中国剰余アルゴリズムを用いた秘密分散スキーム　多項式 version


Prime : 29      ... 有限体  F29 = Z/29Z  上の多項式を用いる
Parties : 5     ... 分割数
Threshold : 3   ... しきい値

Modulus : 

m[1] = 12 + 2*x + 18*x^2 + 5*x^3 + 19*x^4 + 10*x^5 + 24*x^6 + 17*x^7 + 
     23*x^8 + 17*x^9 + 23*x^11 + 26*x^12 + 23*x^13 + 19*x^14 + 9*x^15 + 
     22*x^16 + x^17 + 23*x^18 + 16*x^19 + 21*x^20 + 21*x^21 + 22*x^22 + 
     6*x^23 + 23*x^24 + 23*x^25 + 15*x^26 + 27*x^27 + 25*x^28 + 20*x^29 + 
     17*x^30 + 12*x^31 + x^32

m[2] = 15 + 7*x + 19*x^2 + 10*x^3 + 25*x^4 + 17*x^5 + 28*x^6 + 12*x^7 + 
     11*x^8 + 11*x^9 + 3*x^10 + 3*x^11 + 24*x^12 + 15*x^13 + 27*x^14 + 
     2*x^15 + 10*x^16 + 4*x^17 + 18*x^18 + 19*x^19 + 13*x^20 + 11*x^21 + 
     13*x^22 + 20*x^23 + 12*x^24 + 2*x^25 + 6*x^26 + 25*x^27 + 16*x^28 + 
     27*x^29 + 16*x^30 + 23*x^31 + x^32

m[3] = 27 + 12*x + 17*x^2 + 2*x^3 + 5*x^4 + 22*x^5 + 7*x^6 + 13*x^7 + 7*x^8 + 
     19*x^9 + 26*x^10 + 19*x^11 + 21*x^12 + 19*x^13 + 11*x^14 + 8*x^15 + 
     22*x^16 + 6*x^17 + 14*x^18 + 21*x^19 + 20*x^20 + 24*x^21 + 9*x^22 + 
     11*x^23 + 14*x^24 + 24*x^26 + 27*x^27 + 24*x^28 + 10*x^29 + 25*x^30 + 
     26*x^31 + x^32

m[4] = 14 + 24*x + 26*x^2 + 22*x^3 + 16*x^4 + 18*x^5 + 19*x^6 + 6*x^7 + 
     22*x^8 + 5*x^9 + 16*x^10 + 8*x^11 + 13*x^12 + 20*x^13 + 27*x^14 + 
     14*x^15 + 25*x^16 + 28*x^17 + 16*x^18 + 26*x^19 + 4*x^20 + 19*x^21 + 
     12*x^22 + 11*x^23 + 2*x^24 + 14*x^25 + 14*x^26 + 16*x^27 + 10*x^28 + 
     20*x^30 + 17*x^31 + 8*x^32 + 27*x^33 + x^34

m[5] = 23 + 17*x + 16*x^2 + 3*x^3 + 27*x^4 + 9*x^5 + 2*x^6 + 21*x^7 + 2*x^8 + 
     26*x^9 + x^10 + 20*x^11 + 27*x^12 + 20*x^13 + 7*x^14 + 4*x^15 + 
     17*x^16 + 10*x^17 + 6*x^18 + 2*x^19 + 3*x^20 + 21*x^21 + 21*x^22 + 
     18*x^23 + 21*x^24 + 3*x^25 + 20*x^26 + 15*x^27 + 6*x^28 + 18*x^29 + 
     12*x^30 + 8*x^31 + 20*x^32 + 3*x^33 + 19*x^34 + x^35

Min(k)   = 96
Max(k-1) = 69
Range of Degree of Secret : deg < 27   ... 秘密情報は27次未満の多項式

Sharing Secrets : 

s[1] = 1 + 10*x + 22*x^2 + 8*x^3 + 27*x^4 + 5*x^5 + 18*x^6 + 22*x^7 + 
     16*x^8 + 18*x^9 + 20*x^10 + 8*x^11 + 26*x^12 + 4*x^13 + 8*x^14 + 
     3*x^15 + 12*x^16 + 10*x^17 + 23*x^18 + 9*x^19 + x^20 + 12*x^21 + 
     11*x^22 + 16*x^23 + 27*x^24 + 15*x^25 + 22*x^26 + 28*x^27 + 17*x^28 + 
     15*x^29 + 19*x^30 + 12*x^31

s[2] = 15 + 10*x + 2*x^2 + 15*x^3 + 6*x^4 + 2*x^5 + 21*x^6 + 22*x^7 + 2*x^8 + 
     22*x^9 + 15*x^10 + 12*x^12 + 2*x^13 + 6*x^14 + 11*x^15 + 19*x^16 + 
     21*x^17 + 24*x^18 + 11*x^19 + 14*x^20 + 2*x^21 + 17*x^22 + x^23 + 
     14*x^24 + 10*x^25 + 15*x^26 + 11*x^27 + 14*x^28 + 15*x^29 + 26*x^30 + 
     26*x^31

s[3] = 6 + 2*x + x^2 + x^3 + 7*x^4 + 18*x^5 + 3*x^6 + 5*x^7 + 18*x^8 + 
     8*x^9 + 13*x^10 + 2*x^11 + 16*x^12 + 8*x^13 + 13*x^14 + 17*x^15 + 
     16*x^16 + 17*x^17 + 3*x^18 + 18*x^19 + 8*x^21 + 21*x^22 + 2*x^23 + 
     22*x^24 + 6*x^25 + 22*x^26 + 26*x^27 + 25*x^28 + 8*x^29 + 7*x^30 + 
     21*x^31

s[4] = 2 + 7*x + 14*x^3 + 28*x^4 + 26*x^5 + 19*x^6 + 27*x^7 + x^8 + 2*x^9 + 
     8*x^10 + 10*x^11 + 20*x^12 + 18*x^13 + 5*x^14 + 24*x^15 + 23*x^16 + 
     x^17 + 5*x^18 + 24*x^19 + 20*x^20 + 25*x^21 + 19*x^22 + 18*x^23 + 
     19*x^24 + 13*x^25 + 8*x^26 + 19*x^27 + 17*x^28 + 14*x^29 + 21*x^30 + 
     2*x^33

s[5] = 18*x + x^2 + 9*x^4 + 4*x^5 + 13*x^6 + 25*x^7 + 9*x^8 + 28*x^9 + 
     20*x^10 + 21*x^11 + 13*x^12 + 14*x^13 + 16*x^14 + 15*x^15 + 10*x^16 + 
     16*x^17 + 27*x^18 + 26*x^19 + 17*x^20 + 23*x^21 + 9*x^22 + 13*x^23 + 
     14*x^24 + 8*x^25 + 21*x^26 + 26*x^27 + 17*x^28 + 8*x^29 + 3*x^30 + 
     5*x^31 + 6*x^32 + 23*x^33 + 10*x^34


Gathered members : {3}

Solution = 2 + 27*x + 18*x^2 + 6*x^4 + 6*x^6 + 8*x^7 + 7*x^8 + 17*x^9 + 
     5*x^10 + 2*x^11 + 3*x^12 + 6*x^13 + 19*x^14 + 4*x^15 + 3*x^19 + 
     15*x^20 + 6*x^21 + 22*x^22 + 3*x^23 + 27*x^24 + 7*x^25

True Secret = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24
     
Gathered members : {1, 5}

Solution = 9 + 27*x + x^2 + 17*x^3 + 4*x^4 + 16*x^5 + 27*x^6 + 2*x^7 + 
     22*x^8 + 8*x^9 + 25*x^10 + 27*x^11 + 28*x^12 + 3*x^13 + 28*x^14 + 
     4*x^15 + 16*x^16 + 22*x^17 + 25*x^18 + 23*x^19 + x^20 + 19*x^21 + 
     11*x^23 + 8*x^24 + 9*x^25 + 18*x^26

True Secret = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24

Gathered members : {1, 4, 5}

Solution = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24

True Secret = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24
     
Gathered members : {1, 2, 3, 4}

Solution = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24

True Secret = 20 + 15*x + 11*x^2 + 15*x^3 + 7*x^4 + 27*x^5 + 3*x^6 + 12*x^7 + 
     15*x^9 + 21*x^10 + 23*x^11 + 23*x^12 + 2*x^13 + 9*x^14 + 9*x^15 + 
     13*x^16 + 28*x^17 + 23*x^18 + 20*x^19 + 4*x^20 + 25*x^21 + 15*x^22 + 
     21*x^23 + 27*x^24