A method of providing blind vertical learning includes creating, based on assembled data, a neural network having n bottom portions and a top portion and transmitting each bottom portion of then bottom portions to a client device. The training of the neural network includes accepting a, output from each bottom portion of the neural network, joining the plurality of outputs at a fusion layer, passing the fused outputs to the top portion of the neural network, carrying out a forward propagation step at the top portion of neural network, calculating a loss value after the forward propagation step, calculating a set of gradients of the loss value with respect to server-side model parameters and passing subsets of the set of gradients to a client device. After training, the method includes combining the trained bottom portion from each client device into a combined model.

A blockchain-implemented transaction from an originator node is to be broadcast. The originator node is communicatively coupled to proxy nodes. The method, implemented by a proxy node, includes: receiving a transaction including an input taking x+r units of computing resources, an output providing x units to the output address and another output providing d+r units to a 1-of-n multi-signature address unlockable by any one of a set of private keys associated the proxy nodes. The proxy node selects a quantity of computing resources, t units, to be allocated to the proxy node for broadcasting the transaction and having it included in the blockchain and generates a further transaction taking d+r units sourced from the multi-signature address and an output providing t units to the proxy node. The proxy node broadcasts both transactions timed to permit their inclusion in the same block of the blockchain.

A share generating device obtains N seeds s.sub.0, . . . , s.sub.N−1, obtains a function value y=g(x, e) ∈ F.sup.m of plaintext x ∈ F.sup.m and a function value e, and obtains information containing a member y.sub.i and N−1 seeds s.sub.d, where d ∈ {0, . . . , N−1} and d≠i, as a share SS.sub.i of the plaintext x in secret sharing and outputs the share SS.sub.i. It is to be noted that the function value y is expressed by members y.sub.0 ∈ F.sup.m(0), . . . , y.sub.N−1 ∈ F.sup.m(N−1) which satisfy m=m(0)+ . . . +m(N−1).

The invention relates to secure determination of a solution (S) to a computational task by a dealer-free threshold signature group. Access to a resource or reward is offered in exchange for the solution. The method enables individuals in said group to work together in a trust-less, or dealer-free manner. To achieve this, individuals generate their own key pair and use their public key to establish with the group an initial shared public key that they can all use, in parallel, to find a solution to the task. Their own private keys remain secret and, therefore, the collaboration is trust¬less, and operates efficiently, because a verified shared public key is created using the initial shared public key that was used when a solution is found and verified. The resource or reward can be secured by the verified shared public key. Because the private keys of each participant were used in the determination of the initial shared public key that lead to the solution then participants must then collaborate to unlock the resource or reward because the corresponding shared private key can only be generated by all participants or a pre-agreed threshold of participants. Efficiency is achievable by using an initial shared public key and calculating with the group a verified shared public key after the solution has been found. The invention enables the task to be trust-less by using the homomorphic properties of elliptic curve cryptography when applying Shamir's secret sharing scheme. The inventive concept resides in the secure, trust-less and efficient way in which a group can collaborate. The invention can be agnostic to the task.

To efficiently determine cross tabulation while keeping confidentiality. A flag conversion unit (11) converts a format of a share of a flag that represents a boundary between groups. A boundary number setting unit (12) generates a share of a vector in which the next element number is set when the flag representing a group boundary is true and the number of records is set when the flag is false. A sorting unit (13) generates a share of a sorted vector which has been sorted by a permutation that moves vectors such that the last elements of each group are sequentially arranged from beginning A count calculation unit (14) sets a difference between the value of one element and the value of the preceding element in the sorted vector and generates a share of a vector representing the number of records in each group.

A method of obtaining a shared prediction model is provided. The method includes: obtaining a prediction model as a neural network; converting each negative numerical value in a plurality of parameters included in the prediction model to a positive numerical value to obtain a converted prediction model; and sharing the converted prediction model by a secret sharing method to obtain shared prediction models while concealing an input data.

Methods and systems for performing demographics filtering based on biometric information are disclosed. An access terminal can capture a biometric instance corresponding to a user, such as a fingerprint scan, iris scan, etc. The access terminal can determine demographics information from the biometric instance, such as the age, biological sex, or ethnicity of the user. The access terminal can compare the demographics information to demographics information stored on a group of mobile devices corresponding to a group of users, in order to identify candidate user mobile devices. Once candidate user mobile devices are identified, the access terminal can perform a biometric match between the biometric instance corresponding to the user and biometric instances stored on the candidate user mobile devices. Once a biometric match and the corresponding mobile device are determined, the access terminal can conduct a further interaction with the mobile device.

The present invention provides a technique for performing confidential sort at a faster speed than in the prior art. A confidential sort system comprises first to Mth apparatuses. The first to Mth apparatuses obtain inverse substitution [[σ.sub.0.sup.−1]] of L-bit stable sort of {.sup..fwdarw.k.sub.0}. The first to Mth apparatuses perform, on i=1, . . . , N−1, a process of converting [[σ.sub.i-1.sup.−1]] to hybrid substitution to obtain {σ.sub.i-1.sup.−1}, a process of inversely substituting {.sup..fwdarw.k.sub.i} with {σ.sub.i-1.sup.−1} to obtain {σ.sub.i-1.sup..fwdarw.k.sub.i}, a process of obtaining inverse substitution [[σ′.sub.i.sup.−1]] of L-bit stable sort of [[σ.sub.i-1.sup..fwdarw.k.sub.i]], a process of synthesizing {σ.sub.i-1.sup.−1} with [[σ′.sub.i.sup.−1]] to obtain [[σ.sub.i.sup.−1]]:=[[σ.sub.i-1.sup.−1σ′.sub.i.sup.−1]], and a process of converting [[σ.sub.N-1.sup.−1]] to hybrid substitution to obtain {σ.sub.N-1.sup.−1}. The first to Mth apparatuses inversely substitute [[.sup..fwdarw.v]] with {σ.sub.N-1.sup.−1} and output [[σ.sub.N-1.sup..fwdarw.v]].

Techniques for performing secure computing of softmax functions at high speed and with high accuracy are provided. A secure softmax function calculation system that calculates a share ([[softmax (u.sub.1)]], . . . , [[softmax (u.sub.J)]]) from a share ([[u.sub.1]], . . . , [[u.sub.J]]) includes a subtraction means for calculating a share ([[u.sub.1−u.sub.1]], [[u.sub.2−u.sub.1]], . . . , [[u.sub.J−u.sub.J]]), a first secure batch mapping calculation means for calculating, [[exp (u.sub.1−u.sub.1)]], [[exp (u.sub.2−u.sub.1)]], . . . , [[exp (u.sub.J−u.sub.J)]], an addition means for calculating a share ([[Σ.sub.j=1.sup.J exp (u.sub.j−u.sub.1)]], . . . , [[Σ.sub.j=1.sup.J exp (u.sub.j−u.sub.J)]], and a second secure batch mapping calculation means for calculating a share ([[softmax (u.sub.1)], . . . , [[softmax (u.sub.J)]]).

Systems and methods of cryptographic key distribution in a plurality of networks, including: sharing, by a first device, a first portion of a first cryptographic key controlled by a server with a second device, sharing, by the second device, a first portion of a second cryptographic key with the first device, signing a first transaction on a first network with data exchange from a first threshold signature address controlled by the first device, to a third address when one or more details of the first transaction are validated by the server; and signing a second transaction on a second network with data exchange from the second threshold signature address controlled by the second device to a fourth address when one or more details of the second transaction are validated by the server.