Authors:Ching-Nung Yang and Hsu-Tun Teng Source:IEEE International Conference on E- Commerce, 2003(CEC 2003), June 2003, Pages: 45 – 48 Date:2005/01/20 Presenter: Jung-wen Lo( 駱榮問 ) An Efficient Method for Finding Minimum Hash Chain of Multi-Payword Chains in Micropayment

2 Outline Introduction Single-Payword Chain Multi-Payword Chain Preliminaries Strategies Example Comparison Conclusions Comments

3 Introduction Rivest & Shamir 1997 Netpay 1999 CustomerVendor 1. Pick w n 2. w 0 =h n (w n ); w i =h(w i+1 ) Payword: {w 0,w 1,…,w n } S(w 0 ) (i,w i ) w ’ 0 =h i (w i ) S(w ’ 0 )?=S(w 0 ) w 0 =h n (w n ) E PK V (S(ID C,w 0 )) ID C,(i,w i ) w ’ 0 =h i (w i ) S(w ’ 0 )?=S(w 0 ) CustomerBrokerVendor ID C,n,IP V E PK C ({w 0,w 1,…,w n }) ※ E PK ():PK Fct S():Signature

4 Introduction: Multi-Payword Chain Denomination: $1, $2, $3, $4, $5, $6 Payword roots: {w 10, w 20, w 30, w 40, w 50, w 60 } w ij =w( ij+1 ); j=n-1,n-2,…,0 & i=1,2,…,6 Ex. $16 = s1={w 61,w 62,w 41 }  Length=3 s2={w 11,w 12,w 13, w 14,w 15,w 16 }  Length=6 Problems (Aim) 1. How to find the minimal hash chain such that the number of hash operations can be reduced as small as possible.  Efficiency 2. How to let the payment be divided equally among every single chain in multi-payword chains such that every single chain has about equal length after each purchasing.  Future Efficiency

5 Preliminaries (1/2) : The number of partition of integer n ’ into m parts n ’ =a 1 +a 2 +a 3 +…+a m h ’ ≧ a 1 ≧ a 2 ≧ … ≧ a m ≧ l ’ : (b 1,b 2,…,b m )= (a 1 -(l ’ -1),a 2 -(l ’ -1),…,a m -(l ’ -1)) n=b 1 +b 2 +b 3 +…+b m =n ’ -m ×(l ’ -1) h=h ’ -l ’ +1 h ≧ b 1 ≧ b 2 ≧ … ≧ b m ≧ 1 can be reduced to Ex. Value 5 LengthNo.Item , ,

6 Preliminaries (2/2) Property 1: (or ) Property 2: Theorem 2.1. The m min of

7 Strategies Aggressive mode 1. Find the smallest parts of partitions (m min of ). 2. Keep the length of each payword chain as equal as possible from the partitions of step 1. Minimal hash operations.  Payword chains with large denomination size will be used up quickly. Balance mode 1. Select the partition results from all of the possible partitions (all possible values of m in ). 2. Keep the length of each payword chain as equal as possible from the possible partitions of step 1. Obtain the length of multi-payword chains for one payment as small as possible Spend each payword with the almost equal length.  Take more time

8 Example (1/2) Four payword chains: $2, $3, $4, $5 Payment=$16 Aggressive mode (b 1,b 2,b 3,b 4 )=(a 1 +1, a 2 +1, a 3 +1, a 4 +1) (5,4,4,3)  {w 11,w 32,w 41 } (5,5,4,2)  {w 11,w 31,w 42 }

9 Example (2/2) Balance mode Keeping the length of each payword chain as equal as possible from Table 3.2. (5,4,3,2,2)  {w 12,w 21,w 31,w 42 }

10 Comparison Rivest-Shamir’s schemeNetpay scheme ComputationStorageComputationStorage Broker Verify multi- payword Chains 1. Create multi- payword chains 2. Verify multi- payword Chains Customer 1. Create multi- payword chains 2. Find minimal multi-payword chains for one payment Store Multi- payword Chains Find minimal multi-payword chains for one Payment Store multi- payword chains Vendor Verify multi- payword chains

11 Conclusions Propose a new partition problems. Shows multi-payword chains with different values efficiently for Aggressive mode and Balance mode. The original single payword chain with h value is a special case of our payword scheme when use the partition.

12 Comments Implementation Aggressive mode: 大面額優先使用 Balance mode: 每一輪回中, 每種面額都儘可能的挑選 Balance mode provide future efficiency Total hash number won’t be changed Do not define m=0 Ex. or set i begin with 1