26 results about "Discrete logarithm" patented technology

The invention provides a geographic information data dynamic encryption method and system based on spatial-temporal characteristics. The method comprises the following steps: dynamically identifying a hot spot region by analyzing a timestamp, geographic coordinates and frequency data of a user access request, and generating a multi-dimensional access weight matrix fusing a time attenuation factor and a spatial distance factor; and dividing data block granularity according to the access popularity value in the matrix, and performing spatial segmentation on the geographic information data. A dynamic key seed is generated in combination with a space-time factor, a temporary encryption key is obtained through discrete logarithm operation, homomorphic encryption is implemented, and a space-time feature identifier is embedded. And during cross-mechanism aggregation, the authority is verified through the identifier, ciphertext superposition is completed, and secure data aggregation is realized. According to the method, through spatio-temporal dynamic encryption and authority verification, secure sharing and efficient aggregation of multi-mechanism geographic information data are realized.

The application discloses a ciphertext decryption method and related equipment applied to ciphertext encrypted according to an RSA algorithm, and the method comprises the following steps: acquiring a large number in ciphertext and a public key of the ciphertext; selecting a number smaller than the large number as a base of a discrete logarithm problem, selecting 1 as a modulus power operation result corresponding to the base, and converting the base and the modulus power operation result into an initial quantum state; inputting the initial quantum state into a quantum computing module for solving the discrete logarithm problem to obtain a first target quantum state in which a solution result of the discrete logarithm problem is stored; extracting the solution result from the first target quantum state, and calculating a private key of the ciphertext based on the solution result; and decrypting the ciphertext based on the private key to obtain plaintext of the ciphertext. Through the technical scheme, the private key can be recovered according to the disclosed information in the case that the private key is not disclosed, and then the ciphertext is decrypted, so that the related technical blank is filled.

A method of proving that a secret committed in a commitment is a discrete logarithm of a public element of a finite group of data elements, comprising: obtaining a first vector used to generate the commitment, the first vector comprising n components, wherein one of the n components of the first vector is at a position which corresponds to the secret; generating a second vector comprising n components, wherein a component of the second vector, at a predetermined position corresponding to the position in the first vector, is set to zero; generating a further commitment to the second vector; transmitting the further commitment to a verifying device; receiving a random challenge from the verifying device; generating a response using the first vector, the second vector and the random challenge; and transmitting the response to the verifying device to prove that the secret is the discrete logarithm of the public element.

The invention discloses a non-interactive zero-knowledge certification implementation method for a universal mixed relationship. The method comprises the following steps: integrating the requirements of an actual application scene into a certification framework; public parameters are initialized through zero-knowledge proof; generating a non-interactive zero-knowledge proof for the general mixed relationship; non-interactive zero-knowledge proof for the generic hybrid relationship is validated. According to the method, perfect completeness, reliability based on a discrete logarithm difficulty problem and zero knowledge based on a lattice difficulty problem can be realized when a value which is committed to be hidden by Pedersen and a plaintext value encrypted by RLWE are in any linear relation.

The invention discloses an anti-malicious opponent confidential two-party character string sorting scheme which can resist active attacks of participants. According to the method, firstly, an ElGamal homomorphic encryption algorithm and ciphertext re-randomization are applied to construct a confidential two-party character string sorting scheme under a semi-honesty model, the character string sorting problem between two participants can be solved, and the method is of great significance to industry information application such as database query operation and DNA comparison. According to analysis of malicious behaviors possibly suffered by the scheme in the execution process, a discrete logarithm zero-knowledge proof method is used to enable participants to discover or prevent the malicious behaviors and to force malicious participants to execute the scheme under a semi-honest model, so that a confidential two-party character string sorting scheme under a malicious model is designed. The method not only can solve the problem of sorting the character strings of the two participants, but also can resist hostile attacks of the participants, and plays an important role in a secure multi-party computing scene of a real application scene.

This invention relates to the field of privacy computing and discloses a collaborative analysis method for potential financial risks based on fuzzy privacy set intersection. The method first protects the privacy of deposit and loan data from various financial institutions through Paillier homomorphic encryption. Then, it utilizes a fuzzy privacy set intersection algorithm based on Unintentional Key-Value Storage (OKVS) and the discrete logarithm problem to achieve fuzzy matching of user identities across multiple institutions. While ensuring the privacy of user feature data, it identifies records of the same user that meet a predetermined distance threshold. Finally, it aggregates the encrypted deposit and loan data of the matched records and compares them with the threshold. A trusted third party decrypts the data and completes the judgment of potential financial risks, thus realizing financial privacy and security risk analysis under cross-institutional data collaboration.

The present application provides a method and system for dynamic encryption of geographic information data based on spatiotemporal characteristics. The method includes: dynamically identifying hotspot areas by analyzing the timestamps, geographic coordinates and frequency data of user access requests, and generating a multi-dimensional access weight matrix that integrates time attenuation factors and spatial distance factors. Divide the data block granularity according to the access heat value in the matrix, and perform spatial segmentation on the geographic information data. Generate a dynamic key seed in combination with the spatiotemporal factor, obtain a temporary encryption key through discrete logarithm operation, implement homomorphic encryption and embed the spatiotemporal feature identifier. When aggregating across institutions, verify permissions through identifiers and complete ciphertext superposition to achieve secure data aggregation. This method achieves secure sharing and efficient aggregation of geographic information data from multiple institutions through spatiotemporal dynamic encryption and permission verification.

The application discloses a ciphertext decryption method and related devices, the method obtains the public key and plaintext parameters corresponding to the ciphertext based on discrete logarithm encryption, the public key and plaintext parameters belong to the elements in the finite field GF(p, k); then the order of the public key in GF(p, k) is determined based on the public key and LUP matrix decomposition; and the ciphertext is decrypted based on the order of the public key in GF(p, k) and the plaintext parameters; the ciphertext based on discrete logarithm encryption is decrypted.

The invention provides a data processing method and an encrypted data query method. The data processing method comprises the following steps: generating a matrix M with a master key; randomly selecting a positive integer sum as an encryption key to encrypt target data to obtain a sum which is an order of an elliptic curve and is respectively a base point of an elliptic curve pair; and uploading the encrypted data to a database, and storing an encryption key sum. The encrypted data query method comprises the following steps: constructing a vector g and randomly selecting a positive integer; calculating a query vector or sending a query request to a database based on the query vector; and receiving a query result of the database or calculating a discrete logarithm f related to the query result by the user side or the database side. According to the method, the encrypted data supports flexible operations such as statistical analysis on the encrypted data, and a basis is provided for realizing a query function for non-data owners.

The invention provides a homology-based signature method and device, equipment and a medium, which can be applied to the technical field of computers. The method comprises: for a private key to be processed, solving a discrete logarithm associated with a first winding point to obtain first homologous data, the first homologous data representing mapping from an initial elliptic curve to a middle elliptic curve; embedding projection processing is carried out on the two-dimensional Abel inter-cluster homologous data to obtain private key homologous data so as to determine a private key, and the private key homologous data represents mapping from an initial elliptic curve to a public key elliptic curve; solving a discrete logarithm of a flexural group of a first smooth number associated with the public key elliptic curve to obtain third homologous data and fourth homologous data; and according to auxiliary homologous data generated by the third homologous data and the fourth homologous data, signing the private key to obtain a target private key, and sending the target private key to the target terminal to perform information encryption operation on the target information.

A method of providing proof that a statement is true keeping a secret input to the statement a secret, comprising: generating a proof using a public input, the secret input, and a proving key linked to an augmented verification circuit which comprises (i) a verification circuit arranged to receive the inputs, supply the secret input to a function circuit representing the statement to generate a function circuit output, and determine whether the public input corresponds to the function circuit output; and (ii) a multiplicative gate arranged to receive the secret input and a dummy value. The proof comprises a commitment to inputs of multiplicative gates of the augmented verification circuit, the commitment generated using a first vector comprising n components from a finite group of data elements. The secret input is a discrete logarithm of a public element of said finite group. The proof is transmitted to a verifying device.

The application discloses a ciphertext decryption method based on quantum calculation and related devices, and the application converts the obtained public key and plaintext parameters corresponding to the ciphertext into a square matrix, the ciphertext is a ciphertext based on discrete logarithm encryption, and the public key and the plaintext parameters both belong to elements in a finite field GF(2 t ); then, a target quantum circuit is constructed and run based on the square matrix, a private key is determined through a running result of the target quantum circuit, and the ciphertext is decrypted through the private key; even if a most efficient number field sieve method is used to decompose a binary number with 795 bits, more than 3000 years are needed in the prior art, compared with the prior art, through superposition and entanglement characteristics of quantum calculation, the ciphertext breaking speed based on discrete logarithm encryption is greatly improved.

The invention discloses a general atomic cross-chain switching method for relieving abort attacks. The invention provides a ShieldSwap scheme for solving the problem that an existing signature-based cross-chain switching scheme is prone to being subjected to abort attacks of participants, and consequently asset locking or switching fails. The method is characterized by comprising the following steps of: firstly, designing a reverse freezing mechanism, and inhibiting an attack motivation of an aborting party by enabling the assets of the aborting party to face longer locking time; secondly, recombining a working process, and completing all signature commitment steps under a chain to avoid an early-stage on-chain locking risk; and finally, a fair completion mechanism is adopted to ensure that the two parties can independently generate final exchange signatures after the assets are frozen. The method is based on general primitives such as adapter signature and verifiable discrete logarithmic time, does not depend on a script function of a specific chain, has high security and strong universality, can effectively guarantee atomicity and fairness of cross-chain exchange, and is suitable for decentralized asset exchange scenes among various block chains.

This invention provides a signature method, apparatus, device, and medium based on homogeneity, applicable to the field of computer technology. The method includes: for the private key to be processed, solving for the discrete logarithm associated with a first eccentricity point to obtain first homogeneous data, the first homogeneous data representing the mapping from an initial elliptic curve to an intermediate elliptic curve; performing embedding projection processing on the homogeneous data between two-dimensional Abelian clusters to obtain private key homogeneous data to determine the private key, the private key homogeneous data representing the mapping from the initial elliptic curve to a public key elliptic curve; solving for the discrete logarithm of the torsion group of a first smooth number associated with the public key elliptic curve to obtain third and fourth homogeneous data; signing the private key based on auxiliary homogeneous data generated from the third and fourth homogeneous data to obtain a target private key, and sending the target private key to a target terminal to perform information encryption operations on the target information.

A method of providing proof that a statement is true keeping a secret input to the statement a secret, comprising: generating a proof using a public input, the secret input, and a proving key linked to an augmented verification circuit which comprises (i) a verification circuit arranged to receive the inputs, supply the secret input to a function circuit representing the statement to generate a function circuit output, and determine whether the public input corresponds to the function circuit output; and (ii) a multiplicative gate arranged to receive the secret input and a dummy value. The proof comprises a commitment to inputs of multiplicative gates of the augmented verification circuit, the commitment generated using a first vector comprising n components from a finite group of data elements. The secret input is a discrete logarithm of a public element of said finite group. The proof is transmitted to a verifying device.

The present invention discloses a multi-party collaborative threshold signature method, device and system based on ECDSA, belonging to the technical field of cryptographic signature. A signature scheme is designed based on ECDSA. Each signature participant generates and saves their respective signature shares without disclosing their partial signature keys. Then, the signatures corresponding to all signature participants are calculated. The entire signature scheme has low computational complexity, a simple data interaction topology, and less stored data, thus solving the technical problem that existing multi-party threshold collaborative signature algorithms often have high computational overhead, communication overhead, and storage overhead. In addition, the legitimacy verification of transmitted information is carried out based on the zero-knowledge proof of discrete logarithm and the verifiable secret sharing technology, and the security under the malicious adversary model can be achieved without introducing high-overhead technologies such as range proof or consistency check with high computational overhead and communication overhead.

The invention relates to the technical field of data security and privacy computing, and discloses a controllable function computing method for data circulation and utilization, which comprises the following steps of: constructing system parameters based on a bilinear mapping group; according to the predicate vector and the function vector, generating a function decryption key containing a permission verification and calculation component; generating a ciphertext containing an attribute and data confusion component according to the attribute vector and the data vector; and carrying out orthogonality verification on the ciphertext by using the key, eliminating random interference only when the attribute and the predicate are orthogonal, executing pairing operation, solving discrete logarithms, and obtaining an inner product of data and a function. According to the method, strict calculation permission control is achieved through an orthogonality verification mechanism of bilinear pairings, meanwhile, attribute hiding and function hiding are achieved through randomized matrix transformation, specific inner product calculation is completed on the premise that original data are not leaked, and data are available and invisible.

The invention provides a partial knowledge proving method and system with friendly range proving, and relates to the technical field of cryptography, and the method comprises the following steps: an initialization stage: initializing common parameters which comprise a group of substrates with unknown discrete logarithmic relations and a cryptographic hash function; a certification stage: the certifier selects k known secret commitments, and generates certification for the k known secret commitments in batches based on the public parameters; in the verification stage, the verifier verifies the received proof, including verifying the index validity of the k secret commitments and verifying the opening correctness of the k secret commitments; wherein the range proving is friendly, the promise value range for proving the k secrets is converted into the promise value range for proving the aggregation re-randomization promise, and the aggregation re-randomization promise of the k secrets is calculated through a correction term. According to the method, the promise of re-randomization is aggregated, and efficient connection range promising is achieved on part of knowledge promising.

The invention discloses an outsourcing graph database-oriented sub-graph matching verification method and device and electronic equipment. The method comprises the following steps of: obtaining a homomorphic signature based on discrete logarithms; integrity verification of sub-graph matching is carried out based on homomorphic signatures and an arithmetic aggregation Merkel Hash tree; the global root abstract of the arithmetic aggregation Merkel Hash tree is generated by the root Hash of the initial state tree, the logic supplement tree and the logic deletion tree through arithmetic operation aggregation; performing freshness verification of sub-graph matching based on a time correlation structure freshness verification protocol; the freshness verification protocol is realized by verifying whether a time association graph structure obtained by mapping query moments exists in graph data maintained by a cloud server or not; performing correctness verification of sub-graph matching based on a correctness verification protocol of private set intersection; the correctness verification protocol is realized by verifying whether the intersection of the query graph and the difference set of the graph database and the result set is null or not in a cryptographic mode, so that the complete and efficient sub-graph matching verification method is realized.

A data processing system and method are disclosed. The system includes a first party and a second party that respectively participate in secure two-party computation using data x and data y. Among them, the first party calculates the modular exponentiation of a part of data x and a part of the obtained data y; the second party calculates the modular exponentiation of another part of data x and another part of the obtained data y; the first party performs a secondary modular exponentiation on the modular exponentiation result obtained from the second party; the second party performs a secondary modular exponentiation on the modular exponentiation result obtained from the first party; and multiplies the x component and the y component in the secondary modular exponentiation results of the first and second parties respectively, and determines whether x and y are equal according to the multiplication result. Among them, the first and second parties perform secret sharing division on their respective x of x and y, and each uses the same private key to perform two modular exponentiations. Thus, based on the discrete logarithm problem, while determining that x and y are equal, it can ensure that the values of x and y are not leaked. The above x and y can be ID items in the entry, so as to facilitate obtaining the matching intersection without leaking the ID identity for subsequent secure operations.

The invention relates to a multi-participant elliptic curve attack method and device and a storage medium, and relates to the technical field of encryption security verification. The method comprises the following steps: collecting public keys of all participants, and obtaining an elliptic curve base point of an elliptic curve digital signature algorithm; for the public key of the first participant in the public keys of all the participants, iteratively and randomly selecting a coefficient # imgabs0 #, calculating a point # imgabs2 # by using a public key Q1 of a current coefficient # imgabs1 # and a base point G, performing collision detection in a point sequence range calculated by the first participant after each random walk calculation point, and if collision occurs, solving a discrete logarithm according to a collision result to obtain a private key; starting from the public key of the second participant, when collision detection is carried out, collision detection is carried out in a point sequence range calculated by the current participant and all previous participants; during collision, the discrete logarithm is solved according to a collision result to obtain a private key.

The invention belongs to the technical field of security, and particularly relates to a block chain-based national dialysis case registration data tamper-proofing method and system. And partitioning data to be registered, sharing the data to a committee node subset through a verifiable secret sharing protocol, and generating an initial data share bound with the data hash. The dominant node aggregates the commitment and generates a random vector as a common initialization parameter of the GMW protocol Boolean operation circuit. The GMW circuit switches an oblivious transport protocol of a discrete logarithm or lattice cryptographic base according to input share sensitivity when performing AND gate calculation. And for the key logic gate of which the fan-out value or the input source exceeds the preset threshold, the committee cooperatively generates and verifies the non-interactive zero-knowledge proof. And the committee generates an aggregation signature and performs anchoring storage with the data block to ensure that the data is tamper-proof.

The present invention discloses a blockchain distributed timestamp generation method that is resistant to quantum computer attacks. Specifically, the data generator calculates the hash value of the data information and transmits the hash value to the distributed timestamp server. All distributed timestamp servers sign the same service request and randomly select a distributed timestamp server as the master server. The master server collects all signatures to form a timestamp. A hash binary tree is established through the timestamp. The root hash value of the tree is output to the block of the blockchain as the input of the VDF.Eval algorithm. The result calculated by the VDF.Eval algorithm is verified by the VDF.Verify algorithm to determine whether the generated timestamp is correct. This invention can not only avoid problems such as servers and users colluding to tamper with or forge timestamps, but also solve the problem of quantum attacks on discrete logarithm calculations.

The invention discloses a method for communicating between two controllers inside a vehicle. The method comprises the steps that the two controllers negotiate by means of a Diffie-Hellman key exchange algorithm and an asymmetric encryption algorithm to obtain a shared symmetric key; moreover, the two controllers encrypt and decrypt the communication message by means of the shared symmetric key and a symmetric encryption algorithm, so as to realize communication interaction. In the invention, the two controllers in the vehicle negotiate by means of the Diffie-Hellman key exchange algorithm and the asymmetric encryption algorithm to obtain the shared symmetric key, on one hand, the Diffie-Hellman key exchange algorithm based on discrete logarithms is difficult to crack, so that the confidentiality of the symmetric key obtained by negotiation of the two controllers is ensured, and on the other hand, the confidentiality of the symmetric key obtained by negotiation of the two controllers is ensured. And on the other hand, the two controllers carry out identity authentication mutually by means of an asymmetric encryption algorithm, so that the identity authenticity of both communication parties is ensured, and an illegal third party is prevented from participating in the negotiation process of sharing the symmetric key.

The invention discloses a method and system for confronting symbolic execution attacks based on double opaque predicates, and the method comprises the steps: 1, constructing a feedforward neural network which comprises an input layer, a plurality of hidden layers, and an output layer; 2, constructing a discrete logarithm problem of formalized linear transformation; and 3, setting a dual opaque predicate scheme, and inserting the feedforward neural network and the discrete logarithm problem of formalized linear transformation into a target program according to the dual opaque predicate scheme. According to the method, multi-level path judgment conditions are constructed by combining the non-interpretability of the feedforward neural network and the calculation complexity of the discrete logarithm problem, so that a symbolic execution tool faces extremely high calculation cost and complexity in the analysis process, and the protection effect on symbolic execution attacks is effectively improved.

The present invention provides a compact quantum-resistant encryption and decryption method and system based on supersingular isogeny. The system initialization process is carried out, including inputting security parameters, large prime numbers, and corresponding supersingular elliptic curves to obtain system public parameters; the key generation process generates public and private keys by the user side, including randomly selecting vectors and according to the corresponding ideal class arithmetic image curve; the encryption process encrypts messages by the encryptor, including randomly selecting vectors, according to the corresponding ideal class arithmetic image curve, calculating the ideal class, calculating the image curve in two steps, and selecting points for point doubling operations during the calculation, and returning the ciphertext; the decryption process decrypts the received ciphertext by the user side to obtain the plaintext. The implementation process is to split the ciphertext, verify whether it is a supersingular elliptic curve, if so, calculate the ideal class, calculate the image curve and select points, and solve the discrete logarithm problem to recover the message.