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Author: javascript-2020

blog/25-12-19/diffie-hellman/ex/diffi-hellman.js

@@ -0,0 +1,219 @@
+```
+
+
+
+                                                                                console.clear();
+                                                                                
+        var dh                  = diffie_hellman();
+                                                                                console.log('bits',dh.bits);
+        var {p,g,q}             = dh.init;
+                                                                                console.log('prime',p,'primitive root',g,' [','q',q,']');
+        var alice               = dh.rnd;
+        var A                   = dh.power(g,alice,p);
+        
+        var bob                 = dh.rnd;
+        var B                   = dh.power(g,bob,p);
+                                                                                console.log('alice',alice,'=>',A);
+                                                                                console.log('bob',bob,'=>',B);
+        var alice_secret        = dh.power(B,alice,p);
+        var bob_secret          = dh.power(A,bob,p)
+                                                                                console.log('secret',alice_secret);
+                                                                                //console.log('secret,bob_secret);
+                                                                                console.log(alice_secret==bob_secret);
+                                                                                
+                                                                                console.log(dh.time);
+        function diffie_hellman(bits=1024){
+        
+          var obj   = {};
+          
+              Object.defineProperty(obj,'init',{get:init});
+              Object.defineProperty(obj,'rnd',{get:rnd_n});
+              Object.defineProperty(obj,'time',{get:time});
+              
+              obj.bits    = bits;
+              
+              var start   = performance.now()
+              
+              
+              function init() {
+              
+                    var q       = gen(()=>rnd_n());
+                    var p       = gen(()=>q*rnd_n()+1n);
+                    var g       = rnd_n()%p;
+                    return {p,g,q};
+                    
+              }//init
+              
+              
+              function rnd_n(){
+              
+                    var bs      = '0b';
+                    for(var i=0;i<bits;i++){
+                    
+                          bs   += Math.floor(Math.random()*2);
+                          
+                    }//for
+                    return BigInt(bs);
+                    
+              }//rnd
+              
+              
+              function rnd(size=100){
+              
+                    var n   = Math.floor(Math.random()*size);
+                    n       = BigInt(n);
+                    return n;
+                    
+              }//rnd
+
+              
+              function gen(fn){
+              
+                    var p;
+                    while(!isPrime(p=fn()));
+                    return p;
+                    
+              }//gen
+              
+              
+              function isPrime(prime){
+              
+                    var result    = lowlevel();
+                    if(!result){
+                          return false;
+                    }
+                    
+                    result    = miller_rabin();
+                    return result;
+                    
+                    
+                    function lowlevel(){
+                    
+                          for(var div of list){
+                          
+                                if(prime%div==0n){
+                                      return false;
+                                }
+                                
+                                if(div**2n>=prime){
+                                      return true;
+                                }
+                                
+                          }//for
+                          
+                          return true;
+                          
+                    }//lowlevel
+                    
+                    
+                    function miller_rabin(){
+                    
+                          var s   = 0;
+                          var d   = prime-1n;
+                          
+                          while(d%2n==0n){
+                          
+                                d   >>= 1n;
+                                s    += 1;
+                                
+                          }//while
+                          
+                          var num   = 20;
+                          for(var i=0;i<num;i++){
+                          
+                                var a   = rnd();
+                                if(composite()){
+                                      return false
+                                }
+                                
+                          }//for
+                          
+                          return true
+                          
+                          
+                          function composite(){
+                          
+                                var x   = power(a,d,prime);
+                                
+                                for(var i=0;i<s;i++){
+                                
+                                      var y   = power(x,2n,prime);
+                                      
+                                      if(y==1n && x!=1n && x!=prime-1n){
+                                            return true;
+                                      }
+                                      
+                                      x   = y;
+                                      
+                                }//for
+                                
+                                if(y!=1n){
+                                      return true;
+                                }
+                                
+                                return false;
+                                
+                          }//composite
+                          
+                    }//miller_rabin
+                    
+              }//isPrime
+              
+              
+              obj.power=power;
+              function power(x,y,p){
+              
+                    var res   = 1n;
+                    x         = x%p;
+                    
+                    while(y>0){
+                    
+                        if(y&1n){
+                              res   = (res*x)%p;
+                        }
+                        
+                        y   = y>>1n;
+                        x   = (x*x)%p;
+                        
+                    }//while
+                    
+                    return res;
+                    
+              }//power
+              
+              
+              var list   = [
+                    2n, 3n, 5n, 7n, 11n, 13n, 17n, 19n, 23n, 29n,
+                    31n, 37n, 41n, 43n, 47n, 53n, 59n, 61n, 67n,
+                    71n, 73n, 79n, 83n, 89n, 97n, 101n, 103n,
+                    107n, 109n, 113n, 127n, 131n, 137n, 139n,
+                    149n, 151n, 157n, 163n, 167n, 173n, 179n,
+                    181n, 191n, 193n, 197n, 199n, 211n, 223n,
+                    227n, 229n, 233n, 239n, 241n, 251n, 257n,
+                    263n, 269n, 271n, 277n, 281n, 283n, 293n,
+                    307n, 311n, 313n, 317n, 331n, 337n, 347n, 349n
+              ];
+              
+              
+              function time(){
+              
+                    var time    = (performance.now()-start).toFixed(1)+'ms';
+                    return time;
+                    
+              }//time
+              
+              
+          return obj;
+          
+        }//diffie-hellman
+        
+        
+        
+        
+        
+        
+        
+        
+```
+
+