computing-assured with known, well-identified attacks and remedies. The present invention can be further understood with reference to the flowchart of FIG. After an Original Secret has been established, it is converted 11 into a first key set by a user.

A first key of the first key set is then converted 13 into a first message key. The Original Secret is replaced 15 by a second key taken from the first key set. Message encryption 17 is then accomplished by expanding 19 the first message key into an expanded first message key, creating 21 a transpose matrix, creating 23 a header key from the first expanded message key, expanding 25 the header key into an expanded header key, using the expanded message key in an OR operation to hide 27 the transpose matrix in an OTP, and encrypting 29 the message content with an expanded first message key.

A second key of the first key set is then converted 31 into a second key set, and a first key of the second key set is converted 33 into a second message key. The following example illustrates some of the details of one particular embodiment of the KXP Process. In this example, it is assumed that Alice and Bob know secret A, which is a number with an even number of digits that is at least 10 digits in length. Various encryption algorithms may be used in the practice of the present invention.

One such algorithm is depicted in FIG. As shown therein, the process assumes that a secret A has been established 41 between two parties, and that this secret comprises a plurality of digits. Each digit of A is then converted 43 into a new value, as through application of a modular arithmetic equation using a random number C.

Next, a random number Y is generated 45 which is twice as long as the required encryption strength. This number is then reduced 47 by half through modular addition of adjacent digits. The reduced Y is then used as the message key to encrypt 49 a language-based message. After message encryption, the message key is expanded 51 , and a header key is obtained by adding 53 adjacent digits of the message key. The header key is then expanded 55 , and header variables are created 57 which may indicate, for example, the technique or techniques used to expand the header key, the length of the message key, and the length of the One Time Pad, if one was used in the encryption.

Next, a transpose matrix is created 59 , and the message text is passed 61 through the transpose matrix. The transpose matrix is then encrypted 63 with the expanded header key, and the transposed text is encrypted 65 with the expanded message key. The following example demonstrates some of the calculations and processes that may be used in a particular embodiment of the KXP process constructed in accordance with the present invention.

No Header mode is included in this example, e. Could use any cipher technique here with the MK. This section specifies the 2factor Authentication System. It is an identity-based, message-independent, one-pass authenticated key establishment protocol. It is designed to fit within communications protocols for remote access. It is the only electronic authentication system with operational efficiency while incorporating the unique capability of updating the long-term authentication keys.

This allows 2factor to be the only remote authentication system that can apply unique trusted credentials at any and every participant interaction. Long-term key update provides the first multi-message protection in a forward next-message direction along with standard break-backward Perfect Forward Secrecy protection to any message with a compromised valid, but not correct long-term key. The system also offers straightforward information-theoretic analytic proof that the applied mathematics provides unconditional security of plaintext exchanges.

Mutual authentication and data security is easy to provide—for a closed, small group. Almost every current method available today will work, and it will work within almost any established benchmark criteria. But what if the group is large, fluctuating and ever expanding? What methods work then—what are the features needed to deliver that security?

This type of group has several thousand or more participants with multiple and changing trust partners and end users. In order to meet the needs of these large groups, the authentication and data security system must meet well-defined benchmark criteria, providing:. Current authentication and data security methods that work on small groups have difficulty scaling to large groups. This is because they begin to add too many components, require too much end user expertise, demand too many resources to operate, perform too slowly with too much computational overhead, provide limited futures due to necessary key size increases and mathematic insecurity and are too costly when compared to the actual security needs of the data transmissions and data ownership.

Even though the criteria are not market apparent for the small groups, the inability of the current methods becomes a stark reality for large ones. Conventions and Terminology. The 2factor description is a concrete process that can easily be fitted to a particular application. The specific implementation details, such as key storage methods and interconnectivity options, are left to the protocol implementer to decide, although some examples are included in this description.

The only particular convention for 2factor is key formatting. This requirement is not limiting since any bit-stream can be segmented for use as key numbers in 2factor. Using each 4-bits of the stream to represent a hexadecimal number accomplishes this. In the case of a bit-stream leaving any 4-bit segments predictably such as where the most-significant 4-bits are all 0, etc. The 2factor Authentication and Data Security System 2factor.

The following is the 2factor method for its identity-based, message-independent, authenticated key establishment protocol:. There is a central repository 2factor store, or 2store , openly located, in which a set of credentials keys , are stored for each participant. The number of keys is dependent on the implementation of the 2factor system. In the following method description, key credentials are labeled ID where will be the appropriate credential for the implementation as defined below, or an explicit for a particular step.

Any new numbers keys or interim values are created by a secure PRNG. All calculations are simple add without carry modular addition using single digit positions of any input; full results are concatenation of all the single digit results. Setup: Each 2factor participant is securely in receipt of two 2store authentication credential keys, ID1 and ID2, each bits, 64 hex digits currently 4-bit representation.

The mathematic equations of the 2factor protocol are shown in two successive messages : Message 1 Message 2 1. First set a pointer to select each digit of ID2. Then select another digit from a different position in ID2 to add to the pointer value where the ID2 position value is selected by another pointer that is moving through S in the identical manner.

Position selection counting is performed with position zero as the first position to the right of the current position in ID2, position one is the second position to the right, etc. The pointer in S identifies an S value that determines which new offset position from the current position in ID2 to use to select the position-digit value.

Cycle around S and repeat from the start if shorter than ID2. Upon reaching a return length of VK 2 , there are unique ways to update VK and OK and repeat; such as adding without carry some or all of the individual cycle return values for VK and simply using one of them as a new OK. Performing several long return versions of short input PDAF values, added without carry together and XORed with plaintext, does have the property of returning statistically sound random ciphertext.

Using this property, though, can extend the parent session key, creating new child keys as in the next step, without the further creation and overhead of continual salt values in Step 1. This is extremely beneficial for specific implementations where there is a need to limit the production of overhead value exchange such as fast wireless voice encryption, etc.

This step has two different types of plaintext that can be operated on: Option A. Numeric plaintext that is unknown to the receiver repetitive or non-repetitive , and Option B. Any other bit-stream plaintext. There are different steps to be performed for each:. The plaintext must be a number P[i.

Perform the current best-of-breed cipher using session key W:. Send the Message to the Intended Recipient:. All messaging participants are known by an OpenID, such that any recipient will know which starting key ID1 to use for decryption.

Also, for message auditing and tracking purposes, each message should have a unique Message Identification MID , either a random or sequenced tag number, alphanumeric, etc. These, along with the public outputs from the process above, are sent from Sender A to the Recipient B. Decryption by Recipient B, is an identical symmetric process based on the shared knowledge of the starting keys ID1 and ID2 the shared secrets.

Unknown numeric exchanges Step 4A are vulnerable to tampering—no knowledge is leaked, but nuisance interventions and dropped bits during communication can cause problems. Using a Message Authentication Code MAC process so the values received can be shown as those intended by the sender solves this type of problem. Those will need to be used for alphanumeric messages, but it is possible and simpler to use the following ID-MAC process to ensure correct numeric ciphertext delivery.

Changes in any CT or OR will be detected and known:. The following are the recommended current ID s sizes as of the publication date of this paper March :. Note that the combined bits of 2factor ID s key lengths is half the current bit recommended size for PKE keys. The 2factor methodology only requires keys of even-digits; there is no necessity or required sizes or size increases or decreases.

The ID sizes can certainly increase in blocks as small 8-bits 2 digits. The effect performance, storage, etc. In order to limit any 2factor system messaging participant to a single key, as desired by most end-users, it is a simple process to connect distributed 2factor 2stores. This connectivity can be through the entirety of a 2store, through just a limited portion, through key format pass-through, etc.

After 2store owners have established the key-sharing paradigm, then message transfer for A to B, through their respective 2stores, is simply:. The transfer is simple and efficient, only decrypting to the point of revealing the appropriate session key for each transfer, until reaching the final destination where the intended 2factor participant performs the final, bulk decryption of the original ciphertext.

The original, full ciphertext is simply passed through any 2store until arriving at the intended destination—or even sent directly on to the final destination, if possible. This additional security feature requires an opponent to store the entire message chain for cryptanalysis. It also entails the possibility of lost or corrupted messages, which would disrupt the key update chain, leaving two participants with different expected ID start values—and the inability to decrypt.

This can be dealt with in several ways; three mentioned here, with the obvious out-of-band delivery of new keys always an option:. If only two versions of each ID are stored, one should be the original version under a MID of zero or some other system defined base value , and the other should be the last version. When a recipient cannot decrypt a received message, perform the following:.

If multiple versions of each ID are stored, one should be the original version, and the others, the last versions. When a recipient cannot decrypt a received message, perform as in the first recovery above, but identify any of the stored MID values as the MID select to reference that ID. At original distribution, send a third key, ID3. The 2factor method provides embedded authentication using the message key W and the resulting ciphertext.

But there are applications where an authentication token verification check may be desired for speed, etc. Using the interim calculated value IDtemp in a PDAF with W creates a W-length token that can be sent with each 2factor exchange and validated quickly before performing any actual decryption on the accompanying ciphertext. Adding this equation and open result has no impact on the underdetermined equation set security, while adding an easy and fast authentication verifier outside of the embedded ciphertext.

See the black-box approach to 2store protection detailed in Appendix C. This saves the end user time and effort, but places a certain formatting restriction on all messages sent using the original set without any leaked information for a passive or active opponent. The restriction is due to the cyclic updating of the long-term ID keys, and once each location has begun a chain, the 2store must recognize the message as starting a new one; adding another OID-linked stored ID set and MID sequence.

This format notifies the 2store through the format and content of MID 1 or a flag of some kind that it should start by using the OID's original ID1 key and continue from that point, creating a new chain for this location. The only information that can be determined from capturing and analyzing all of the multi-location sends for the same OID-ID original keys is that S 1 is up or down in value in each position from the others.

It does nothing to help actually determine any ID following key or the makeup of the original ID1 key. The knowledge of attempting to store large sequences of data and watching S 1 in relation to ID1-O 1 is of no value. See the Appendix A. This section discusses an authentication and key-exchange system that protects data communications and exchanges keys across an untrusted network.

This system improves security by eliminating the need for computationally expensive and multi-keyed public key systems for authenticating key exchanges and creating secure session keys for data encryption. It also removes the need for multiple transmission symmetric key exchange protocols where the exchange basis is again computationally expensive mathematics or low-entropy passwords. This system accomplishes identical logic basics as existing authentication and key exchange systems, while adding a new fundamental improvement in protection of future messages.

Appendix A provides specific detailed mathematics on the security as well as the binomial probability discussion for future message authentication and protection even with compromised long-term credentials. Appendix B provides a description of the 2factor defeats of both authentication and key-establishment attacks. Appendix C provides descriptions of original key distribution techniques as well as key storage 2store security options. This future protection will be called Future Secrecy FS.

Binary Search. Pages Insertion Sort. Fast Sorting Algorithms. Parallel Sorting - The Need for Speed. Searching Texts - But Fast! The Boyer-Moore-Horspool Algorithm. Cycles in Graphs. The Euclidean Algorithm. Public-Key Cryptography. How to Share a Secret. Playing Poker by Email. Converting Numbers into English Words. Winning Strategies for a Matchstick Game. Scheduling of Tournaments or Sports Leagues. Eulerian Circuits. High-Speed Circles.

Dynamic Programming - Evolutionary Distance. Shortest Paths. Marriage Broker. Joachim Gehweiler, Friedhelm Meyer auf der Heide.

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