A method is suggested for providing a response, wherein the method comprises: obtaining a challenge from a host, determining the response based on the challenge, determining an auxiliary value based on the response or the challenge, providing the auxiliary value to the host, obtaining a random value from the host, checking the validity of the challenge based on the random value, and providing the response to the host only if the challenge is valid. Also, according methods running on the host and system are provided. Further, corresponding devices, hosts and systems are suggested.

A low-latency digital-signature with side-channel security is described. An example of an apparatus includes a coefficient multiplier circuit to perform polynomial multiplication, the coefficient multiplier circuit providing Number Theoretic Transform (NTT) and INTT (Inverse NTT) processing; and one or more accessory operation circuits coupled with the coefficient multiplier circuit, each of the one or more accessory operation circuits to perform a computation based at least in part on a result of an operation of the NTT/INTT coefficient multiplier circuit, wherein the one or more accessory operation circuits are to receive results of operations of the NTT/INTT coefficient multiplier circuit prior to the results being stored in a memory.

Combined post-quantum security utilizing redefined polynomial calculation is described. An example of an apparatus includes a first circuit for key encapsulation operation; a second circuit for digital signature operation; and a NTT (Number Theoretic Transform) multiplier circuit, wherein the NTT multiplier circuit provides for polynomial multiplication for both the first circuit and the second circuit, wherein the apparatus is to remap coefficients of polynomials for the first circuit to a prime modulus for the second circuit, and perform polynomial multiplication for the first circuit utilizing the remapped coefficients of the polynomials for the first circuit.

An electronic device includes a memory storing data from an external source, an application processing unit (APU) transmitting a secret key and public key generation command, an isolated execution environment (IEE) generating a secret key in response to the secret key generation command, generating a public key based on the secret key in response to the public key generation command, and storing the secret key, and a non-volatile memory performing write and read operations depending on a request of the APU. When the data are stored in the memory, the APU transmits a public key request to the IEE and in response the IEE transfers the public key to the APU through a mailbox protocol. The APU generates a ciphertext by performing homomorphic encryption on the data based on an encryption key in the public key, and classifies and stores the public key and the ciphertext in the non-volatile memory.

In one implementation, the disclosure provides systems and methods for generating a secure signature using a device-specific and group-specific moving target authentication protocol. According to one implementation, generating the secure signature entails determining a state of a first device in association with a select time interval. The state of the first device is defined by one or more time-variable characteristics of the first device. The device computes an output for a signing function that depends upon the determined state of the first device associated with the first time interval.

An apparatus comprises an input register comprising an input polynomial, a processing datapath communicatively coupled to the input register comprising a plurality of compute nodes to perform a number theoretic transform (NTT) algorithm on the input polynomial to generate an output polynomial in NTT format. The plurality of compute nodes comprises at least a first butterfly circuit to perform a series of butterfly calculations on input data and a randomizing circuitry to randomize an order of the series of butterfly calculations.

An apparatus comprises an input register comprising an input polynomial, a processing datapath communicatively coupled to the input register comprising a plurality of compute nodes to perform an incomplete number theoretic transform (NTT) algorithm on the input polynomial to generate an output polynomial in NTT format, the plurality of compute nodes comprising at least a first NTT circuit comprising a single butterfly circuit to perform a series of butterfly calculations on input data; and a randomizing circuitry to randomize an order of the series of butterfly calculations.

A grouping means 11 that extracts basis vectors from a set of basis vectors for a lattice having a predetermined relationship with a matrix used to generate a public key, and that groups the basis vectors such that a predetermined condition is satisfied. A sampling means 12 that samples, for at least one group, the same number of arbitrary values as the number of a plurality of basis vectors included in that group, in parallel for the individual basis vectors, onto a lattice constituted by the plurality of basis vectors, the arbitrary values serving as random numbers following a discrete Gaussian distribution. The predetermined condition is that each of the basis vectors included in a group is orthogonal to the other basis vectors included in the same group and is also orthogonal to Gram-Schmidt basis vectors, which are vectors obtained by orthogonalizing the other basis vectors by Gram-Schmidt orthogonalization.

The technical idea of the present invention relates to a method for forming a virtual private network and a virtual private network operating system, which provide a virtual private network by performing signature and authentication based on a post quantum cryptography. A method for forming a virtual private network performed by a server according to the technical idea of the present invention comprises the steps of: generating a private key including a first key vector corresponding to a grid and a second key vector having a first distance from the first key vector; receiving a handshake request from a client; performing a signature by using the private key; and transmitting a certificate and an authentication message including the signature to the client.

Bitcoins and the underlying blockchain technology are one of the main innovations in building decentralized applications. The effects of quantum computing on this technology are analyzed in general. Provided herein are effective solutions to address security vulnerabilities in a blockchain-based system that can be exploited by a quantum attacker.