Shamir Swot Analysis

A Novel Mathematical Model for Group communication with Trusted Key Generation and

Distribution Using Shamir’s Secret Key and USB

Security

George Thomas, Jashim Jamaludheen Ky, Levin Sibiz, Maneesh Px and Mufeedh{

Department of Computer Science & Engineering

College of Engineering Thalassery,Kannur,Kerala,670101

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Abstract—Authentication and confidentiality are two sides of a coin. A group communication is said to be secure if and only if it preservers both authentication and confidentiality. A group communication is secure if each member of the group is a trusted person. So, individual

Here, each group is uniquely identified by one time session keys. Each group member has a share with

Fig. 1. Registration Process him that can only be accessed by submitting his long term secret. With the knowledge of additional half of total share, each person is able to reconstruct the group key. The data is protected using asymmetric encryption. Individual security has a great influence in group security. Each person need to register with an usb key, which will be considered as his identity together with username and password. The key is divided into n shares in such a way that key is easily reconstructable from any k shares, but even complete knowledge of k - 1 shares reveals absolutely no information about key. This mechanism enables the construction of robust key management schemes or cryptographic schemes that can function efficiently, securely and reliably.

II. PROPOSED SOLUTION

Assume that there are n members U1. . . Un in a group.

In order to achieve secure communication, the groups session keys must be securely distributed among all authorized group members prior to exchanging communication messages. The major responsibility of KGC is to select fresh session

SECRET SHARING

Shamir’s Secret Sharing algorithm in cryptography is developed by Adi Shamir. It is a method of secret sharing, where a secret is divided into pieces, giving each authenticated member its own unique part, where at least half the parts or more than half are needed together to reconstruct the secret.

All shares required together seems to be not practical, and therefore sometimes the threshold scheme is used where any no. of share are sufficient to reconstruct the original secret.

Shamirs (t, n)-threshold scheme. A scheme of Shamir provide an elegant construction of a perfect (t, n)-threshold scheme using a classical algorithm called Lagrange interpolation.

 Goal is to divide some data D (e.g., the safe combination) into n shares D1,D2.D3 in such a way that:

Fig. 3. Secret sharing

Fig. 4. Key reconstruction procedure

– Knowledge of any k or more D shares makes D easily computable.

– Knowledge of any k -1 or fewer shares leaves D completely undetermined.

 This scheme is called threshold scheme. If k equals n then all group members are required together to reconstruct the secret.  Suppose we want to use threshold scheme to share our secret S where k ¡ n.

 Select at random k-1 coefficients a1, a2