one way functionIn this paper, we show that the L -functions attached to Elliptic curves are good candidates to construct a hash function which can be used as a MAC for cryptographic purpose. This is actually du
In addition, the mapping function required by the EC-ElGamal cryptosystem must have certain characteristics. They are as follows: (1) The mapping function needs to be deterministic such that it can uniquely associate each plaintext value to an elliptic curve point and vice versa. (2) The ...
H() One-way cryptographic hash function (e.g., MD5) ‖ The message concatenation operator (·) The elliptic cure scalar point multiplication A The Adversary 5.1. System initialization phase In this phase, S initializes system parameters as done in Tan’s 3PAKE protocol (Tan, 2010a). In ...
Cryptographic primitives and utilities OPRF Oblivious pseudo-random functions This is an implementation ofdraft-irtf-cfrg-voprf-21ciphersuiteOPRF(ristretto255, SHA-512)usinglibsodium. An Oblivious Pseudorandom Function (OPRF) is a two-party protocol between client and server for computing the output of...
TS}, since these messages are based on the keys 𝐾K and 𝐾′K′, respectively, which in turn are a function of the private random number 𝑣v selected by the server. In this way, the proposed ECSSP-SC is forward secure, since the past messages cannot be obtained by an 𝐴𝑡...
Elliptic Curve Point Counting Elliptic curve primality proving Elliptic Curve Scalar Multiplication Elliptic cylinder elliptic differential equation Elliptic filter Elliptic function Elliptic function Elliptic Function, Second-Order Ripple-Phase Approximation Elliptic functions Elliptic functions ▼Face...
In this code snippet, a curve and a generator are selected, the user randomly generates a private key and uses it for all uses of the ECDH protocol. The function find_curves_with_small_subgroup finds pairs of points and orders, such that the order of each point is relatively small, and...
On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields. Nagoya Math. J., 43:199–208, 1971. MathSciNet MATH Google Scholar G. Shimura. On the zeta-function of an abelian variety with complex multiplication. Ann. of Math. (2), 94:504–533...
to use a hash function that provides the desired hash value output size, and no more. There are security risks with using keys not associated with well- known and widely reviewed curves. For example, the curve may not satisfy the Menezes-Okamoto-Vanstone (MOV) condition [X9.62] or the ...
x The floor function rounds the number down to the nearest integer. Examples: 4 . 2 = 2; 6 . 2 = 2; 4 . 2 − = -3; 6 . 2 − = -3 The floor function is also called the integer part function and is denoted int(x) x The ceiling function rounds the number ...