Enhanced Biometric Recognition for Secure Authentication Using Iris Preprocessing and Hyperelliptic Curve Cryptography

Algorithm 1: Extended Complex Multiplication (ECM).

 Input: 64 bit large prime number

 Output: HEC of Genus-2 with larger cardinality N

 Process:

 While true

 Do Repeat

 Repeat choosing p=64 bits

 Until factoring of as prime ideals

 Compute all the expected cardinality N

 Until at least one of them desires cardinality N

 For s=1,2,3 then p=4s+3 where

 Compute roots as

 Where

 Calculate conic

 If a point lies with =0 then

 Calculate and intersecting polynomial

 If intersecting polynomial contain a root in then

 Locate Genus-2 HEC

 Identify the random divisor

 Compute N and If N is seems to be favor

 Stop and return Curve C and cardinality N

Algorithm 1: Extended Complex Multiplication (ECM).