CA2638134A1 - Multi-dimensional cryptography - Google Patents

Description

The proposed new encryption technology can be directly applied to variety of applications such as:

= Highly secure communications between two or multiple remote locations. This kind of communications include governments, military, defenses, etc. For these communications, the pre-shared key(s) have been provided when the secret relationship is first established. Due to lack of secure key distribution technology, periodically refreshing key reduces the security of communications. They require a new technology which can theoretically prove that it is perfect during the course of long time communications.
= Financial institutes. They need absolutely secure communications between their branches, offices for financial transactions, daily updates, etc. In this kind of communications, they usually follow a client-server model. Their server and client machines usually have pre-shared keys. The proposed technology can directly apply to them. There are only a very minor changes to the existing applications.
For senders, the application will call "encryption" API with key(s) and data and then send the encrypted cipher text. At the remote side, the application needs to call "decryption" API and data will be decrypted without security risk.
= This proposed technology can be provided to all virtual private networks (VPN).
Most VPN network use device authentication with tunneling between peers. The pre-shared key between peers is natural. This disclosure can provide perfect security between two remote VPN communications.
= With proposed ID-based key agreement, the shared key between communication parties can be automatically established by providing a public "salt" plus shared secret such as password, secret question-n-answer:
o Secure email service: this is a client-server communication. Client user usually has a user name and a password.
^ Username can be used to identify the user and password can be used to generated shared secret key ^ When a user tries to login to the secure email server, the server can send a run-time generated "salt" - any run-time string, to the client ^ The client enters his/her username/login ID and password. The username may not need to encrypt. The password will be used to generate a shared secret key. This key will be used to encrypt email contents and send to the email server.
^ The email server will use the username/login ID to identify the user and then find the password. The email server will use the "salt" and the password to generate the shared secret key to decrypt the email content.
^ For view email, the procedure will be the same. The email server uses the generated secret key to encrypt all emails for the user.
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And the user will use the same shared key to decrypt all emails and view them.
o Online banking service: this is a client-server model too. An account holder and his/her bank share account ID, personal info, and user password:
^ When a user open the personal banking website, the bank server picks up "salt" and send to the user. The salt should be associated with a session.
^ The user gets the "salt". After the user enters his ID and password, the password and "salt" will be used to generate the shared key to encrypt all data sent to the server.
^ The server will use the "ID" to identify the user and then look for the password. If the password is found with the ID. The server will use the password and the "salt" to generate the shared key. The key can be used to decrypt data received.
o Secure wireless communication:
o Wireless sensor network: this invention can be a perfect candidate for wireless sensor network. For this kind of wireless network, the communication need highly secure level and also less processing power.
This invention meets all requirements for wireless sensor network.

What is the marketable advantage that your invention has over the existing systems (i.e. why would someone buy your product rather than another)?

A: Theoretically proven perfect secrecy. Except for one-time-pad (OTP), existing security technologies are not proven to be perfectly secure. They are all built based on computing difficulties. For example, AES (advanced encryption standard) is built for the reason that an established shared key (usually through D-H protocol) can be reused for a period (key refresh period).

The advantages of AES are:
= It is fast = The key length can be extended from 128 bits to 256 bits or 512 bits to increase security level.
= Key can be reused The disadvantages of AES are:

= It is a non-linear method which leads the worst case that brute force attack can break the AES encryption.
= It needs periodical key refreshing to reduce the risk. In return, the key exchanging itself is not perfectly secure.
= The large S-box table (4096 bytes) makes the possibility for cache-timing attack which is faster than brute force attack.
= It needs more than 10 rounds for encryption/decryption = The performance for decryption is worse than that for encryption.
The proposed solution keeps all AES's advantages:

= It is a first time theoretically proven to be perfect secure technology by using the so-called multi-dimensional key.
o ID-based key agreement with the uniquely equally likely key generation o M-K-C: 1 - N - 1 mapping -* key re-usable = It is faster than AES. In general, the proposed idea just needs CPU
equivalent to 3-4 rounds in AES: in 2-dimensional key, o it needs just one addition and one XOR operations for encryption.
o In the receiving side, it just needs one subtraction and one XOR
operations.
o Roughly one operation here equals one round in AES.
o It also overcomes the slow decryption in AES. In the proposed solution, encryption and decryption have the same speed.
= The key length is scalable. Because it is theoretical perfect, it does not need to increase key length to raise security level. Even 64-bit key is good enough.
= The key can be reused as long as you want. Key re-sharing can be easily achieved through our ID-based key agreement. There is no need to exchange keys during communications.
= No worry on the security of communications, regardless what the network infrastructures between communication peers.
= All disadvantages in the existing secure technologies disappear.

In general terms, how does the invention provide this marketable advantage?
A:

1. Use the same shared secret info as the existing secure technologies, the proposed invention can provide unbreakable, perfect secure communications 2. Even more, the proposed invention can provide even faster than the existing fastest encryption/decryption technologies.

3. Mathematically proven 100% secure. No more worry about insecure communications.

What technical features are required, as a minimum, to implement the invention that gives this marketable advantage?

A: No specific requirements are needed. There is no any difficulty to implement the invention in any existing operation system by hardware or by software.

2. Put another way:

What is the problem the invention is trying to solve?

A: the existing well-known security problem is: No perfect security for practical uses. The only theoretically perfect secure encryption algorithm is OTP.
However, the drawbacks of OTP:

= True random generated key and the key length must be the same as the length of message = There is no authentication:
o Identity authentication o Message authentication, also called message integrity check, or message access code (MAC).
= There is no technology available for perfect secure key distribution. Even quantum key distribution (QKD) cannot provide perfect key distribution without using classical authentication method.

Thus, the OTP is not practical. That is the reason why it is not widely used.

To be clear that people desperately look for a practically usable method for perfectness of security. The proposed disclosure is to solve this problem from both theoretical and practical aspects.

How does the invention solve this problem?

A: here is how the invention solves the problem:

= Identify the origin of the problem: it is due to the fact that we treat key (better to call classical key) to be a one dimensional bit string (can be considered as an integer):
o The max entropy H(K) of n bits key, based on Shannon, is n bits, which is obtained from a truly random number generation o The max entropy H(M) of an n bit message is also n bits.
o H(K) > H(M) gives the lower limit for perfect secrecy.
o Perfect secrecy from Shannon have two conditions:
^ True random key ^ Message-key-cipher text (M-K-C) is 1-1-1 mapping. This leads to the result that it can be easily broken by known plaintext attack.
= In order to raise key entropy dramatically, we need to redefine key terminology. In the proposed disclosure, a key can be defined as a multi-dimensional key operator with n-bit in length:
o Key operator is defined as a bit string (also an integer) with an operation associated. For example, k+ is a key operator which operates on a message by adding them together. Kx is a key operator which operates on a message by XORing them.
o Multi-dimensional key operator is defined as a concatenation of non-exchangeable key operators.
o Each dimensional n-bit string is independently selected: entropy for each dimension is n bits o m dimensional key operator can have entropy H(K) = m n, m? 2, which is at least double the entropy of one dimensional true random key.
o Each dimension of the key operator can be expressed by a variable ki, i= 1, ..., m.
o Total possible keys are: ( 2n)m o Each m-dimensional key will uniquely transform all messages from the n-bit message space into all possible cipher texts in the n-bit cipher text space.
o For a given message M, m-dimensional key space will automatically group into n groups with (m-1)n keys in each group:
^ Each key group will transform the message into a different cipher text in the cipher text space ^ So the M-K-C mapping 4 1-(m-1) N - 1 mapping. For a special case of 2 dimensional key space, the M-K-C
mapping is 1-N-1, where N = 2n.
^ So the known-plaintext-attack does not work in this algorithm o In order to make the m-dimensional key space is irreducible, reduced to a lower dimensional key space, two neighbor operations between key variable should not be exchangeable (i.e.
order of operations is important). For example, M represents n bits message integer ^ ki +(k2 XOR M) #( ki + k2 )XOR M, ^ but ki XOR (k2 XOR M) = (ki XOR k2) XOR M= ka XOR M, 4 reduce to 1-dimensional ^ andki +(k2+M)=(k,+k2)+M=k3+M4 reduce to 1-dimensional o for a long and biased message, the strong internai logics between message blocks may potentially leak key operator information by applying a brute force attack. To solve this problem, this invention proposes:
^ Introduce a pseudo random generated block, initial vector (IV):
= IV is used to actively avoid "choosing plaintext attack".
= IV also takes an important role on message integrity check ^ Add a block for message integrity check, also called message access code (MAC), after the last message block = Take shared secret with block size - 2 bytes = The last 2 bytes are used to carry message length = Using message block chaining to remove the logic between blocks.
= starting from IV
= At the i-th block, the (i-1)-th chained message block is combined with the i-th block to be chained by using a different operation as in the key operator applied to the block:
o If k+x operator is used for the i-th block, the chaining operation at the i-th chaining block will be "+", then the encryption will be like : ki +
k2 XOR mi' = ki + k2 XOR (mw' + mi), and mo = IV

o If kX+ operator is used, the chaining operation at the i-th chaining block will be "XOR", then the encryption will be like : ki XOR k2 + mi' = ki XOR k2 +(mi-,' XOR mi), and mo = IV
^ Run-time selection of encryption key operator:
= For a given pair of keys (ki, k2), in a 2-dimensional key operator system, we at least have 4 different key operators:
o Ko+X = ki + k2 XOR
o Ki+x = k2 + ki XOR
o K2X+ = ki XOR k2 +
o KsX+ = k2 XOR ki +
= By using shared secret between communication peers such as password, a key generated from an ID-based key generation with RC4 key scheduling algorithm to produce a state table called ctrTable[256]. For the example here, at block i, the selected key operator should be at an index keylndex = ctrTable[i mod 2561 mod 4. If keylndex = 0, the selected key operator will be Ko+X and keylndex = 2, then selected key operator should be K.
= For IV encryption, the key operator is always determined by ctrTable[0]. All other blocks can be optionally combined IV with block index to select ctrTable element. For example, keylndex = ctrlTable[
(IV + i) mod 256] mod 4. In such a way, the adversary must try all operators for each block for a given selected key pair (ki, k2). This leads an exponential complexity for each try in the brute force attack.
= By increasing potential key operators, the complexity of each step in a brute force attack is exponentially increased. For each step in the brute force attack is equivalent to a new brute force.
^ introducing a control table to control selection of encryption key operator for each message block:
= Using shared secret, such as password, secret answer, or a generated key from an ID-based key agreement, etc, but not ki or k2, on both sides of communication peers, = Using a key scheduling algorithm such as RC4 to generate a 256 bytes state table called ctrTable[256]. The size of the table can be any size in practical but both sides must agree on it.
= For the example here, at block i, the selected key operator should be at a key index keylndex =
ctrTableji mod 2561 mod 4. If keyindex = 0, the selected key operator will be Ko+x and keylndex = 2, then selected key operator should be K211+
= For IV encryption, the key operator is always determined by ctrTable[Olmod 4.
= All other blocks can be optionally combined IV with block index to select ctrTable element. For example, keylndex = ctrlTable[ (IV + i) mod 2561 mod 4. In such a way, the adversary must try all operators for each block for a given selected key pair (ki, k2) and a given key operator right before the message block.
This leads an exponential complexity for each try in the brute force attack.
= Due to the control table is independent from the message, the cipher text, or the keys, it is impossible to determine which key operator is used for a specific message block. In order to apply brute force attack on the long and biased message encryption, the adversary must successfully guess the shared secret for her to generate right ctrTable. Otherwise, the attacker must apply brute force (exhaust all key pair (ki, k2)), and for each key pair, all possible key operators (for the example here 4 operators) for each block:
o IV: 4 o Block 1: 42, o Block 2: 43 o Block 50: 451 0 ....

So each "try" is equivalent to a new brute force.
^ This run-time determining encryption key operator method can generally apply to any dimensional key operator space, D

even for 1-dimensional space where one need to use at least 2 keys at the same time.

What is required to implement this solution?

A: it is very straightforward to implement this solution:

= it can be easily implemented by pure software. The key bit length is scalable.
= It can also be implemented by hardware 3. Are there any existing solutions, or attempts to address the problem noted in item 2 (only one paragraph required for each existing method)?

A: AES is most common used standard today. It tries to solve key reuse problem in two ways:
= Enlarge key length: 128 bits, 192 bits and 256 bits. Longer is harder.
= Multiple rounds:
0 128 bits key: 10 rounds 0 192 bits key: 12 rounds 0 256 bits key: 14 rounds The round key is non-linearly set up based on shared secret key. By using multiple rounds, the complexity is introduced to the solution. However, it still can't avoid the worst case attack, brute force attack. There are other found attacks existing: cache-timing attack, etc.

Basically, there is no solution found which can solve both perfect security and key long time reusable.

What problems do these solutions leave that the invention corrects?

A: all existing solutions just make it harder to break (then a key can be used for longer time), however, the invention cannot be broken.

The proposed disclosure invents a new algorithm which can't be broken even if a key is continuously used.

4. Any additional options?

A: the left options can be:

= Different multi-dimensional key construction: I always use 2-dimensional key in my examples to make the idea much easier to understand. Any number of dimensions may be used.
= Initial key establishment:
o I propose a new ID-based key agreement here. Someone can use this or its variety.
o Someone can propose a different initial key agreement. Any shared secret or key sharing agreement could be used.

5. In detail, how will the invention be implemented in your current application?
A:

Ctrtable: RC4 KSA - input seceret[], sLen (length of secret) for i from 0 to 255 S[i] .= i endfor j .= 0 for i from 0 to 255 j := (j + S[i] + secret[i mod slen) mod 256 swap(S[i],S[j]) endfor Encryption: example for a 2-dimensional key operator INPUT := kl, k2, msg[], buf[], len //generated a pseudo random IV
iv := pseudRand(;

for i from 0 to blocks switch (S[i] % 4) case 0: C = kl +(k2 A (iv += m)); break;
case 1: C = k2 +(kl A (iv += m)); break;
case 2: C = kl A (k2 +(iv A=m)); break;
case 3: C = k2 A (kl +(iv A= m)); break;
//put the cipher text C into buf /D

endfor Decryption: just a reverse procedure of the encryption.

6. If you are aware of problems others might expect in implementing the invention in their environments, describe ways of overcoming these problems will support broader claims.

A: the software itself is very straightforward. There is no any problem to implement it in any environment.

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Conclusions The present invention has been described with regard to one or more embodiments.
However, it will be apparent to persons skilled in the art that a number of variations and modifications can be made without departing from the scope of the invention as defined in the claims.

The method steps of the invention may be embodied in sets of executable machine code stored in a variety of formats such as object code or source code. Such code may be described generically as programming code, software, or a computer program for simplification. Clearly, the executable machine code or portions of the code may be integrated with the code of other programs, implemented as subroutines, plug-ins, add-ons, software agents, by external program calls, in firmware or by other techniques as known in the art.

The embodiments of the invention may be executed by a computer processor or similar device programmed in the manner of method steps, or may be executed by an electronic system which is provided with means for executing these steps.
Similarly, an electronic memory medium such computer diskettes, hard drives, thumb drives, CD-Roms, Random Access Memory (RAM), Read Only Memory (ROM) or similar computer software storage media known in the art, may be programmed to execute such method steps. As well, electronic signals representing these method steps may also be transmitted via a communication network.

All citations are hereby incorporated by reference.

5q

Claims (18)

1. A method of encryption comprising the steps of:
producing a set of encryption keys;

generating an expanded set of encryption keys using a set of equations where order of operations must be maintained; and encrypting data using said expanded set of encryption keys.

2. The method of claim 1, wherein said data set is a message.

3. The method of claim 2, further comprising the step of dividing said message up into n-bit blocks.

4. The method of any one of claims 1 to 3, wherein said set of equations comprises addition and XOR operations.

5. The method of any one of claims 1 to 4, wherein said step of encrypting comprises the step of encrypting multiple sets of data, each of said sets being encrypted with a separate one of said expanded set of encryption keys.

6. A method of encryption comprising the steps of:
beginning with N messages;

encrypting said N messages in an N2 key space; and producing N ciphers.

7. A method of encryption comprising the steps of:

producing an encryption key, said encryption key having a longer bit-length than a data set to be encrypted by said key;

encrypting said data set using said key.

8. The method of claim 6, further comprising the step of communicating said encryption key to two or more software entities, one of said software entities using said encryption key to encrypt said data set, and the second of said software entities using said encryption key to decrypt said data set.

9. The method of claim 6, wherein said data set is a message.

10. The method of any one of claims 1 to 9, wherein said method is applied to financial services, email, Internet communications, online banking, wireless communications, wireless sensor networks, government communications, corporate communications, military, defense applications, and similar applications.

11. An encryption system comprising:
.cndot. a computing device including a visual display, a user interface, read-only memory and random-access memory;
.cndot. a plurality of servers; and .cndot. a network for interconnecting said computing device with said plurality of servers;
.cndot. said plurality of servers being operable to:
.circle. produce a set of encryption keys;
.circle. generate an expanded set of encryption keys using a set of equations where order of operations must be maintained;
.circle. encrypt data using said expanded set of encryption; and .circle. transmit said encrypted data to said computing device.

12. An encryption system comprising:
.cndot. first and second computing devices including a visual display, a user interface, read-only memory and random-access memory; and .cndot. a communication network for interconnecting said first and second computing devices;
.cndot. one of said first and second computing devices being operable to:

~ produce a set of encryption keys;
~ generate an expanded set of encryption keys using a set of equations where order of operations must be maintained;
~ encrypt data using said expanded set of encryption; and ~ transmit said encrypted data to the second one of said first and second computing devices.

13. A computer readable memory having recorded thereon statements and instructions for execution by a computer to carry out the method of any one of claims 1 to 10.

14. A computer program product, comprising: a memory having computer readable code embodied therein, for execution by a CPU, for performing encryption, said code comprising:

means for producing a set of encryption keys;

means for generating an expanded set of encryption keys using a set of equations where order of operations must be maintained; and means for encrypting data using said expanded set of encryption keys.

15. A computer program product, comprising: a memory having computer readable code embodied therein, for execution by a CPU, for performing encryption, said code comprising:

means for beginning with N messages;

means for encrypting said N messages in an N2 key space; and means for producing N ciphers.

16. A computer program product, comprising: a memory having computer readable code embodied therein, for execution by a CPU, for performing encryption, said code comprising:

means for producing an encryption key, said encryption key having a longer bit-length than a data set to be encrypted by said key;

means for encrypting said data set using said key.

17. A carrier wave embodying a computer data signal representing sequences of statements and instructions which, when executed by a processor cause the processor to perform the method steps of any one of claims 1 to 10.

18. A memory for storing data for access by an application program being executed on a data processing system, comprising: a data structure stored in said memory, said data structure including information resident in a database used by said application program and including a set of encryption keys.