**Proxy Blind Signature Scheme based on Non-commutative
Division Semi-rings**

**R. Vijayaragavan **

Associate Professor, Department of
Mathematics, Thiruvalluvar University, Serkkadu, Vellore-632 115

*Corresponding Author E-mail: **rvijayaraagavantvu@gmail.com**

**ABSTRACT:**

Proxy signatures, introduced by Mambo, Usuda and Okamoto, allow a designated person to sign on
behalf of an original signer. Division semi-ring has been playing an important
role in the theory of cryptography as these are non-commutative division
semi-rings used in cryptography. Some digital signature schemes have been given
but no proxy blind signature has been introduced over division semi-rings .In
this paper we have proposed blind proxy signature scheme using conjugacy search problem over non-commutative division semi
rings.

**KEYWORDS:** Proxy blind Signature, Conjugacy
Decision Problem, non-commutative division semi-rings, Conjugacy.

**INTRODUCTION:**

The concept of blind
signatures was introduced by D. Chaum [1]. A blind
signature scheme is a cryptographic primitive in which two entities a user and
a signer are involved. It allows the user to have a given message signed by the
signer, without revealing any information about the message or its signature.
Blind signatures are the basic tools of digital cash payment systems,
electronic voting systems etc. Proxy signatures as mentioned in [2] allow a
designated person called proxy signer, to sign a message on behalf of an
original signer. According to the delegation type, the proxy signatures are
classified as full delegation, partial delegation and delegation by warrant. In
production of coins, the user makes the bank blindly sign a coin using blind
signature schemes. The user is in possession of a valid coin such that the bank
itself cannot recognize nor link with the user. Whenever a user goes through a
valid branch to withdraw a coin, he needs the branch to make proxy blind
signature on behalf of the signee bank. This application leads to the need of
proxy blind signature schemes.

In this paper we are
introducing a proxy blind signature scheme over non-commutative division
semi-rings. The base for our construction is conjugacy
search problem in non-commutative division semi-rings. In conjugacy
decision problem is easy to compute and conjugacy
search problem is computationally hard. In this article we propose a first
blind proxy signature scheme over non-commutative division semi-rings. This
demonstrates the usefulness of division semi-rings in cryptography as
implementation over a computer system.

**1. ****Preliminaries**

**Definition 1**

A semi-ring _{}is a non-empty set, on which operations of addition and
multiplication have been defined as follows

i.
_{} is a commutative monoid
with identity element _{}

ii.
_{}is a monoid with identity element _{}

iii.
Multiplication
distributes over addition from either side

iv.
_{} for all _{}in _{}

**Definition 2**

An element r of a semi-ring _{}, is a “unit” if and only if there exists an element _{} of _{} satisfying _{}The element _{} is called the inverse
of _{} in _{}**. **If such an inverse _{} exists for a unit_{}, it must be unique. We will normally denote the inverse of _{} by _{}. It is straightforward to see that, if _{} and _{} units of_{}, then _{} and In particular _{}. We will denote the set of all units of _{}, by _{}.This set is non-empty, since it contains _{} and is not all of _{}, since it does not contain _{}**.** we have just noted that _{} is a sub-monoid of _{}, which is infact a group. If _{}, Then _{}, is a *division semi-ring.*

**1.1
****Further
cryptographic assumptions on non-commutative division semi-rings**

We
consider some mathematically hard problem in division semi-rings. We say that _{}and _{}are conjugate if there is an
element _{} such that_{}.

**Conjugacy**** Decision Problem (CDP):**

**Instance:**

_{}such that _{}for some _{}

**Objective:
**

Determine
whether _{}and _{}are conjugate or not

**Conjugacy**** Search Problem (CSP):**

**Instance: **

** _{}** such that

**Objective:**

Find
_{}such that _{}

_{ }

**2. ****Proposed Proxy blind Signature Scheme**

In
this section we analysis proposed scheme. Let the message to be signed be _{}be one way hash functions.

**3.1 Key generations using non-commutative division
semi-ring in conjugacy problem**

**Generation of secret and public keys: **

Select a _{}and compute _{}such that _{}is secret key and public key is_{}.

**Temporary key generation by the user: **

Alice choose a random _{}such that _{} and compute _{}as the self-proxy and _{}as the proxy public key.

**Generation of Self proxy warrant:**

Alice user her proxy key to generate the self- proxy warrant as follows:

_{}

is considered as the
warrant on message _{}

Anyone can verify the
warrant as_{}

_{}

**Generation
of self-proxy signature:**

Alice chooses a random ** _{}**and computes

_{}

Is signature generated by
Alice on message _{}

**Verification of Self proxy signature:**

One can compute _{}and accepts iff the conjugacy of the following can proven:

_{}

**3. ****Analysis of Proposed Schemes:**

The security of the proposed
scheme depends on conjugacy search problem as finding
_{}from _{}is conjugacy search problem.
Also find _{}from _{}is a base problem 1.

**Verifiability: **

Alice public key _{} self-proxy
public key _{} and message
warrant _{} appears in the
verification process _{} which is
sufficient for the verifier to get convinced that the signatures are generated
by Alice using the self- proxy concept.

**Strong Identifiability:**

Warrant _{} used in the
verification of the signatures includes original signer and self- proxy
signer’s identity and moreover, their public keys are used in the signature
verification _{}so, it is easy to identify the original and the proxy signer.

**Strong undeniability:**

** _{}**is
used in the verification that indirectly involves

**Strong unforgeability:**

Alice used her secret key_{}and random number _{} to create the
self- proxy key as ** _{}** and proxy
public key as

**CONCLUSION:**

In this paper we propose a
proxy blind signature scheme with which a proxy user is able to make proxy
blind signature and verifier may verify it very similar to proxy signature
schemes. Our protocol meet security attributed based on conjugacy
problem and we analysed the security aspects. Conjugacy search problem and base problem 1 forms the
building blocks for the security in terms of verifiability, strong Identifiability, strong undeniability
and strong unforgeability.

**REFERENCESS:**

1. Chaum D. Blind signature systems*.*
Proceedings of Crypto 83, Springer Verlag. 1984: 153-
158.

2. Mambo M, Usuda K. and Okamoto E. Proxy signatures for delegating signing operation. in
proceedings of the 3rd ACM conference on Computer and Communication Security
(CCS). 1996: 48-57.

3. Kim S, Park S and
Won D. Proxy signatures: Revisited*.* in Y. Han, T.
Okamoto, S. Quing, editors, Proceedings in
International Conference on Information and Communications Security (ICICS), of
LNCS#1334. 1993:223-232.

4. Diffie W. and Hellman M
E. New directions in cryptography*.*
IEEE transaction on Information Theory, 22(6); 1977:74-84.

5. Pointcheval D and Stern J. Probably secure blind signature schemes*. *Proc.
Asiacrypt-96, LNCS#1163.1996:252-265.

6. Boldyreva A. Efficient threshold signature, multisignature and blind signature schemes based on the
Gap-Diffie Hellman group signature schemes.* *available
at http://eprint.iacr.org/2002/118.

7. Anshel I, Anshel M and Goldfeld D. An algebraic method for public key
cryptography. Math. Research Letter (6);1999:287-291.

8. Chaum D, Fiat A and Naor M. Untraceable
electronic cash.* *Proceedings of Crypto 88, LNCS#403; 1988:319-327.

9. Verma GK. Blind signature schemes over Braid group*.*
2008, available at http://eprint.iacr.org/2008/027.

10. Boldyreva A, Palacio A and Warinschi B. Secure
proxy signature schemes for delegation of signing rights. available at
http://eprint.iacr.org/2003/096.

11. Lal S, Awasthi A. K. Proxy blind signature scheme. Journal of
Information Science and Engineering. Cryptology ePrint
Archive, Report, 72,2003.

Received on 18.05.2016
Modified on 30.05.2016

Accepted on 04.06.2016 ©
RJPT All right reserved

*Research J. Pharm. and Tech. 2016; 9(7):913-915.
*

**DOI:** **10.5958/0974-360X.2016.00174.8**