Post-quantum key agreement mechanism for preserving confidentiality of digitally transmitted secret and method thereof
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- UNIVERSITI PUTRA MALAYSIA
- Filing Date
- 2025-07-11
- Publication Date
- 2026-08-06
Smart Images
Figure MY2025050045_06082026_PF_FP_ABST
Abstract
Description
[0001] POST-QUANTUM KEY AGREEMENT MECHANISM FOR PRESERVING CONFIDENTIALITY OF DIGITALLY TRANSMITTED SECRET AND METHOD THEREOF
[0002] FIELD OF THE INVENTION
[0003] In this invention, post-quantum cryptography is the focus. This invention specifically pertains to an enhanced post-quantum cryptography system that ensures the security of electronic transmitted agreed secret parameter in transactions between senders and recipients via certified authority over a data transmission system.
[0004] BACKGROUND OF THE INVENTION
[0005] In banking, business, and other important facets of daily life, computers are becoming more and more necessary. It is more crucial than ever to protect your computer from dangerous software. A secure communications network must be established in order to permit data transfers or transactions within a particular Community while guaranteeing that there is no unauthorized or unintentional access from outside the Community.
[0006] Post-quantum cryptography is a type of cryptography technique that is believed to be immune to quantum computer attacks. The most popular non-post-quantum publickey techniques at the moment, which rely on the discrete logarithm problem, the elliptic- curve discrete logarithm problem, and the integer factorization problem, can be successfully broken by Shor's algorithm. Therefore, it is necessary to carefully consider the threat that quantum computing poses to existing non-post-quantum public-key algorithms, develop action plans, and take prompt action.
[0007] Many post-quantum cryptography techniques share the characteristic of requiring bigger key sizes than conventional "pre-quantum" publicly available cryptographic algorithms. It is frequently necessary to make trade-offs between ciphertext or signature, computational efficiency, and key size. Since the development of the quantum computer, cryptographers have, of course, conducted several studies on post-quantum cryptography methods that are impervious to quantum computer attacks. Since postquantum cryptography is a relatively new area, the majority of its algorithms have not undergone enough cryptanalysis to be suitable for usage in production.The requirement of larger keys sizes compared to traditional "pre-quantum" publicly available cryptographic algorithms is a common trait in many post-quantum cryptography techniques. Tradeoffs are often required to size keys, computational efficiency and ciphertext or signature. Naturally, there have been a lot of studies into post-quantum cryptography techniques that are immune to attacks by quantum computers by cryptographers since the invention of quantum computer. Post-quantum cryptography is a very young field, and most of the post-quantum cryptographic algorithms have not undergone sufficient cryptanalysis to be capable of being used during production. The issue with post-quantum cryptography algorithms is that the majority of encryption and digital signature algorithm contenders have the potential for analytically proven decryption or verification failures. Ensuring that the secrecy, integrity, authenticity, and special feature that prevents the sender from repudiating the data are not compromised during transmission or transit is crucial.
[0008] Therefore, improved post-quantum cryptography systems and techniques are required to solve the shortcomings and problems of the existing state of the art while maintaining data confidentiality and integrity. There is still a lot of space for improvement in many real-world applications of post-quantum cryptography, despite the methods and processes of the earlier post-quantum cryptography art.
[0009] SUMMARY OF THE INVENTION
[0010] In order to provide an understanding of the various features of the invention, a summary of the invention is provided below. The invention is not described in detail in this overview. The primary goal of this proposal is to give a summary of some inventive concepts before a more thorough explanation is given.
[0011] Therefore, the current invention provides a post-quantum key agreement mechanism (KA) to ensure the confidentiality of a transmitted agreed secret parameter between a sender and a recipient over a data communication system. The transmitted agreed secret parameter would be used to encrypt an electronic or digital message, M, into its corresponding ciphertext via a symmetric cryptosystem and decrypt the ciphertext back into its corresponding electronic or digital message, M via the corresponding symmetric cryptosystem. The KA process would guarantee the confidentiality of the transmitted agreed secret parameter.The cryptography system of the present invention may be characterized by a cryptographic unit comprising a memory having a key generation module and a cryptographic module, wherein the key generation module is configured for generating private seeds having a minimum length of 128 bits either from a true random number generator or a pseudo random number generator and comprises an algorithm for generating partial agreed secret parameter and the agreed secret parameter which sources from the KAZ-KA Problem, whilst a trapdoor associated thereof are random elements from a public list, a key agreement mechanism which sources from the KAZ-KA Problem, wherein the KA employs a key derivative function (KDF), for deriving secret symmetric encryption keys from a secret value, wherein the cryptographic module is configured for generating a corresponding agreed secret parameter from a partial agreed secret parameter to be transformed by a selected KDF into a symmetric encryption key and also to generate the same corresponding agreed secret parameter from the transmitted partial agreed secret parameter, to be transformed by a selected KDF into a symmetric decryption key, wherein the symmetric cryptographic module utilizing the said symmetric encryption key is configured for encrypting an electronic or digital message, M to be transmitted and decrypting a ciphertext of the electronic or digital message, M utilizing the said symmetric decryption key; and a processor.
[0012] Preferably, the KDF includes the standard hash algorithm-2 (SHA- 2) hash function.
[0013] Preferably, the symmetric cryptosystem includes the standard Advanced Encryption Standard (AES) algorithm.
[0014] Preferably, the cryptographic unit is deployed at the sender, the recipient and a certifying authority (CA) which is in communication with the sender and the recipient in respect of the transaction thereof.
[0015] Preferably, the CA residing on a server is configured to authenticate the transaction thereof by verifying an identifier of the sender that is provided by the recipient.
[0016] Preferably, the CA generates and distributes the system parameters, for each of the recipient through a dedicated telecommunication line.
[0017] Preferably, the sender and the recipient have respective identifiers which are assigned by and stored in a database of the CA.In accordance with another aspect, the present invention provides a method of preserving confidentiality of an electronic or digital message in a transaction over a data communication system between a sender and a recipient.
[0018] The method of the present invention may be characterized by the steps of the KAZ-KA algorithm digitally generating in parallel an agreed secret parameter on both the sender and recipient ends, where the symmetric key which is generated by the KDF upon the agreed secret parameter on both the sender and recipient ends, is utilized by the corresponding symmetric cryptosystem residing in a cryptographic module of a cryptographic unit at the sender’s end to encrypt an electronic or digital message, M which upon execution generates a ciphertext of the electronic or digital message, M, wherein the KAZ-KA algorithm sources from the KAZ-KA Problem and employs a KDF for generating the symmetric encryption key from an agreed secret parameter where the agreed secret parameter is to be generated in agreement; transmitting the ciphertext of an electronic or digital message, M along with an identifier of the sender to the recipient; notifying, by the recipient, receipt of the ciphertext of an electronic or digital message, M and providing the identifier of the sender embedded in an accompanying digital signature to a CA; authenticating, by the CA, the transaction thereof by verifying the identifier of the sender; retrieving, by the recipient, the corresponding symmetric encryption key by deploying the corresponding KDF for generating the symmetric decryption key from the corresponding agreed secret parameter thereof; decrypting the ciphertext using a symmetric cryptosystem residing in a cryptographic module of a cryptographic unit at the recipient’s end with the symmetric decryption key derived by the corresponding KDF upon the agreed secret parameter, wherein the algorithm employs a KDF for generating the symmetric decryption key from the agreed secret parameter.
[0019] Preferably, the KDF includes the standard hash algorithm-2 (SHA- 2) hash function.
[0020] Preferably, the symmetric cryptosystem includes the standard Advanced Encryption Standard (AES) algorithm.
[0021] Reading the in-depth explanation provided herein below with proper reference to the accompanying drawings will help better understand the aforementioned as well as other objects, features, aspects, and benefits of the present invention.BRIEF DESCRIPTION OF THE DRAWINGS
[0022] A more complete appreciation of the invention and many of the attendant advantages thereof will be readily as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:
[0023] Figure 1 is a schematic block diagram depicting a post-quantum cryptographic system according to one embodiment of the present invention;
[0024] Figure 2 is a schematic block diagram depicting the sender, the recipient and the CA in a transaction over a data communication system according to one embodiment of the present invention; and Figure 3 is a flow diagram showing the steps involved in a method for preserving confidentiality of data sent according to one embodiment of the present invention.
[0025] It is noted that the drawings may not be to scale. The drawings are intended to depict only typical aspects of the invention, and therefore should not be considered as limiting the scope of the invention. In the drawings, like numberings represent like elements between the drawings.
[0026] DETAILED DESCRIPTION OF THE INVENTION
[0027] It is an object of the present invention to provide a post-quantum KA and a method thereof for preserving confidentiality of an agreed secret parameter in a transaction over a data communication system between a sender and a recipient that employs an algorithm developed in the present invention entitled KAZ-KA that is post quantum secure and is based on the KAZ-KA Problem.
[0028] In accordance with one preferred embodiment of the present invention, the postquantum cryptographic system comprises a cryptographic unit 100 as shown in Figure 1. The cryptographic unit 100 preferably comprises a memory 200 which comprises a key generation module 201 and a cryptographic module 202 and a processor 300. In a minimum configuration, the cryptographic unit 100 is essentially a computer having the processor 300 and the memory 200 that are connected to each other.
[0029] The cryptographic unit 100 is adapted to generate random private parameters of minimum length equal to at least 128 bits. The algorithm to generatethe key resides in the key generation module 201 in the memory 200. The algorithm carries out a computation based on the KAZ-KA algorithm. It may generate private keys which will next be used to generate partial agreed secret parameter to thus consequently enable the generation of the agreed secret parameter to be utilized with a KDF to produce a symmetric encryption key to encrypt and decrypt the transmitted electronic or digital message, M for secure data transmission applications without compromising the confidentiality of the electronic or digital message, M with the corresponding symmetric cryptosystem. This execution utilizes minimum memory requirements.
[0030] The key generation module 201 comprises of an algorithm that once executed is capable of generating random private seeds with a minimum length equal to 128 bits without compromising the security strength of the key. Depending on the security needed, the length of the private seed generated could be made to be greater than 128 bits.
[0031] The key generation module 201 is configured for generating private seeds having a minimum length of 128 bits and for generating partial agreed secret parameter and agreed secret parameter which sources security from the hardness of solving the KAZ-KA Problem whilst a trapdoor associated thereof are random elements from a public list and requires exponential time to brute force the correct elements from the list. The key generation module 201 preferably employs a true random number generator or a pseudo random number generator.
[0032] The key generation module 201 which implements a trapdoor function in which the private parameters of the modeled system are computationally infeasible to be computed by means of reverse computations based on the public parameters of the modeled system. The sample space for each private key is at minimum of the size 2128
[0033] The cryptographic module 202 may be adapted for generating a partial agreed secret parameter and generating the agreed secret parameter, a KA of which sources security from the hardness of solving the KAZ-KA Problem.
[0034] The cryptographic module 202 is configured to execute the KAZ-KA algorithm. It comprises an algorithm that employs a KDF for generating a symmetric encryption key to be utilized by a corresponding symmetric cryptosystem to encrypt and decryptan electronic or digital message, M. Preferably, the KDF includes the standard hash function algorithm-2 (SHA-2) hash function and the symmetric cryptosystem includes the standard Advanced Encryption Standard (AES).
[0035] In addition to the aforementioned processor 300 and memory 200, the cryptographic unit 100 may also include peripheral hardware such as an electronic data storage device, a network card and other related components as generally known in the art.
[0036] To understand the fundamental operation of the KAZ-KA algorithm of the present invention, the following definitions phrased in mathematical language should be taken into consideration:
[0037] Definition 0
[0038] Let KDF(-) be a key derivative function. Let ℓ(·) be the function that outputs the bit length of a given input. Let DLogg(·) denote a discrete logarithm algorithm solver over ℤN.
[0039] Definition 1
[0040] The public prime number list of j-elements greater than 2 is the list P = {pi}ji=1. This public list will be embedded within the cryptographic unit 100 executing the KAZ-KA algorithm to be distributed among parties intending to execute secure communication with the system of the present invention.
[0041] Definition 2
[0042] The public modular is N = ∏ji=1pi. The public modular will be made known to all parties involved in the secure communication provided by the cryptographic unit 100 executing the KAZ-KA algorithm. Let ℓ(N) be the bit length of N.
[0043] Definition 3
[0044] Choose random primes g, h ∈ ℤNwhere DLogg(h) does not exist in ℤN. The system parameters are (g, h, N). The system parameters will be made known to all parties involved in the secure communication provided by the cryptographic unit 100 executing the KAZ-KA algorithm. Let OghNbe the order of be the order of gh in ℤN. That is, gh(O+1)≡ gh mod N. Let OghN2be the order of be the order of gh-1in ℤN. That is,
[0045]
[0046] = gh-1mod N.Definition 4
[0047] Choose random a, α ∈ ℤφ(N). Compute A1≡ gahαmod N and A2≡ gαhamod N. Compute y1≡ A1A2mod N. Compute y2= DLoggh(y1) modulo N. Compute y3≡ A1A2-1mod N. Compute y4= DLoggh(y3) modulo N. Compute y5≡ y2+ y4mod OghN, y6≡ 2a mod OghN, y7≡ y2+ y4mod OghN2, y8≡ 2a mod OghN2, y9= y5- y6and y10= y7- y8. If y9= 0 or y10= 0 repeat proceed choosing a, α ∈ ℤφ(N), computing A1≡ gahαmod N, A2≡ gαhamod N and evaluating y9and y10. The sender KAZ-KA partial agreed secret parameter is given by the tuple (A1, A2, N).
[0048] Definition 5
[0049] Choose random ephemeral parameters b, β ∈ ℤφ(N). Compute B1≡ gbhβmod N and B2≡ gβhbmod N. Compute y1≡ B1B2mod N. Compute y2= DLoggh(y1) modulo N. Compute y3≡ B1B2-1mod N. Compute y4= DLoggh(y3) modulo N. Compute y5≡ y2+ y4mod OghN, y6≡ 2b mod OghN, y7≡ y2+ y4mod OghN2, y8≡ 2b mod OghN2, y9= y5- y6and y10= y7- y8. If y9= 0 or y10= 0 repeat proceed choosing b, β ∈ ℤφ(N), computing b1≡ gbhβmod N, b2≡ gβhbmod N and evaluating y9and y10. The recipient KAZ-KA partial agreed secret parameter is given by the tuple (B1, B2, N).
[0050] Definition 6
[0051] Upon sender receiving (B1, B2) from recipient, sender computes yA≡ B1aB2αmod N. Upon recipient receiving (A1, A2) from sender, recipient computes yB≡ A1bA2βmod N. Both sender and recipient computes compute skA' = KDF(yA) and skB' = KDF(yB). The parameter skA' = skB', and is to be used to encrypt an electronic or digital message M via a corresponding symmetric cryptosystem and decrypt the accompanying ciphertext of an electronic or digital message M via a corresponding symmetric cryptosystem.
[0052] Definition 7
[0053] The KAZ-KA Problem is defined as the task to obtain parameters (a, α) such that one would have the relations A1≡ gahαmod N and A2≡ gαhamod N.
[0054] Remark 1
[0055] Let OgNbe the order of be the order of g in ℤN. That is, g(O+1)≡ g mod N. The complexity to obtain corresponding a or α is O(2k) where OgN≈ 2k. When deployingGrover’s algorithm on a quantum computer, the complexity to obtain corresponding a or cr is 0 I 22 j.
[0056]
[0057] More particularly, the operation to generate partial agreed secret parameter based on the KAZ-KA algorithm of the present invention is described with reference to aforementioned Definitions 1-5. While the agreed secret parameter generation procedure is described with reference to the aforementioned Definition 6.
[0058] With reference to Figures 2 to 3, the cryptographic system of the present invention employs a CA to authenticate a transaction between the two correspondents, i.e. the sender and the recipient over a data communication system. The CA residing on a server is configured to authenticate the transaction thereof by verifying an identifier of the sender that is provided by the recipient. The CA, the sender and the recipient are preferably interconnected to each other by a communications link (see thick line). More particularly, the communication link interconnects the sender and the recipient, and the communication link interconnects each respective correspondent, i.e. the sender and the recipient to the CA. These communication links may include but not limited to telephone lines or wireless communication links that thus serve to allow the correspondents and the CA to route messages to the intended recipients.
[0059] Each of the correspondents, i.e. the sender and the recipient, and the CA incorporates the cryptographic unit 100 that contains an algorithm that executes the KAZ-KA algorithm for generating a partial agreed secret parameter to be generated into the agreed secret parameter, where the agreed secret parameter would be transformed into a symmetric encryption key sk by a corresponding KDF and generating the agreed secret parameter from the partial agreed secret parameter which would be transformed into a symmetric decryption key sk by a corresponding KDF. In other words, the cryptographic unit 100 is deployed at the sender and the recipient as well as the CA. Each cryptographic unit 100 employed thereof can perform a KDF mechanism according to the industry standard SHA-2 algorithm or any other suitable KDF mechanism. The cryptographic unit 100 is also capable of generating random seeds needed.
[0060] Each correspondent in the provisions of the KA system of the present invention has system parameters and a unique identifier. The system parameters are generated randomly by the CA.
[0061] With reference to Figures 2 to 3, a transaction involving the recipient and the sender that have been authenticated by the CA will now be described by way of following nonlimiting example.Example 1
[0062] This transaction involves both the sender and recipient sending partial agreed secret parameter to each other, the sender sending an encrypted electronic or digital message, M via a corresponding symmetric cryptosystem, where the symmetric cryptosystem utilizes a symmetric encryption key derived from the said agreed secret parameter via a transformation by a KDF, to the recipient.
[0063] The sender has a unique identifier, IDAand partial agreed secret parameters (A1, A2, N). The recipient has partial agreed secret parameters (B1, B2, N) which was generated randomly by sender and recipient.
[0064] The identifier ID is a unique element that the CA uses to distinguish between correspondents in a particular data-communication system. The CA stores the unique identifier corresponding to correspondent A IDAinits database. The unique identifier IDA conveniently remains the same for all correspondence originating from the sender. Whether the unique identifier IDA falls within the validity period, it shall be a distinguisher as to whether a communication process is valid or not.
[0065] To initiate an exchange of an electronic or digital message, M for example, between the sender and the recipient, the electronic or digital message will be encrypted by a corresponding symmetric cryptosystem which utilizes a symmetric encryption key sk. The symmetric encryption key sk is given by sk = KDF(y), where y was transmitted via exchanging partial agreed secret parameters between sender and recipient; (A1, A2, N) and (B1, B2, N), derived using the KAZ-KA algorithm as developed by the present invention. The ciphertext C of the encrypted electronic or digital message M, will be sent together with the sender’s unique identifier, IDA-
[0066] The agreed secret parameter, is a result of an operation upon the partial agreed secret parameters between sender and recipient; (A1, A2, N) and (B1, B2, N). The operation conducted by the cryptographic unit 100 is phrased using the language of mathematics which is in line with Definition 5 as follows:- A1≡ gahαmod N and A2≡ gαhamod N
[0067] B1≡ gbhβmod N and B2≡ gβhbmod N
[0068]
[0069] where a, α, b, β ∈ ℤφ(N)are random ephemeral parameters.Finally, with reference to the sender, the cryptographic unit 100 relays to the recipient the partial agreed secret parameter (A1, A2, N), generated thereof. The recipient transmits to the sender the partial agreed secret parameter (B1, B2,fV). Upon the exchange, both sender and recipient proceed to generate the agreed secret parameter y and the symmetric key sk = KDF(y) via the KDF. Following through, the sender symmetrically encrypts an electronic or digital message M,and relays the ciphertext C together with a unique identifier ID A of the sender to the recipient.
[0070] Upon receipt of the sender’s symmetrically encrypted electronic or digital message M ciphertext C and its unique identifier ID, the recipient notifies the CA that it has received a message from the sender by sending sender’s unique identifier IDA, to the CA. Said communication by the recipient to the CA of the sender’s unique identifier IDA, was communicated via a dedicated communication link. Upon receiving the notification, the CA returns to the recipient information on the validity of sender’s identity. This was done by the CA through locating the validity information of sender’s identity using sender’s unique identifier IDA in its database of subscribers.
[0071] The next step is, since at the onset both sender and recipient have generated an agreed secret parameter y and the symmetric key sk = KDF(y) via the KDF, the decryption process is carried out by the recipient where it involves step of decrypting a symmetrically encrypted electronic or digital message M ciphertext C via a corresponding symmetric cryptosystem which utilizes the symmetric decryption key sk. The generation of the agreed secret parameter process by the sender and recipient is phrased by using the language of mathematics which is in line with Definition 6.
[0072] Upon sender receiving (BI, B2) from recipient and recipient receiving (A1, A2) from sender, both sender and recipient will conduct the following in parallel;
[0073] A) Sender conduct the KAZ-KA procedure by computing yA≡ B1aB2amod N.
[0074] B) Recipient conduct the KAZ-KA procedure by computing yB≡ A1βA2βmod N.
[0075] C) Sender compute skA' = KDF(y ). Parameter skA' is the symmetric key sk to be used to encrypt the accompanying ciphertext of an electronic or digital message M via a corresponding symmetric cryptosystem.
[0076] D) Sender compute skB' = KDF(yB). Parameter skB' is the symmetric key sk to be used to decrypt the accompanying ciphertext of an electronic or digital message M via a corresponding symmetric cryptosystem.It is apparent that the utilization of the agreed secret parameter computational process by both the sender and recipient in accordance with the above equations will be able to decrypt the accompanying ciphertext of an electronic or digital message M via a corresponding symmetric cryptosystem with probability equal to 1. This is because, by the design of the KAZ-KA algorithm of the present invention, the agreed secret parameter generation procedure will not fail. That is, the probability of agreed secret parameter generation procedure failure is 0.
[0077] Henceforth with the implementation of the scheme mentioned above, both the sender and recipient can conclude has generated the agreed secret parameter y correctly, both the sender and recipient has generated sk = KDF(y) correctly, the recipient has decrypted the ciphertext C to obtain the electronic or digital message M correctly via a corresponding symmetric cryptosystem which utilizes the symmetric decryption key sk correctly.
[0078] The implementation of the KA as described in the preceding paragraphs of the description demonstrates and ensures that a minimal interaction between the individual correspondents, i.e., the sender and the recipient and the CA, hence reducing web traffic. The CA only needs to have a database of all the correspondent’s unique identifiers. The CA only produces the information of the validity of the identifier of the sender when being requested by an enquiring correspondent that furnishes the CA with the unique identifier of a correspondent that sends a message to said enquiring correspondent.
[0079] Example 2
[0080] The steps involved in the method of the present invention in which a simple transaction of partial agreed secret parameter and a symmetrically encrypted electronic or digital message M via a corresponding symmetric cryptosystem by a sender to a recipient will now be described in a more concise manner, with reference to Figure 3.
[0081] In step 400, sender generates partial agreed secret parameter (A1, A2, N) using KAZ-KA algorithm and transmits to recipient, in parallel the recipient generates partial agreed secret parameter (B1, B2, N) using KAZ-KA algorithm and transmits to sender. Following suit, in parallel, both recipient and sender generates agreed secret parameter y using KAZ-KA algorithm, which results in both recipient and sender generating identical symmetric encryption key sk = KDF(y). An electronic or digital message M was then encrypted via a corresponding symmetric cryptosystem which utilizes the symmetricencryption key sk = KDF(y). Following that, in step 401, the sender transmits the ciphertext C of the encrypted electronic or digital message M to the recipient. The data transmitted also comprises the sender’s unique identifier ID A.
[0082] In the next step, i.e. step 402, the recipient contacted the CA for notifying the receipt of the encrypted electronic or digital message M ciphertext C from the sender while providing the sender’s unique identifier IDA- Subsequently, i.e. step 403, involves the CA verifying the sender’s validity by means of the sender’s unique identifier IDA-
[0083] In step 403, the CA decides as to whether to reject or to accept the unique identifier ID A- If the identifier from sender is still valid, i.e. the CA has a copy of the same identifier in its database and the IDA is still within the validity period, the CA will accept the identifier as an identifier originating from the sender that still has an identifier within the validity period and will subsequently proceed to send to the recipient an acknowledgement to proceed decrypting the encrypted electronic or digital message M ciphertext C.
[0084] If, on the other hand, the unique identifier IDA sent by the recipient to the CA is identified either to be not located in the CA’s database or no longer within the validity period, then that identifier does not belong to the sender, hence not a valid identifier from a valid correspondent and consequently the encrypted electronic or digital message M ciphertext C sent to the recipient can be disregarded. As a result, the CA will reject the identifier.
[0085] In the final step of 404, the recipient will proceed to decrypt the electronic or digital message M from the ciphertext C, via a corresponding symmetric cryptosystem which utilizes the symmetric decryption key sk = KDF(y).
[0086] The terms “a” and “an,” as used herein, are defined as one or more than one. The term “plurality,” as used herein, is defined as two or more than two. The term “another,” as used herein, is defined as at least a second or more. The terms “including” and / or “having,” as used herein, are defined as comprising (i.e., open language).
[0087] While this invention has been particularly shown and described with reference to the exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims
CLAIMS1. A post-quantum cryptographic system for preserving confidentiality of an agreed secret parameter in a transaction over a data communication system, characterized in that, the post-quantum cryptographic system comprising:a cryptographic unit (100) a memory (200) having a key generation module (201) and a cryptographic module (202);wherein the cryptographic unit (100) are deployed at a sender, a recipient and a CA residing on a server in respect of the transaction thereof;wherein the CA residing on the server is configured to authenticate the transaction thereof by verifying an identifier of the sender that is provided by the recipient;wherein the key generation module (201) is configured for generating private seeds having a minimum length of 128 bits either from a true random number generator or a pseudo random number generator and comprises an algorithm for generating partial agreed secret parameter and the agreed secret parameter which sources from the KAZ-KA Problem, whilst a trapdoor associated thereof is a random choice of elements from a public list;wherein the cryptographic module (202) is configured for generating a partial agreed secret parameter and the agreed secret parameter y which sources from the KAZ-KA Problem, where sk = KDF(y) is used to symmetrically encrypt an electronic or digital message M via a corresponding symmetric cryptosystem; wherein the symmetric cryptosystem employs a KDF to generate the sk value from the agreed secret parameter y, and a processor (300).
2. The post-quantum cryptographic system according to Claim 1, wherein the KDF includes the standard hash algorithm-2, SHA-2 hash function or any other suitable KDF.
3. The post-quantum cryptographic system according to Claim 1, wherein the symmetric cryptosystem includes the standard Advance Encryption Standard (AES) or any other suitable symmetric cryptosystem.
4. The post-quantum cryptographic system according to Claim 1, wherein the CA generates and distributes system parameters for each of the recipient and sender through a dedicated telecommunication line.
5. The post-quantum cryptographic system according to Claim 1, wherein the sender and the recipient have respective identifiers which are assigned by and stored in a database of the CA.
6. The post-quantum cryptographic system according to Claim 1, wherein the cryptographic unit (100) can generate the agreed secret parameter y from the exchanged partial agreed secret parameter, compute sk = KDF(y) and then decrypting asymmetrically encrypted electronic or digital message M ciphertext C via a corresponding symmetric cryptosystem which utilizes the symmetric decryption key sk.
7. The post-quantum cryptographic system according to Claim 1, wherein the sender and recipient random ephemeral parameters are unknown to any unauthorized party.
8. The post-quantum cryptographic system according to Claim 1, wherein the trapdoor are the sender and recipient random ephemeral parameters from a public list.
9. A method of preserving confidentiality by a sender of an electronic or digital message M in a transaction over a data communication system between a sender and a recipient, characterized in that, the method comprising the steps of:generating partial agreed secret parameter and the agreed secret parameter y, symmetrically encrypting an electronic or digital message M into the ciphertext C, via a corresponding symmetric cryptosystem which utilizes the symmetric key sk = KDF(y) using an algorithm residing in a cryptographic module of a cryptographic unit at the sender’s end (400), wherein the algorithm is executed by KAZ-KA key agreement mechanism that sources from the KAZ-KA Problem and employs a KDF for generating sk = KDF(y) from the agreed secret parameter y and; transmitting the ciphertext C of the encrypted electronic or digital message M along with an identifier of the sender to the recipient (401);notifying, by the recipient, receipt of the ciphertext C of the accompanying encrypted electronic or digital message M and providing the identifier of the sender embedded in the digital signature to a CA (402);authenticating, by the CA, the transaction thereof by verifying the identifier of the sender (403);computing sk = KDF(y) from the agreed secret parameter y and then decrypting a symmetrically encrypted electronic or digital message M via a corresponding symmetric cryptosystem which utilizes the symmetric decryption key sk using an algorithm residing in a cryptographic module of a cryptographic unit at the recipient’s end (404), wherein the algorithm utilizes a KDF upon the agreed secret parameter y.
10. The method according to Claim 9,wherein the step of authenticating (403) includes comparing the identifier of the sender and validity information against that of stored in a database of the CA;wherein the KDF includes the standard hash algorithm-2, SHA-2 hash function, or any other suitable KDF; andwherein the symmetric cryptosystem includes the standard Advanced Encryption Standard (AES), or any other suitable symmetric cryptosystem.