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Due to the rapid growth of online transactions on the Internet, authentication, non-repudiation and integrity are very essential security requirements for a secure transaction. To achieve these security goals, digital signature is the most efficient cryptographic primitive. Many authors have proposed this scheme and prove their security and evaluate the efficiency. In our paper, we present comprehensive study of conventional digital signature schemes based on RSA, DSA and ECDSA (Elliptic Curve Digital Signature Algorithm) and the improved version of these scheme.

Nowadays all important works and transactions come in various electronic mechanism forms such as E-com- merce, E-government, E-shopping, E-mails, E-learning etc. All these E-services need to establish an electronic framework that achieves the security, confidentiality, authenticity, integrity and non-repudiation of the sensitive information is being moved among deferent parties; because the success of these services is entirely dependent on security. The most important solution to address these critical challenges is digital signature. All information transmitted must be first signed by its original sender digitally. In our professional lives, the person might reject which he implemented signature in a instrument of a session, but to reject a digital signature is impossible be- cause making that is to principally evidence which the security for private key is jeopardized before establishing for digital signature. Thus, the matter of fact which creation for digital signature might need secure private key, while the symmetric public key is applied to declare the signature. Thus, non repudiation is basic characteristic for digital signature. There are some correcting schemes, like digital signature, that might link simultaneously the identity for an organization or system to person with the private key and the public key, so hard of individual rejects of digital signature. Thus, the digital signature will respond for the following necessities [

− The receiver might check the signature for transmitter. However he could not change.

− While the transmitter transmits the signature message to the receiver, he can not reject of the transmit message.

− While the transmitter or receiver had contention about the content and source of message, they might offer the tightener to proof which the transmitter has set that the signature of the message which previously been transmit.

But digital signature is various on signatures that written by hand. The handwritten signature is similar and also differs from one individual to another one. Thus, simulation be potential, no attention for any language is applied. In computer science, digital signature is a chain composition, from digits that are 0 and 1, which differs through the message and is impossible to simulate. Digital signatures are being used to achieve integrity, non-repudiation and authentication of the digital data in transmission among different end users. Digital signature offers suitable architecture for sending secure messages by using different algorithms. The digital signature algorithms generally are consisting of three sub phases:

1) Key generation symmetric or asymmetric algorithm.

2) Signing algorithm.

3) Signature verification algorithm [

The symmetric key algorithm generates single key that is shared by sender and receiver. On other hand, the asymmetric key algorithm generates two keys: public and private keys. The public keys are shared between two parties; in contrast the private keys are keeping secret. During second phase signing algorithm the digital signa- ture is generated by taken plain text i.e. private key, sensitive data, and message as input. After that, the sender sends the message along with generated signature to the intended recipient. Signature verification algorithm is executed at recipient end to ensure the received data [

RSA/DSA | ECC-Based Scheme |
---|---|

1024 | 160 |

2048 | 224 |

3072 | 256 |

7680 | 384 |

15,360 | 512 |

order to overcome some of vulnerabilities. We review some of the improvement techniques of digital signature schemes that achieved with respect to various perspectives. In RSA, it is fault tolerance perspective, while in DSA, they are speed of operation computational perspective and longtime of computations perspective. And in ECDSA, they are efficiency perspective and speed of operation computational perspective.

This paper is organized as: section II briefs about digital signature schemes, Section III presents a comparison between improved schemes and original schemes and section IV shows the unresolved problems and further re- search.

The RSA (short of Rivest Shamir Adleman) used modulo concept in arithmetic for perform signature of a message digitally [

− Both sender and Receiver create primes

− Computes

− Selects a integer number

− Computes integer

− Signature Generation process are as the following:

A message

Sender computes the signature

− Verification process of Alice Signature is as the following:

Bob chooses the public key

Bob computes

Bob verifies that

DSA(short of Digital signature algorithm) that use different domain parameters such as

− A prime modulus is

− A prime divisor for

− A generator for the sub group for order

− The private key that is a randomly integer elected in the range

− The public-key is

− Message has

The message

−

−

−

Alice transmits message

−

−

−

−

−

If

Elliptic Curve Digital Signature Algorithm(ECDSA) is the version for elliptic curve cryptographic for digital signature algorithm [

− Parameter generation: The two field elements in

Selects integer

Computes

Public key of Alice is

− Signature generation: For perform signature of a message

By domain parameters

She Computes

Computes

Computes

Thus, the signature of the message

− Signature Verification: For verify of Alice’s signature

Check which two integers

Calculates

Calculates

Calculates

The message signature is valid if

We describe two improved schemes for original RSA which can maintain the fault tolerance function. These schemes provide security requested when data transmitted over network.

Fault Tolerance Perspective: There are a security vulnerability in Lin et al.’s scheme [

In proposed scheme, the major method is to provide two matrix of the prime numbers. In order to overcoming a security vulnerability. While a somebody intercepts matrix of message which transferred then try to permu- tation columns and rows in the matrix. In order establish a new message where has same signature

Since

where

In the next section, we offer some improved schemes based on traditional DSA. The researchers modified of this scheme from two perspectives which are speed of operation computational perspective and a long time of computations perspective. On Speed of Operation Computational Perspective, the security of big data the environment demanded and especially, with the sharp increment of data capacity. So, necessity utilization various security technologies are demanded to achieve more speed. The researchers in [

On long Time of Computations Perspective, it is known in advance, traditional DSA algorithm requires a new unique and random integer

ECC is a methodology of public-key cryptography that based on algebraic structure. An ECC scheme helps in obtaining the wanted security level with smaller keys than that of the corresponding RSA schemes. Speed and efficient use of power, and storage are some of the important merits of utilizing smaller keys. Next we will review some enhancement techniques of ECDSA.

− Efficiency Perspective: ECDSA became a standard and will be used in information security system. But it could not be used in the devices that have limited compute and storage capacity such as ATM, smart card and PDA. In [

− Speed of Operation Computational Perspective: The key factor to the overall performance of ECDSA is the optimization of scalar multiplication because it is time consuming process. [

In this survey, we have presented a comparison between the improved digital signatures schemes and original conventional schemes as shown in

In this section, we presents the computational costs for key generation, signing and verification.

Scheme | Advantages | Drawback |
---|---|---|

Lin et al.’s Scheme [ | Is able to detect error which occurs in computational operations or the process of data transfer. Also it can able to correct such error. Applied in cloud computing. | None |

Xue et al.’s Scheme [ | Integrates fault tolerance It is secure and more reliable with respect to chosen cipher text attack. | It is slow. |

Scheme | Advantages | Drawback |
---|---|---|

Z. Hairong et al.’s Scheme [ | It improves the computational speed. Without using the pre-computation condition verification is speedup. It does not require modular inversion operation in verification. | It improve effectively the operation speed particularly for a large no of message to be signed & verify. Verification speed is less than IDSA. |

G. Han et al.’s Scheme [ | Value of k may not be changed for every new signature. More secure than the original scheme. | None |

Scheme | Advantages | Drawback |
---|---|---|

H. Junuru et al.’s Scheme [ | Can be embedded on devices that have limited computational & storage capacity. Reduce the computational cost of signer. | Can not reduce the computational cost of verifier. |

H. Li et al.’s Scheme [ | Speed up the computation of Elliptic Curve Scalar Multiplication without extra memory Suitable for hardware implementation. Small growth rate with k-bit length. | None |

S. Lamba et al.’s Scheme [ | No of point addition, multiplication and doubling. Improve execution speed and security Reduces no of parameters made public. Removes the overheads with regards to calculating the parameter r. | None |

signature generation and verification.

The following signature schemes are suitable if they meet the requirements of key lengths and parameter values, which were suitable for the creation of qualified electronic signatures and qualified certificates.

We have explored some unresolved problems and difficulties in different digital signature schemes that are considered as good new research opportunities. There are some aspects for future works, the idea to optimize and enhance security level and increase performance for different schemes [

− In order running, the RSA algorithm requires more time and lots of memory [

− Speed of processing is a main drawback of RSA algorithm to each of hardware or software execution [

− DSA needs for more time of processing, computational overhead and increased key storage necessity.

− DSA consumes a big amount of computing resources like CPU time, battery power, and memory.

− ECDSA shares three points publicly which makes it feasible for an adversary to measure the private key of the signer.

− ECDSA performances depend on most expensive operation i.e. scalar multiplication, elliptic curve point multiplication and modular inversion operation. These unsolved problems are considered as good new research opportunities for researchers a digital signature field.

Operation | Signature Scheme |
---|---|

Generation | ECDSA is faster, then DSA, and RSA. |

Verification | RSA is fastest means several times faster than ECDSA and DSA. |

Encryption/Decryption | encryption is very fast in RSA. slow decryption and slow key exchange due to key pair generation. |

Scheme | Security depend on | Parameter bit length |
---|---|---|

RSA | Integer Factorization Problem | 1976 |

DSA | Discrete Logarithm Problem | |

ECDSA | Elliptic Curve Discrete Logarithm Problem |

Due to the increase of online transactions on the Internet, the importance of authentication continues to increase. Thus, there is a need for us to develop mechanism for an authentication of computer-based information. One of the authentication mechanisms is a digital signature. And also digital signature can provide authorization and non-repudiation in information security field. This paper gives deep insight for original digital signature schemes and recently improvement schemes. It described a brief survey of some proposed schemes to improve traditional digital signature schemes RSA, DSA and ECDSA. The improvements in original schemes are achieved from several perspectives. In RSA scheme, it is fault tolerance perspective, while in DSA, they are speed of operation computational perspective and longtime of computations perspective. And in ECDSA, they are efficiency perspective and speed of operation computational perspective. Then it offers a comparative study between original and improved schemes.

We would like to thank to Dr. Jayaprakash Kar for his valuable suggestions and comments that helped im- proving this works. This support is greatly appreciated.