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How Mimblewimble Could Make Bitcoin Work Better

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Bitcoin

Mimblewimble claims to use a new cryptographic protocol that could revolutionize the way bitcoin works, making it more scalable and private.

The protocol generates a blinding factor that can prove ownership of bitcoins, making private keys unnecessary, and offering a solution to the need to balance bitcoin privacy against fungibility while also improving scalability, according to a white paper that appeared mysteriously on a bitcoin research site authored by a person using a pseudonym.

The author refers to himself as “Tom Elvis Jedusor,” a name taken from the Harry Potter novels.

Bitcoin’s Verification Challenge

Verification

Bitcoin is the first widely used financial system for which all the necessary data to validate the system status can be cryptographically verified by anyone, the white paper notes.

It accomplishes this by storing all transactions in a public database called “the blockchain.” Someone who wants to check this state has to download the whole chain and replay each transaction, checking each one as they go.

It would be easier if an auditor only had to check data on the outputs themselves, but this is not possible since they are only valid if the output is at the end of a chain of prior outputs. The whole blockchain has to be validated to confirm the final state.

Considering that the transactions are cryptographically atomic, the outputs that go into and emerge from every transaction are very clear. The “transaction graph” that results reveals a lot of information and is subjected to analysis by numerous companies whose business model is to monitor and control the lower classes.

This makes it very non-private and even dangerous to use.

Proposed Solutions

Some solutions to this have been proposed, Jedusor notes. Greg Maxwell discovered how to encrypt the amounts so that the graph of the transaction is faceless but still validates the sums. Maxwell also produced CoinJoin, a system for bitcoin users to combine interactively transactions, confusing the transaction graph.

Nicolas van Saberhagen developed a system to blind the transaction entries, further clouding the transaction graph. Shen Noether combined the two approaches to obtain the “confidential transactions” of Maxwell and the “darkening” of van Saberhagen.

These solutions would make bitcoin safe, Jedusor observes. But too much data can make things worse. Confidential transactions require multi-kilobyte proofs on every output. van Saberhagen signatures require every output to be stored forever, as it is not possible to truly tell when they are spent.

Maxwell’s CoinJoin needs interactivity. Yuan Horas Mouton fixed this by making transactions freely mergeable, but he had to use pairing-based cryptography which can be slower and harder to trust. He called this “one-way aggregate signatures” (OWAS).

OWAS combined the transactions in blocks. It could be possible to combine across blocks (perhaps with some glue data) so that when the outputs are created and destroyed, it is as if they never existed, Jedusor notes.

Then, to validate the entire chain, users only need to know when money enters the system (new money in each block as in bitcoin or Monero or peg-ins for sidechains) and final unspent outputs. The rest can be removed and forgotten.

Confidential transactions hide the amounts and OWAS to blur the transaction graph by using less space than bitcoin to enable users to verify the blockchain.

Mimblewimble prevents the blockchain from referencing all of a user’s information, Jedusor observes.

Confidential Transactions

The first step is to remove bitcoin Script. It is too powerful, so it is impossible to merge transactions using general scripts.

Instant transaction

Maxwell’s Confidential Transactions are enough (after some small modification) to authorize the spending of outputs and also to make combined transactions without interaction. This is identical to OWAS, enabling the relaying nodes to take some transaction fee or the recipient to change the transaction fee. Bitcoin cannot do these additional things.

In Confidential Transactions work, the amounts are coded by the following equation: C = r*G + v*H.

C is a Pedersen commitment, G and H are fixed nothing-up-my-sleeve elliptic curve group generators, v is the amount, and r is a secret random blinding key.

Attached to this output is a rangeproof proving that v is in [0, 2^64], so the user cannot exploit the blinding to produce overflow attacks, etc.

To validate a transaction, the verifier will add commitments for all outputs, plus f*H (f being the transaction fee that is given explicitly) and subtracts all input commitments. The result must be 0, proving no amount was created or destroyed overall.

To create such a transaction, the user has to know the sum of the values of r for commitments entries. Therefore, r-values (and their sums) serve as secret keys. If the r output values are made known only to the recipient, an authentication system exists. Unfortunately, by keeping the rule that commits all to add up to zer0, this is impossible since the sender knows the sum of all his r values, and therefore knows the recipient’s r values sum to the negative of that.

Instead, the transaction is allowed to sum to a non-zero value,  k*G, and require a signature of an empty string with this as key, proving its amount component is zero.

The transactions can have as many k*G values as they want, each with a signature, and sum them up during verification.

Creating Transactions

To create transactions, the sender and recipient do the following:

1) The sender and recipient agree on the amount to send. Call this b.

2) The sender creates a transaction with all inputs and change output(s), and gives the recipient the total blinding factor (r-value of change minus r-values of inputs) along with the transaction. The commitments sum to r*G – b*H.

3) The recipient chooses random r-values for his outputs, and values that sum to b minus fee, then adds these to the transaction (including range proof). Now the commitments sum to k*G – fee*H for some k that only the recipient knows.

4) The recipient attaches the signature with k to the transaction, and the explicit fee.

Creating transactions like this supports OWAS already. To demonstrate this, consider two transactions that have a surplus k1*G and k2*G, and the attached signatures with these. Then combine the lists of inputs and outputs of the two transactions, with both k1*G and k2*G to the mix, and it is again a valid transaction. From the combination, it is not possible to know which outputs or inputs are from which original transaction.

Because of this, the block format changes from bitcoin to this information:

1) Explicit amounts for new money (block subsidy or sidechain peg-ins) with whatever else data this needs. For a sidechain peg-in, it may reference a bitcoin transaction that commits to a specific excess k*G value.

2) Inputs of all transactions.

3) Outputs of all transactions.

4) Excess k*G values for all transactions.

Each is grouped together because it does not matter what the transaction boundaries are originally. In addition, lists 2, 3 and 4 should be coded in alphabetical order, since it is quick to check and prevents the block creator from leaking any information about the original transactions.

The outputs are now identified by their hash, rather than their position in a transaction that could easily change. Therefore, it should be banned to have two unspent outputs equal at the same time to avoid confusion.

Merging Transactions

Maxwell’s Confidential Transactions has already been used to create a non-interactive version of his CoinJoin. Another idea is needed. A non-interactive version of this is created to show how it is used with several blocks.

Each block can be seen as one large transaction. To validate it, add the output commitments together, then subtract the input commitments, k*G values, and the explicit input amounts times H. The transactions from two blocks can be combined to form a single block, resulting again in a valid transaction.

The difference is that output commitments have an input commitment equal to it, where the first block’s output is spent in the second block. Both commitments can be removed and still have a valid transaction. There is not even the need to check the rangeproof of the deleted output.

The extension of this idea, all the way from the genesis block to the latest block, shows that each non-explicit input is deleted with its referenced output. All that remains are the unspent outputs, explicit input amounts and every k*G value.

The entire mess can be validated as if it were one transaction by adding all unspent commitments output, subtracting the values k*G, validating explicit input amounts (if there is anything to validate) and subtracting them times H. If the sum is zero, the complete chain is good.

When a user downloads the chain, the following data is needed from each block:

1) Explicit amounts for new money (block subsidy or sidechain peg-ins) with whatever else data this needs.

2) Unspent outputs of all transactions, along with a merkle proof that each output appeared in the original block.

3) Excess k*G values for all transactions.

Bitcoin currently has about 423000 blocks, totaling around 80GB of data on the hard drive to validate everything. The data represents around 150 million transactions and 5 million
unspent, non-confidential outputs.

Each unspent output on a Mimblewimble chain is around 3Kb for rangeproof and Merkle proof. Each transaction adds around 100 bytes: a k*G value and a signature.

The block headers and explicit amounts are negligible. Added together this is 30Gb – with an obscured transaction graph and a confidential transaction.

Also read: Mimblewimble: A stripped down version of bitcoin improves privacy, fungibility and scalability 

Questions and Intuition

The following questions arise.

Q: If you delete the transaction outputs, the user cannot verify the rangeproof and may be a negative amount is created.

A: This is acceptable. For the entire transaction to validate, all negative amounts must have been destroyed. Users have SPV security only that no illegal inflation happened in the past, but the user knows that at this time, no inflation occurred.

Q: If you delete the inputs, double spending can happen.

A: In fact, this means someone may claim that unspent output was spent in the old days. But this is impossible, otherwise the sum of the combined transaction could not be zero.

An exception is that if the outputs amount to zero, it is possible to make two that are negatives of each other, and the pair can be revived without anything that breaks. So to prevent consensus problems, outputs 0-amount should be banned. Just add H at each output.

They all amount to at least 1 at present.

Future Research

Here are some questions that cannot be answered at the time of this writing.

1) What script support is possible? One would need to translate script operations into some discrete logarithm information.

2) Users are required to check all k*G values when in fact all that is needed is that the sum is of the form k*G. Instead of using signatures, is there another proof of discrete logarithm that could be combined?

3) There is a denial-of-service option when a user downloads the chain. The peer can give gigabytes of data and list the wrong unspent outputs. The user will see that the results do not add up to 0, but cannot tell where the problem is.

For now, maybe the user should just download the blockchain from a Torrent or something where the data is shared between many users and is reasonably likely to be correct.

Images from Shutterstock.

Important: Never invest (trade with) money you can't afford to comfortably lose. Always do your own research and due diligence before placing a trade. Read our Terms & Conditions here. Trade recommendations and analysis are written by our analysts which might have different opinions. Read my 6 Golden Steps to Financial Freedom here. Best regards, Jonas Borchgrevink.

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3.9 stars on average, based on 8 rated postsLester Coleman is a veteran business journalist based in the United States. He has covered the payments industry for several years and is available for writing assignments.




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  1. Ade

    September 4, 2016 at 11:25 pm

    Is that you Dr Satoshi ?

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Bitcoin

Bitcoin Price Consolidates After Steep Loss as Market Cap Holds Below $100 Billion

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Bitcoin’s market capitalization remains firmly capped below $100 billion on Friday, as prices struggled to regain momentum following a catastrophic selloff earlier in the week. Although bitcoin remains firmly in the grip of the bears, price action over the last 24 hours suggests the worst of the downshift had passed.

BTC/USD Update

The bitcoin price is currently trading at $5,555.00 on Coinbase, having gained 2.6% over the previous 24 hours. The leading digital currency is still trading at a premium on Bitfinex, though the price spread has narrowed to around $120. BTC printed a low of $5,530.90 on Bitfinex but has since recovered near $5,674.

Aggregate pricing data provided by CoinMarketCap show a 24-hour return of 2.3% for BTC. Based on those metrics, the digital currency is averaging a price-per-coin of $5,616. That gives bitcoin a total market capitalization of $97.6 billion, down from $111 billion earlier in the week.

Bitcoin suffered a double-digit loss on Wednesday, with prices eventually piercing below $5,200 in the following session. That marked the lowest level in well over a year. At the same time, the broader cryptocurrency market plummeted to a low of around $176 billion as altcoins and tokens lost nearly $30 billion in value in less than two days.

At the time of writing, the combined crypto market cap had recovered to around $184.8 billion, though trade volumes had declined by roughly a quarter to $18.8 billion.

Virtual currency exchanges processed more than $6.3 billion worth of bitcoin trades in the last 24 hours. BitMEX, a leading derivatives platform, processed a whopping 29.3% of all bitcoin trades. No other exchange even came close in terms of daily turnover.

Recovery Likely

Bitcoin’s steep and sudden reversal followed a period of unprecedented calm for the virtual currency. As of Monday, bitcoin’s volatility index had fallen to the lowest level in over two years. The 30-day volatility index has since more than doubled to 2.15%, according to bitvol.info.

The sudden rush to liquidate BTC and other crypto holdings occurred on the eve of the bitcoin cash hard fork. The fork, which was initiated Thursday, has divided the bitcoin cash community into two camps with an ensuing tug of war over hash rate and user support. At the time of writing, the bitcoin ABC implementation was in the lead in terms of blocs mined.

Bitcoin’s massive decline, which has pushed prices deeply into oversold levels, is likely to be scooped up by bargain hunters in the coming days. The means a return to $6,000 – a level commonly associated with mining costs – shouldn’t be ruled out. If history is any indication, the market has a vested interest in keeping prices above that level.

Disclaimer: The author owns bitcoin, Ethereum and other cryptocurrencies. He holds investment positions in the coins, but does not engage in short-term or day-trading.

Featured image courtesy of Shutterstock.

Important: Never invest (trade with) money you can't afford to comfortably lose. Always do your own research and due diligence before placing a trade. Read our Terms & Conditions here. Trade recommendations and analysis are written by our analysts which might have different opinions. Read my 6 Golden Steps to Financial Freedom here. Best regards, Jonas Borchgrevink.

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4.6 stars on average, based on 665 rated postsSam Bourgi is Chief Editor to Hacked.com, where he leads content development for one of the world's foremost cryptocurrency resources. Over the past eight years Sam has authored more than 10,000 articles and over 40 whitepapers in the fields of labor market economics, emerging technologies, cryptocurrency and traditional finance. Sam's work has been featured in and cited by some of the world's leading newscasts, including Barron's, CBOE and Forbes. Contact: sam@hacked.com Twitter: @hsbourgi




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Analysis

Crypto Update: Coins Consolidate After Key Breakdown

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The cryptocurrency segment is still under the influence of this week’s key technical breakdown that carried several majors below crucial support levels. Bitcoin’s moves have been dominating the market in recent days, and as the most valuable coin formed a short-term bottom, the top coins entered a choppy consolidation phase, retracing some of their steep losses.

Ripple and Stellar continue to outperform the broader market from a technical perspective, and some other coins, like Ethereum and Monero are also holding up above their previous bear market lows, but the overall picture is still overwhelmingly bearish in the market. The total value of the coins is slightly above the $180 billion mark, but further losses are likely in the coming weeks, with all of the majors being well below the breakdown levels, confirming the move.                

BTC/USDT, 4-Hour Chart Analysis

Bitcoin found support near the $5350 price level even though it spiked as low as $5200 during the rout, while the bounce carried the coin up to $5650. The breakdown is clearly intact in BTC and our trend model remains on sell signals an all time-frames, with a test of the $5000-$5100 zone still being likely in the coming period.

Bitcoin faces strong resistance in the long-term zone near $5850, with further key levels at $6000, $6275, and traders and investors shouldn’t open new positions here, with the long-term downtrend clearly being intact.

XRP/USDT, 4-Hour Chart Analysis

Ripple overtook Ethereum in terms of market capitalization again, thanks to its relative strength this week, and the coin is still clearly holding up above the long-term support zone between $0.42 and $0.46.

That said, our trend model is still on a short-term sell signal, and given the bearish segment-wide trends traders shouldn’t enter new positions here, even as the coin will likely be among the leaders of the future rally attempts. Further support levels are found near $0.375 and $0.355, while resistance is still ahead at $0.51, $0.54, and $0.57.

Ethereum Holding Its Ground above Bear Market Low

ETH/USD, 4-Hour Chart Analysis

While Ethereum failed to recapture the $180 resistance level during the bounce, it also avoided a sustained move below the previous bear market low near $170, despite the spikes towards the $160 support. Ethereum short-term stability is a slightly positive sign, but without further signs of strength, the coin remains in a clearly bearish technical setup. With that in mind, traders and investors should still stay away from the coin, as odds still favor the continuation of the broader downtrend.

LTC/USD, 4-Hour Chart Analysis

Litecoin continues to trade below the $44 support/resistance level after the clear break to new bar market lows, and it remains one of the weakest major from a technical perspective. A move towards the next major support zone near $38 is likely in the coming weeks, even if a bounce up to the $47 level is in the cards. Litecoin is on sell signals on both time-frames in our trend model as well, with further strong resistance levels ahead at $51 and $56.

EOS/USD, 4-Hour Chart Analysis

EOS is hovering around the key support zone near $4.50 since a spike towards the bear market low near $4.30 during the steep selloff. The weak bounce didn’t change the technical setup, and the coin is still likely to fall below the previous low, as the declining long-term trend is clearly intact. Our trend model is on sell short-, and long-term trend signals, with strong resistance levels ahead at $5 and $5.35.

Featured image from Shutterstock

Disclaimer:  The analyst owns cryptocurrencies. He holds investment positions in the coins, but doesn’t engage in short-term or day-trading, nor does he hold short positions on any of the coins.

Important: Never invest (trade with) money you can't afford to comfortably lose. Always do your own research and due diligence before placing a trade. Read our Terms & Conditions here. Trade recommendations and analysis are written by our analysts which might have different opinions. Read my 6 Golden Steps to Financial Freedom here. Best regards, Jonas Borchgrevink.

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4.7 stars on average, based on 396 rated postsTrader and financial analyst, with 10 years of experience in the field. An expert in technical analysis and risk management, but also an avid practitioner of value investment and passive strategies, with a passion towards anything that is connected to the market.




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Bitcoin

Bitcoin Price Rebounds After Market Evacuation; XRP Kickstarts Decoupling Process?

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After two days in which $38 billion left the global crypto market cap, anyone who was in doubt over the fragility of the market at large has now been firmly answered.

Two competing theories have arisen over the source of the crash, with many suggesting the ongoing Bitcoin Cash hardfork saga as a possible culprit.

However, the more likely explanation appears to be the closing of Bitcoin future trades on the Chicago Board Options Exchange (CBOE). The same thing happened on the exact same date last year, right before the big bull run, and can be explained by traders selling off BTC just before the closure date (to be bought back later at a cheaper price).

Bitcoin Price Stabilizes…?

Bitcoin actually withstood the worst of the dip for the first few hours on Wednesday, and it originally  looked like we were witnessing an altcoin-only crash.

But eventually BTC got dragged into the mess and sunk 15% down to the $5,358 mark. Since then the price has stabilized at $5,500, and it has been there for six hours at time of writing. However, the previous level of $5,600 was also held for six hours before eventually continuing to plunge, so this may not turn out to be the last of it.

BTC volumes hit six-month highs during the sell-off, reaching $9 billion – a volume not seen since May. Surprisingly, if we exclude the BitMEX derivatives trading, then the highest concentration of BTC trades have come from the BTC/JPY (Japanese yen) pair. The $300 million worth of trades on the Liquid exchange represents 92% of all activity on that platform, and the dominance of Japanese money in BTC’s charts is a rare sight.

The Great Decoupling

Even those who aren’t fans of Ripple and XRP have been noticing the coin’s tendency to move independent of BTC for a while now. There’s an idea circulating that XRP is in the process of decoupling from Bitcoin, and its reaction in the wake of the market wide crash lends credence to the notion.

Following the crash, XRP shot up by 9.4%, as the coin price rose from $0.432724 up to $0.473791. That’s the biggest growth out of all the major altcoins, and it was also enough to send XRP to second place in the market cap rankings, as covered here earlier.

While most other major alts neared September-August lows during the recent dip, XRP is still way above that range, and is already pushing past the $0.45 price which we had gotten used to during October’s stasis.

Like Bitcoin, if we exclude the XRP transaction mining on the ZBG exchange, the most concentrated trade is the XRP/JPY pair on Bitbank.

Disclaimer: The author owns bitcoin, Ethereum and other cryptocurrencies. He holds investment positions in the coins, but does not engage in short-term or day-trading.

Featured image courtesy of Shutterstock.

Important: Never invest (trade with) money you can't afford to comfortably lose. Always do your own research and due diligence before placing a trade. Read our Terms & Conditions here. Trade recommendations and analysis are written by our analysts which might have different opinions. Read my 6 Golden Steps to Financial Freedom here. Best regards, Jonas Borchgrevink.

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4.4 stars on average, based on 89 rated postsGreg Thomson is a full-time crypto writer and digital nomad. He eats ICOs for breakfast and bleeds altcoins. Wherever he lays his public key is his home.




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