Abstract: We present new designs to choose the parameter sets for more efficient HFEv-based signature schemes. The key method is to reduce the degree of the central HFEv-polynomial while, at the same time, increasing the number of Vinegar variables and Minus equations. The new design speeds up the signature generation process by two orders of magnitude (hundreds of times) compared to QUARTZ. We present also new methods to use multivariate signature schemes to build a white box encryption scheme. This technique is applicable to all existing multivariate signature designs including the HFEV-design and the improvements.

Abstract: Using a secure hardware or other form secure elements, where we securely implement the decryption and then encryption function to perform the re-encryption function, we build a hybrid fully homomorphic encryption system, where the boot-strap step is replaced the re-encryption function in the hardware module. This new hybrid system are very efficient because the re-encryption is much more efficient than the bootstrap function, which is the main bottleneck in terms of computations in FHE. In such a system, we make the system secure by making this hardware module secure using all or some of known techniques including temper proof, self-destruction and etc. This module can be controlled by either the server or the client or jointly.

Abstract: Using the same mathematical principle of paring with errors, which can be viewed as an extension of the idea of the LWE problem, this invention gives constructions of a new key exchanges system, a new key distribution system and a new identity-based encryption system. These new systems are efficient and have very strong security property including provable security and resistance to quantum computer attacks.

Abstract: Using the same mathematical principle of paring with errors, which can be viewed as an extension of the idea of the LWE problem, this invention gives constructions of a new key exchanges system, a new key distribution system and a new identity-based encryption system. These new systems are efficient and have very strong security property including provable security and resistance to quantum computer attacks.

Abstract: A group key management approach based on linear geometry is disclosed.

Abstract: A hierarchical group key management approach based on linear geometry is disclosed.

Abstract: A hierarchical group key management approach based on linear geometry is disclosed.

Abstract: A group key management approach based on linear geometry is disclosed.

Abstract: Multivariate public key cryptosystems (MPKC) are public key cryptosystems, whose public key are a set of multivariate polynomials over a finite field (or ring). MPKC can be used for encryption, authentication and signatures. The invention develops three new methods that could be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems that are better in terms of security and efficiency. These three methods are called the internal perturbation plus (IPP), the enhanced internal perturbation (EIP) and the multi-layer Oil-Vinegar construction (MOVC). These three methods can be combined in any 2 or all 3 to be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems as well.

Abstract: Multivariate public key cryptosystems (MPKC) are public key cryptosystems, whose public key are a set of multivariate polynomials over a finite field (or ring). MPKC can be used for encryption, authentication and signatures. The invention develops three new methods that could be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems that are better in terms of security and efficiency. These three methods are called the internal perturbation plus (IPP), the enhanced internal perturbation (EIP) and the multi-layer Oil-Vinegar construction (MOVC). These three methods can be combined in any 2 or all 3 to be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems as well.

Abstract: The invention relates to two cryptographic processes based on composition of multivariable maps: 1) low degree maps for asymmetric cryptographic communication process; 2) high degree maps for symmetric cryptographic communication process. The cryptographic process establishes a correspondence through either a low degree (asymmetric) or a high degree polynomial map (symmetric) between a first vector (X) represented by (x1, x2, . . . , xn) of a finite field (K) and a second vector (Y)=(y1, y2, . . . , ym) of the same field, n and m being integers not too small. The said polynomial map yi=fi(x1, x2, . . . , xn) is derived from composition of various nonlinear and linear maps. The novel elements for the asymmetric invention include the use of inseparable small variable maps with hidden equations, generalized de Jonquiere maps, and the combination of these maps with other maps.

Abstract: The invention relates to two cryptographic processes based on composition of multivariable maps: 1) low degree maps for asymmetric cryptographic communication process; 2) high degree maps for symmetric cryptographic communication process.