爲什麼在MATLAB中實現的Elgamal數字簽名算法無法正常工作？

Question

%%%CODE: 

clc; 

disp('Implementation of ELGAMAL Digital Signature'); 

clear all; 
close all; 

%%Hardcoded values (vpi stands for VariablePrecisionIntegers, and are used to store large values) 
g = vpi(5) %alpha in example 
k = vpi(9) %Random number 1<k<p-1 and gcd(k, p − 1) = 1. 
p = vpi(23) %Prime Number 
x = vpi(3) %Secret Key 1 < x < p − 1 
m = vpi(7) %Message 

y = vpi(2) 
r = vpi(2) 
s = vpi(2) 

%%Key Generation 
y = powermod(g,x,p)  %y = g^x mod p 


%%Signature Generation 
r = powermod(g,k,p)  %r = g^k mod p 

multinver = mulinv(9,23) %Generates multiplicative inverse k^-1 mod p 

s = mod(((multinver)*(m-x*r)),p-1)  %s = (k^-1)*(m-x*r) mod p-1 


%%Verification 
zvg = vpi(2); 
zvg = powermod (g,m,p)  %zvg = g^m mod p 

zvyr = vpi(2); 
zvyr = mod(((y^r)*(r^s)),p) %zvyr = y^r * r^s mod p 

輸出：

Implementation of ELGAMAL Digital Signature 
g = 5 
k = 9 
p = 23 
x = 3 
m = 7 
y = 2 
r = 2 
s = 2 
y = 10 
r = 11 
multinver = 18 
s = 16 
zvg = 17 
zvyr = 5 

zvg應該等於zvyr，但它的到來了錯誤。

Answer 1

您計算multinver錯誤

應該

multinver = mulinv(k,p-1) %Generates multiplicative inverse k^-1 mod (p-1) 

注意，我們計算反模（P-1）不MOD（P）。