Application of Improved Elliptic Curve Digital Signature Algorithm in Bitcoin

Digital signatures algorithm uses to secure transactions of Bitcoin. In all peer to peer electronics transactions don’t need any third party to check the ledger for transfer the amount. Without using any authority, this platform secures all transactions among different people together. It provides security, integrity and non-repudiation for safe and secure transaction.

A decentralized electronic peer-to-peer currency system was launched as Bitcoin in 2009. In end october 2009, this e-currency was launched as more secure with no controlling authority. That time in financial market nobody has taken this seriously. The reason behind developing this e-currency was building most secure public currency in global market. In 2011, a Japanese company MtGox started to exchange Bitcoins against money, Bitcoin arose media’s attention and an increasing number of miners got involved in mining Bitcoins. Bitcoins and all other cryptocurrencies prices goes up and down according to demand, not supply. Why? Because supply or total number of bitcoin is fixed. Cryptography is the science behind security. To secure these transactions without any authority, the evolution begins with security system that we call Digital Signature. A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or document, as analogous to a physical signature on paper. Authentication can be defined as a process by which one corroborates that someone is who they claim they are The purpose of digital signature is to provide a means for an entity to bind its identity to a piece of information. The process of signing entails renovating the message and some secret information held by an entity into a tag called signature. Digital signature represents one of the most widely used security technologies for ensuring un-forge-ability and nonrepudiation of digital data.

Improved version of current security on Digital signatures or Digital authentication is hot topic for researchers in cryptography because of severe crimes and funding of terrorist groups through Cryptocurrencies. Economic warfare to financial havoc, illegal weapons to fund for terrorism is happening through different sources or wiping the amount of bitcoin or security breaches. That’s why this is an important topic.

2018, February 19, University of Oxford, Professor Sean Foley and Jonathan R. Karlsen published a paper on illegal activities related to Cryptocurrencies with collected data from various resources. According to this paper, they find that illegal activity accounts for a substantial proportion of the users and trading activity in bitcoin. For example, approximately one-quarter of all users (25%) and close to one-half of bitcoin transactions (44%) are associated with illegal activity. The estimated 24 million bitcoin market participants that use bitcoin primarily for illegal purposes (as at April 2017) annually conduct around 36 million transactions, with a value of around $72 billion, and collectively hold around $8 billion worth of bitcoin.

A digital signature algorithm (DSA) refers to a standard for digital signatures. It was introduced in 1991 by the National Institute of Standards and Technology (NIST) as a better method of creating digital signatures. Along with RSA, DSA is considered one of the most preferred digital signature algorithms used today. DSA, on the other hand, does not encrypt message digests using private key or decrypt message digests using public key. Instead, it uses unique mathematical functions to create a digital signature consisting of two 160-bit numbers, which are originated from the message digests and the private key. DSAs make use of the public key for authenticating the signature, but the authentication process is more complicated when compared with RSA.

How Does Bitcoin Work?

Bitcoin is a decentralized peer-to-peer digital currency based on public-key cryptography first proposed by Satoshi Nakamoto in 2008, and fully operated in 2009. Bitcoin has various nice properties which makes this cryptocurrency so popular worldwide. The existence of bitcoin is non-inflationary. But according to demand and supply the price goes ups and down with world currency as per exchange. Number of transactions at single time is the highest transaction as per safety and speed. The currency is own by the owner. It provides the separate key to make it more safe. “We will talk about the security logic and how are incidents happening in bitcoin mining and Bitcoin transactions?” It is a proof-of-work based cryptocurrency which allows miners to mint Bitcoin through computation. Different from other traditional financial currencies, willing parties make secure transactions relying on cryptographic protocols rather than trust on third parties. Since there are no central authorities to keep records of transactions, they are confirmed by consensus procedure and stored in a distributed manner. Thus, privacy of users in public transactions is protected using pseudonyms called Bitcoin addresses.

In every electronic document creation or modified document, we use time stamp. You must have seen that on Google Docs or Microsoft Word or any other Word Processor “Last time Modified at 6:30 pm. ” So Time stamping is a use of electronic timestamp to prove the temporal sequence among events. It is first proposed by Haber and Stornetta in 1991 certifying when an electronic document created or last modified. Since Bitcoin transactions are publicly announced, timestamp system is needed for participants to agree on the order of the transaction. The principle of timestamp is that information stored in the blocks is arranged in a chain, and hash of block of items is timestamped while each timestamp includes previous timestamps in its hash value. With the timestamp, data has existed at the time can be proved.

What Validates Currency Transactions?

Till digital currency, we all were verifying from third party( Bank or Government) to verify the details before transaction. In Cryptocurrency transaction, use a cryptographic scheme that is easy to verify but hard to produce the defined form of result without getting a large amount of computational work. This scheme is proposed in Adam Back’s Hack-hash. The principle of proof of work is that for many hash functions, finding an input to generate a value with a predefined leading substring is a low probability event and requires a lot of trial and error. In Bitcoin, finding such suitable inputs is used in block creation which is called mining. The main block in Bitcoin contains transaction to be validated, hash of previous block (implements the timestamp) and a nonce. The hash algorithm used is secure hash Standards (SHA256), and different nonces will be tried until the SHA256 hash value of the block satisfied with the requirements. This will consume a lot of computational power and it is a proof of the miners’ work. Besides validating the transaction to ensure the block integrity, proof-of-work protocol is also used to regulate the Bitcoin supply and reward miners Merkle tree is an important element in Bitcoin. It is a binary tree of hashes proposed by Ralph Merkle that is used to verify data integrity efficiently and securely.

In this tree, every non-leaf node is the ‘concatenate then hash’ value of its child node, and the leaves are computed over data blocks. The final hash value - n in the Merkle tree - is called Merkle root which will be stored in the block header. Since the non-leaf node is expected to have two child nodes, the missing child node is a special case of Merkle tree, just like child node. In this kind of situation, the solution in Bitcoin is straightforward. When forming the nodes in a row, if there are an odd number of nodes, the last node will be duplicated. One of the strengths of Merkle tree is that there is no need to recompute the hash of all data if one data block changes. For example, if the block changed, only one branch from, and finally root n will be recomputed. It requires a much smaller number of hash computations and makes the process more efficient.

Signature and Hashes

In Bitcoin transaction, two cryptographic primitives are used to prevent malicious users breaking the system. A digital signature is used to make sure that the information is signed by the claimed person as well as to test whether the information is modified by some malicious people. Signature process contains signature generation and signature verification. Given a message, the signatory generates a signature by using his private key, and the verifier can use signatory’s public key to verify the message’s authenticity. A cryptographic hash function is applied to the original message to produce a message digest for performance reason. Digital Signature Algorithm (DSA) was the first digital signature scheme accepted legally by government of USA and proposed by NIST in August 1991. ECDSA is a digital signature scheme based on public key cryptosystem ECC, instead of working in a subgroup of Zp ⇤ in DSA, ECDSA works in the group of elliptic curveE(Zp). It has been standardized by many standard committees such as ISO, ANSI, IEEE and FIPS. Hash function is any function that maps data with arbitrary length to a fixed-size, hard-to-inverse value. A little modification on the inputs will produce outputs with big difference. Therefore, hash functions can be used to ensure data integrity. Hash functions are adopted by Bitcoin system mainly in

1. Bitcoin address generation
2. Transactions and blocks generation.

Bitcoin addresses are generated by hashing the public key of ECDSA. As for Bitcoin transaction and blocks generation, two consecutive SHA256 hashes are used.

Transaction and Malware in Transactions (Attacks)

Transaction in Bitcoin is the process of transferring Bitcoin ownership from one Bitcoin address to another. A Bitcoin address is a 160-bit hash of ECDSA public key and stored in Bitcoin wallet together with its related private key. Bitcoin wallet stores one or more Bitcoin addresses and each one can be used only once. One Bitcoin transaction contains zero or more inputs and outputs. An input is reference to outputs of another previous transactions, and the values of transactions are added up and used in the current transaction. An input normally contains three parts: Previous tx is hash of previous transaction, Index is referenced transaction output, and ScriptSig contains a signature and a public key. The ECDSA signature is generated by signing the hash of the transaction, and public key belongs to the payer. Both the signature and public key prove the transaction is created by the owner of the Bitcoin address. An output has two parts: one is value, which is the number of Satoshis that are to be transferred, the other is scriptPubKey, specifying Bitcoin addresses of the one of more payees. Satoshi gave a simplified description of how transaction functions. Considering the middle transaction from owner 1 to owner 2, owner 1 uses his private key sign over the hash value of previous transaction together with owner 2’s public key to create owner 1’s signature. The signature can be verified using owner 1’s public key. Once validated, the transaction is confirmed and put into the block.

Malware in transaction or getting the key without knowing by third party. First time in the history it was raised by a Japanese company MtGox. All the withdrawals happened because of this attack. Basic process of attack into a system to break the code is get the unique ID or Change/Modify the Unique ID. Unique ID is the cryptographic hash of the entire transaction including the signature to identify the Transaction. All the information involved is protected by the signature and cannot be modified by attackers. Because of scripting language that Bitcoin uses, signatures can be modified in some way but still considered as valid. The changes in signature will lead to change of the hash value, that is the transaction ID. If client or exchange software makes Bitcoin transactions by only identifying transaction hashes, it will cause a lot of problems. If one transaction has two different hashes then they need to modify the hash, ScriptSig and scriptPubKey use script language which is a stack-based, complete language using single byte opcode. The original transaction scriptSig specifies that N-bytes of data is pushed onto stack by using opcode PUSHDATA, and the modified scriptSig uses OP PUSHDATA2 (0x4d) to specify the number of bytes to be pushed is its next two bytes.