4 added 707 characters in body
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Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

UntilAfter January 2017, Monero does not hide the amount sent in each transaction. In January, RingCT will hidehid the amounts of each transaction by default, which will makemade Monero much more private. From ZCash's currently scheduled release date in October 2016 until January 2017,This helped Monero reach feature parity with ZCash is, which was the only coin that should be able tocould hide the amount of a transaction amountsfor a few months.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you cannot find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In Monero, all transactions are private by default. For ZCash, transactions are transparent by default and optionally private. This is a problem for ZCash since less than 5% of the total ZCash coin supply is "hidden" at the time of writing. Thus, Monero benefits from all its users using privacy features, whereas for ZCash, an attacker can simply isolate the few users who are using the privacy features. In Bitcoin, transactions appear suspicious if mixing services are used. For ZCash, this is basically the same story. For Monero, few transactions appear suspicious because they all look similar.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota. This was presented shortly before the ZCash launch. Monero now has RingCT implemented and a GUI wallet, and ZCash has obviously launched.

Monero slide

ZCash slide

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2017, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's currently scheduled release date in October 2016 until January 2017, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you cannot find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

After January 2017, RingCT hid the amounts of each transaction by default, which made Monero much more private. This helped Monero reach feature parity with ZCash, which was the only coin that could hide the amount of a transaction for a few months.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you cannot find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In Monero, all transactions are private by default. For ZCash, transactions are transparent by default and optionally private. This is a problem for ZCash since less than 5% of the total ZCash coin supply is "hidden" at the time of writing. Thus, Monero benefits from all its users using privacy features, whereas for ZCash, an attacker can simply isolate the few users who are using the privacy features. In Bitcoin, transactions appear suspicious if mixing services are used. For ZCash, this is basically the same story. For Monero, few transactions appear suspicious because they all look similar.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota. This was presented shortly before the ZCash launch. Monero now has RingCT implemented and a GUI wallet, and ZCash has obviously launched.

Monero slide

ZCash slide

3 fixed typo, added clarity on dates
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Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 20162017, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's currently scheduled release date in October to2016 until January 2017, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you can notcannot find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2016, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's release date in October to January, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you can not find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2017, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's currently scheduled release date in October 2016 until January 2017, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you cannot find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

2 added slides; added 8 characters in body
source | link

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2016, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's release date in October to January, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you can not find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2016, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's release date in October to January, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you can not find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Adding this answer to make it simpler to those who can not understand the top response.

ZCash uses a new cryptography tool called zk-SNARK (don't worry about the name). This is different than the ring signatures that Monero uses. Without getting into too much detail, this is how they both work:

zk-SNARKs use the entire blockchain when making transactions, whereas ring signatures in Monero instead hide it in certain parts of the blockchain chosen randomly (4 parts by default). Ring signatures have been around for much longer and have undergone years of peer review, while zk-SNARKs are new and have little to no review in their current state.

Until January 2016, Monero does not hide the amount sent in each transaction. In January, RingCT will hide the amounts of each transaction, which will make Monero much more private. From ZCash's release date in October to January, ZCash is the only coin that should be able to hide the transaction amounts.

ZCash introduces a new risk where a group of users can collude (work together) to counterfeit an unlimited number of coins without detection. Since you can not find out how many coins are in circulation at any given time, it would be very difficult or impossible to tell if this had happened. You can still check how many total coins are on the Monero blockchain.

In a much more general sense, ZCash may represent what private coins will look like in the future, but it is still trying to figure out how to deal with new vulnerabilities. Monero is not finished either, although everything that is a part of the current code works very well.

Attached are a few slides from a PowerPoint regarding anonymous cryptocurrency coins presented at the University of Minnesota.

Monero slide

ZCash slide

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