Secret Sharing and CIDR

Secret Sharing  Threshold Scheme (t,n)( 門檻式 ) Master key (mK) Sub key (sK) Threshold Value t N0. of sub keys n Object: any one of n if gathered the t members would construct the master key.

 Order t-1 polynomial h(x)=a t-1 x t-1 + a t-2 x t-2 … +a 1 x 1 +a 0 (a 0 =mK) mod p  Each partial secret holder i with an IDi, and find h(IDi) to obtain the holder h(IDi). e.g., mK=237, p=257, and h(x)= 37x 2 +29x Assume n=5, t=3 i.e., (3,5) For secret holder 1,with ID1=1, get h(1)=46, [1,46] For 2~5, get [2,186], [3,143], [4,174], [5,22]

 How to obtain the value mK? Find t members to construct the polynomial and therefore, get the mK. Method: Lagrange interpolation method Assumed [2,186], [3,143], [5,22]

n to n+1  how to increase n to n+1: h(x)=a t-1 x t-1 + a t-2 x t-2 … +a 1 x 1 +a 0 (a 0 =mK) mod p  Find the new ID n+1 and put into the polynomial to find h(ID n+1 ) to obtain the new holder [ID n+1,h(ID n+1 ) ].  What will that be if the dealer can not exist.

Problems with proposed scheme  One refinement: Hold mk expose g mk as a secret Assume gather t and multiply the above value can get g mk

CIDR  Classless Inter-Domain Routing (CIDR, pronounced "cider"), introduced starting in 1993, It replaced the previous generation of IP address syntax, classful networks. It allowed increased flexibility when dividing ranges of IP addresses into separate networks. It thereby promoted:1993classful networks More efficient use of increasingly scarce IPv4 addresses.IPv4 Greater use of hierarchy in address assignments (prefix aggregation), lowering the overhead of the Internet- wide routing.hierarchyInternetrouting

IPv4 CIDR  IPv4 CIDR blocks are identified using a syntax similar to that of IPv4 addresses: a four-part dotted-decimal address, followed by a slash, then a number from 0 to 32: A.B.C.D/N. The number following the slash is the prefix length, the number of shared initial bits, counting from the left- hand side of the address..

/27

 For example /11, MCI. Automation Research Systems, a Virginia VAR, leased an Internet connection from MCI and was assigned the /22 block, capable of addressing just over 1000 devices. ARS used a /24 block for its publicly accessible servers, of which was one.MCIVirginiaVAR

Subnet  A subnet mask is a bitmask that encodes the prefix length in a form similar to an IP address - 32 bits, starting with a number of 1 bits equal to the prefix length, ending with 0 bits, and encoded in four-part dotted-decimal format. A subnet mask encodes the same information as a prefix length, but predates the advent of CIDR.subnet maskbitmask  CIDR uses variable length subnet masks (VLSM) to allocate IP addresses to subnets according to individual need, rather than some general network-wide rule. Thus the network/host division can occur at any bit boundary in the address. The process can be recursive, with a portion of the address space being further divided into even smaller portions, through the use of masks which cover more bits.recursive

See IPv4 subnetting reference.IPv4 subnetting reference CIDR ClassHostsMask /321/256 C /311/128 C /301/64 C /291/32 C