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Revatthy Krishnamurthy^{1}, K.P. Kaliyamurthie^{2}

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Cloud computing is a technology and large  scale computing resources to effectively integrate, and the resources are computed based on cryptographic secure hash functions. The biggest problem of one time signature scheme is the key management. An efficient key management is needed to make onetime signature scheme and the Merkle signature schemes feasible. This paper presents detailed study on onetime signature and Merkle signature schemes.
KEYWORDS 
Cloud computing, onetime signature scheme, Merkle signature scheme, Key generation. 
I. INTRODUCTION 
Cloud is a large group of interconnected computers, which is a major change in how we store information and run application. Cloud computing is used for many bigdata applications and it is cost effective. Data storage and sharing services in the cloud with three entities such as the cloud, the third party Auditor (TPA), and users who participate as a group includes one original user and a number of group users. 
The original user is an original owner of data, and shares data in the cloud with other users [2]. A single message using a given piece of private or public information. The conventional signature schemes like RSA, the same key pair can be used to authenticate large number of documents. Onetime signatures by Merklecalled Merklesignature scheme, which does not require new key pairs for each message. Simple digital signature scheme for fixed  length messages using a oneway function is Lamport's onetime signature scheme. Diffie OTS [3], the merkle OTS [4], the Winternitz OTS [4,5], etc are different signature schemes. The security of onetime signatures is based on cryptographic secure hash functions. The Lamport onetime signature scheme is a signature scheme in which the public key can only be used to sign a single message. The Winternitz onetime signature scheme, the signature size can be reduced at the cost of hash operations of onetime signature scheme is an efficient key management that reduces the amount of public keys and their size is needed. The Merklesignature scheme, in which one public key is used to sign many messages [6][10]. 
The organization of the paper is as follows. Section II presents the review of related work. Onetime signature schemes are explained in section III. Merkle signature scheme is discussed in section IV and section V concludes the paper. 
II. REVIEW OF RELATED WORK 
Cloud computing provides services to customers.Private, community, public and hybrid are the four models of cloud computing [7] [8] [9]. One  time signatures are efficient and secure. Typically, signature parameters are initialized well ahead of the time when messages are to be signed and verified. Several schemes were proposed that use classical authentication schemes such as digital signatures RSA.[EIGamal] for groupbased transformations. However, these conventional methods typically have a high computational costs, and regard to the efficiency of the emerging applications. In contrast, onetime signatures provide the required security services with less computation overhead. 
III. ONETIME SIGNATURE SCHEMES 
In onetime signature scheme[10], we must know in advance how many signatures the user will ever plan on sending. In this scheme, we have to generate on pairs (PKi, SKi) and build a tree using a collision  resistant hash function, h, by hashing each pair of adjacent nodes recursively up the tree to the root. The root is the public key, r. 
A tree is built with onetime signature schemes (PK, SK)s at the nodes. The tree grows from the top to bottom and expensive than the onetime signature scheme. Every time a new pair generated is an expensive task of generating new pairs. 
1. Lamport one  Time signature scheme 
The security of Lamport signature is based on cryptographic hash function. Here, the public key is used to sign a single message. Other secure hash functions also can be used because this signature scheme is very adjustable. If a hash function becomes insecure, it can be easily exchanged by another secure function. The key generation,signing algorithm and verification algorithm are described as follows[10]. 
Key generation 
Consider a hash function 
H : (0, 1)* 
H : (0, 1)s be a cryptographic hash function. 
To sign a message M = (0, 1)k and choose 2 * k random numbers Xij with 1 ≤ i ≤ k and j = {0,1}. 
For each i and j computeYij= H (Xij). 
Here Yijare the public by key and the Yijare the private key values for each 2 * k values. 
Signing a message 
Signature verification 
2. Winternitz Onetime signature scheme 
Key Generation 
We then split the binary representation i = 1of length w. Let us take bi as the integer encoded by the block bi and compute sigi = Hbi (xi) for i = 1,...... t with Ho (xi) = (xi). The signature sig = (sig1//...... // sigt) of the message M is the concatenation of all sigi for i = 1, .....t. 
Signature verification 
IV. MERKLE  SIGNATURE SCHEME 
Key management is the biggest problem in onetime signature scheme. Public key exchanging is very complex and it has not been modified and should be rather short. A new public key is used for every signature and it is quite big in Onetime signature scheme. Using an efficient key management, the amount and size of public key used is reduced to make onetime signature scheme feasible. Merkle introduced the Merkle signature Scheme (MSS), in which one public key is used to sign many messages[10]. 
Key generation 
The root of the tree an,o is the public key pub of the Merkle signature scheme. The Merkle Signature Scheme can only be used to sign a limited number of messages with one public key pub. The possible number of messages as N = 2n. The first step of generating the public key pub is to generate the public keys Xi and private keys Yi of 2n onetime signatures for each public key Yi, with 1 ≤ i ≤ 2n, a hash value hi = H (Yi) is computed. With these hash values hi a Merkle tree is build. The node of the tree ai,j, where i denotes the level of the node. The distance between the leaf and node is the level of the node. Therefore, level i=0 is the leaf of the tree and level i=n is the root of the tree.We number all nodes of one level from the left to right, so that ai,ois the left most node of level i. In the Merkle tree, the hash values hi = ai,o. Each inner node of the tree is the hash value of the concatenation of its two children. So, 
ai,o= H (ao,o// ao,1) and a2,o = H (a1,o // a1,1). 
Therefore, a Merkle tree with 2n leaves and 2n+1 l nodes is build[10]. 
Signature generation 
The Merkle signature scheme, the message M is signed with a onetime signature scheme, resulting in a signature sig1.sig1is evaluated by using one of the public and private key pairs (Xi, Yi). The corresponding leaf of the hash tree to a onetime public key Yi is ao,i= H (Yi). The path of root is A. The path A consists of n+1 nodes i.eAo, ..... An, with Ao = ao,i= pub being the leaf and An = an,0 = pub being root of the tree. To compute this path A, we need every child of the nodes A1, ......An is a child of Ai + 1.The next node is calculated by a brother node called as authi, so that Ai+1 = H (Ai // authi). Hence, to compute every node of the path A, we need brother nodes. These nodes, plus the onetime signature sig' of M is the signature sig = (sig' // auth2 // auth3 // .... authn1) of the Merkle Signature Scheme[10]. 
Signature Verification 
When the receiver verifies the signature of the message i.esig' ,once if it is valid. Then Ao = H (Yi) is calculated and verified by the receiver. Here, Ao = H (Yi) is hash value of the public key of onetime signature. 
V. CONCLUSION 
Onetime signature schemes are effective methods, used for key generation and signature verification. The biggest complexity of onetime signature scheme is the key management. The Merkle signature scheme which is used to overcome the problem of reducing the amount and size of the public key and is used to sign many messages. This paper deals detailed study about the importance of onetime signature scheme and Merklesignature scheme on cloud computing. 
REFERENCES 
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