A public-key scheme of Homomorphic Encryption (HE) in the framework Quotient Algebra Partition (QAP) comprises: encryption, computation and decryption. With the data receiver choosing a partition or a QAP, [n, k, C], a public key Key.sub.pub=(VQ.sub.en, Gen.sub.ε) and a private key Key.sub.priv=.sup.†P.sup.† are produced, where VQ.sub.en is the product of an n-qubit permutation V and an n-qubit encoding operator Q.sub.en, Gen.sub.ε an error generator randomly provides a dressed operator Ē=V.sup.†EV spinor error E of [n, k, C]. Then, by Key.sub.pub, the sender can encode his k-qubit plaintext Ix) into an n-qubit ciphertext |ψ.sub.en, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation U.sub.en=PV.sup.†Q.sub.en.sup.† for a given k-qubit action M and sends to cloud, where is the error-correction operator of [n, k, C], =I.sub.2.sub.n−k.Math.M the tensor product of the (n−k)-qubit identity I.sub.2.sub.n−k and M , and V.sup.†Q.sup.†.sub.en and P the complex-transposes of VQ.sub.en and

An inner-product functional encryption scheme in which the maximum length of a ciphertext and the maximum length of a secret key are not restricted can be constructed. An encryption device (20) generates a ciphertext ct.sub.x in which a vector x is encrypted, using encryption setting information that is of a size depending on the size of the vector x and is generated using as input public information of a fixed size. A key generation device (30) generates a secret key sk.sub.y in which a vector y is set, using key setting information that is of a size depending on the size of the vector y and is generated using as input the public information. A decryption device (40) decrypts the ciphertext ct.sub.x with the secret key sk.sub.y to calculate an inner-product value of the vector x and the vector y.

A one-time self-powered timer circuit whose state can be measured only once, after which the timer will de-synchronize itself. In this manner, the timers can only be used for one-pad authentication. The security of the public-key distribution algorithms that will exploit the synchronization between billions of hardware-software timers, time reversibility of software timer and time irre-versibility of hardware timers and one-time read-out to deliver classical and quantum-like benefits. System-on-chip and circuit imple-mentation of the self-powered timer array, read-out, programming and initialization modules that implements the proposed public-key distribution algorithms.

Various embodiments relate to a method for masked decoding of a polynomial a using an arithmetic sharing a to perform a cryptographic operation in a data processing system using a modulus q, the method for use in a processor of the data processing system, including: subtracting an offset δ from each coefficient of the polynomial a; applying an arithmetic to Boolean (A2B) function on the arithmetic shares of each coefficient a.sub.i of the polynomial a to produce Boolean shares â.sub.i that encode the same secret value a.sub.i; and performing in parallel for all coefficients a shared binary search to determine which of coefficients a.sub.i are greater than a threshold t to produce a Boolean sharing value {circumflex over (b)} of the bitstring b where each bit of b decodes a coefficient of the polynomial a.

A public value 2.sup.σ/m is obtained, and secure computation of public value division [x]/(2.sup.σ/m) using a secret share value [x] and the obtained public value 2.sup.σ/m is performed, so that a secret share value [mx].sub.r of a value obtained by right-shifting mx by σ bits is obtained and output. Here, x is a real number, [•] is a secret share value of •, σ is a positive integer that is the number of bits indicating a right shifting amount, and m is a real number.

A computer processing hardware architecture system for the Kyber lattice-based cryptosystem which is created with high resource reuse in the compression and decompression module, the operation unit, the binomial samplers, and the operation ordering.

A public-key scheme of Homomorphic Encryption (HE) in the framework Quotient Algebra Partition (QAP) comprises: encryption, computation and decryption. With the data receiver choosing a partition or a QAP, [n, k, C], a public key Key.sub.pub=(VQ.sub.en, ) and a private key Key.sub.priv=.sup.†P.sup.\ are produced, where VQ.sub.en is the product of an n-qubit permutation V and an n-qubit encoding operator Q.sub.en, an error generator randomly provides a dressed operator Ē=V.sup.†EV of spinor error E of [n, k, C]. Then, by Key.sub.pub, the sender can encode his k-qubit plaintext |x into an n-qubit ciphertext |ψ.sub.en, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation U.sub.en=PV.sup.†Q.sub.en.sup.† for a given k-qubit action M and sends to cloud, where is the error-correction operator of [n, k, C], =I.sub.2.sub.n−k.Math.M the tensor product of the (n−k)-qubit identity I.sub.2.sub.n−k and M, and V.sup.†Q.sub.en.sup.† and PMANAGING COMMUNICATIONS BETWEEN A VEHICLE AND A USER DEVICE