Methods, systems, and computer readable media for providing Decentralized Finance (DeFi) are disclosed. According to one method, a method for providing digital property swap occurs at a computing platform executing a DeFi protocol, wherein the computing platform is acting as a digital property exchange center. The DeFi protocol method comprising: receiving one kind of digital property from a user; calculating an equivalent amount of another digital property; sending the said equivalent amount of the said other digital property to the said user. According to one system, a system for providing Decentralized Finance (DeFi) includes at least one computing platform, wherein the computing platform is executing a DeFi protocol and is acting as a swapping platform of the DeFi protocol. The DeFi platform is configured for: receiving digital properties as liquidity from liquidity providers; receiving one kind of digital properties from a user; and sending another kind of digital properties to the said user. The DeFi platform described herein is comprised of mathematical curves that satisfy the supply and demand principle. The main difference between the proposed DeFi protocol and known variants of DeFi systems (such as Uniswap V2) consists in the way that a liquidity provider does not need to provide both kinds of digital properties to establish a market maker. This means that a liquidity provider can establish a market by providing only one kind of digital property and establish the so-called Initial Coin Offer (ICO) process.

Authentication with security in wireless networks may be provided. A first confirm message comprising a first send-confirm element and a first confirm element may be received. Next, an Authenticator Number Used Once (ANonce) may be generated and a second confirm message may be sent comprising the ANonce, a second send-confirm element, and a second confirm element. Then an association request may be received comprising a Supplicant Number Used Once (SNonce) and a Message Integrity Code (MIC). An association response may be sent comprising an encrypted Group Temporal Key (GTK), an encrypted Integrity Group Temporal Key (IGTK), the ANonce, and the MIC. An acknowledgment may be received comprising the MIC in an Extensible Authentication Protocol (EAP) over LAN (EAPoL) key frame and a controller port may be unblocked in response to receiving the acknowledgment.

An arithmetic apparatus includes an interface and a circuity. The interface is connected to an information processing apparatus that is connected to a client apparatus and that processes data in an encrypted state. The circuitry acquires, from the information processing apparatus, encryption input data or encryption target data encrypted with a first encryption key. The circuitry decrypts the acquired, encryption input data or encryption target data with a first decryption key. Then, the circuitry executes a predetermined arithmetic operation on the decrypted arithmetic operation target data, encrypts data of an arithmetic operation result obtained by the predetermined arithmetic operation with the first encryption to key, and outputs the encrypted data of the arithmetic operation result to the information processing apparatus.

A system, method and computer-readable medium provide secure communication between a first and a second computer system based on supersingular isogeny elliptic curve cryptography. The first computer system and the second computer system each determine kernels K.sub.A and K.sub.B including computing mP+nQ by accessing a lookup table stored in a memory that contains a range of doubles of an end point of the respective kernels, where P and Q are points on the public elliptic curve and m and n are integers. The first computer system and the second computer system compute secret isogenies by determining a respective kernel K.sub.BA and K.sub.AB using mixed-base multiplicands with a single inversion, including computing the respective kernel K.sub.BA and K.sub.AB by converting the multiplicands to base 32, and computing scalar multiplications using the base 32 multiplicands.

An elliptic curve random number generator avoids escrow keys by choosing a point Q on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the x-coordinate of a point Q on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid, the x-coordinate is decompressed to the point Q, wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and Q is used as an escrow key and stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

A method for performing an elliptic curve cryptographic process to generate output data based on input data, the elliptic curve cryptographic process based on an elliptic curve over a finite field, wherein the generation of the output data comprises generating, based on a predetermined point V of the elliptic curve and a positive R-bit integer k, a first point of the elliptic curve that is based, at least in part, on the point kV of the elliptic curve, wherein k=Σ.sub.r=0.sup.R−1 2.sup.rb.sub.r and, for each r=0,1, . . . , R−1, b.sub.r is the bit value of k at bit position r of k, wherein the method comprises: storing, according to a partition of the R bit positions for k into T groups of bit positions P.sub.t (t=0, 1, . . . , T−1), a corresponding lookup table L.sub.t having, for each of the 2.sup.|P.sup.t.sup.|possible options for assigning to the |P.sub.t| bit positions s ∈ P.sub.t a respective bit value x.sub.s, a corresponding point of the elliptic curve that is based, at least in part, on the point (Σ.sub.s∈P.sub.t2.sup.sx.sub.s)V of the elliptic curve; obtaining k; and determining the first point as Σ.sub.t=0.sup.T−1l.sub.t, where l.sub.t is the point of the elliptic curve that corresponds, in lookup table L.sub.t, to the option for assigning to the |P.sub.t| bit positions s ∈ P.sub.t the corresponding bit value b.sub.s.

A processor with an elliptic curve cryptographic algorithm and a data processing method thereof are shown. The processor has first register storing a Hash value pointer, and a second register, storing a private key pointer. In response to a first elliptic curve cryptographic instruction of an instruction set architecture, the processor reads a first storage space within a system memory by referring to the first register to get a Hash value of the data to be signed, reads a private key by referring to the second register, performs a signature procedure using the elliptic curve cryptographic algorithm on the Hash value based on the private key to generate a digital signature, and programs the digital signature into a second storage space within the system memory.

A processor with an elliptic curve cryptographic algorithm and a data processing method thereof are shown. The processor has a first register, storing a public key pointer pointing to a public key. In response to a single elliptic curve cryptographic instruction of an instruction set architecture, the processor reads a plaintext input from a first storage space within a system memory, performing an encryption procedure using the elliptic curve cryptographic algorithm on the plaintext input based on the public key obtained by referring to the first register to encrypt the plaintext input and to generate a ciphertext output, and programming the ciphertext output into a second storage space within the system memory.

A processor with an elliptic curve cryptographic algorithm and a data processing method thereof are shown. The processor has a first register, storing a private key pointer pointing to a private key. In response to a single elliptic curve cryptographic instruction of an instruction set architecture, the processor reads a ciphertext input from a first storage space within a system memory, performing a decryption procedure using the elliptic curve cryptographic algorithm on the ciphertext input based on the private key obtained by referring to the first register to decrypt the ciphertext input and generate a plaintext output, and programming the plaintext output into a second storage space within the system memory.

A processor with an elliptic curve cryptographic algorithm and a data processing method thereof are shown. Three elliptic curve cryptographic instructions are proposed in the instruction set architecture for key exchange between an initiator and a responder. The initiator device executes the first elliptic curve cryptographic instruction to generate a key pair (r.sub.A, R.sub.A). In addition to considering the first temporary public key R.sub.A, the responder device further takes the second temporary public key R.sub.B into consideration when executing the second elliptic curve cryptographic instruction to generate the responder-generated shared key K.sub.B. Based on the temporary private key r.sub.A, and the temporary public keys R.sub.A and R.sub.B, the initiator device executes the third elliptic curve cryptographic instruction to generate the initiator-generated shared key K.sub.A.