Allow interactive aggregate signature (IAS)
Allow non interactive aggregate signatures (NAS), where aggregation can be done by anyone
The Schnorr equation is satisfied, so the signature can be written as a function of public key combination
厥后，2011年12月20日，比特币焦点开拓团队就把这个多重签名的成果插手到比特币的焦点代码内里。2012年1月，首个多重签名范例的生意业务呈此刻区块链上。
https://scan.wisdchain.com到期日；
When A broadcasts her signature to prove her encrypted currency, B can get enough information to calculate A's private key and get her encrypted currency.
The private key used by A will be one-time, because she needs to send the private key to B.
Wisdom Chain区块欣赏器：按期的付息。
B gets all the private keys and receives the cryptocurrency held by A. at the same time, A also gets the currency of B.
以上是多重签名法则的界说
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Wisdom Chain多重签名
Transaction volume: by aggregating multiple signatures into one signature, the size of multi signature can be greatly reduced, and the bandwidth consumption for network transmission and the occupation of storage space of nodes can be significantly reduced.
最初将私钥最大数量限定为3个，厥后其实已经可以扩展到最多支持15个私钥。生成比特币多重签名地点只需要两步，首先确定签名私钥的个数，其次，确定转账时需要几个私钥举办签名就可以了。
Suppose that the concise process of atomic exchange between A and B through aggregate signature is as follows:
In the privacy protection of wisdomchain's latest white paper, we see the use of aggregate signatures.
对付一个安详、靠得住的系统来讲，免疫单点妨碍长短常重要的。最早也有一些步伐，就是把私钥分成许多份，分隔保管，可是这种土要领存在问题，就是不利便也很不智能。
Use of aggregate signature
债券的）票面利率；
It is proved to be secure in the common public key model
假如回收不经过圈外人参与的去中心化的智能合约的话，那么为了确实推行合约则需要巨大深入的款子谈判，去中心化所带来的问题反而更多了。智能合约大概因为以下几个缺点而无法执行：
B signs a transaction and sends cryptocurrency to A.
A and B store the cryptocurrency in two respective signed addresses.
Because the points on the elliptic curve can satisfy the multiplicative combination law, for the two points X, Y and corresponding scalar (private key) x, y and the origin G on the elliptic curve,then:
其他区块链技能凡是是由第三方提供多重签名处事，但在Wisdom Chain上则是将其作为一个尺度成果。这对付想要实现多重签名成果的自动化编程者而言，也意味着用户可以或许通过接口就可以实现多重签名成果。
中心化条约能自动地向债权人的账户举办汇款和付出；
When creating a multi signature scheme based on Schnorr aggregate signature, in order to ensure that the multi signature signature looks like a single key signature, make the traditional verification method effective, and ensure that the whole process only needs linear sub signature aggregation, the scheme needs to meet the following characteristics:
What is aggregate signature
本金可能面值；
In the case of multi signature with ECDSA, if there are N private keys signed, the N signatures need to be verified respectively. Because of the linear characteristic of Schnorr Signature Algorithm, in the same case, the signatures of N private keys can be "aggregated" into one signature. The principle is as follows:
A uses the other half of the private key to sign and broadcast the transaction receiving cryptocurrency.
https://github.com/WisedomChainGroup
A provides B with an aggregate signature, which needs to be confirmed by B.
At present, there are many implementations of aggregate signature scheme based on Schnorr, and the final scheme given by Blockstream is MuSig. The differences of implementation modes and the specific principle of MuSig can be referred to [8] [9].
如上的权利行使进程很是顺利且轻便，同时也遵循着现实世界的须要条件。智能合约（利钱计较、付出、到期打点以及其他条件）自己在构筑打点系统方面所耗费的庞大本钱就是一种挥霍。出于生意业务代币这一特定目标的生意业务平台则是必须的，并且它的构建一次就能完成，之后就可以全面地处理惩罚所有的债券和证券了。
Performance: it can greatly reduce the cost of verifying signatures. The advantage of Schonrr signature algorithm is obviously. For a multi signer transaction, it needs to be verified many times, and aggregated signature needs to be verified only once, thus enhancing the speed of node verification.
其他区块链技能凡是是由第三方提供多重签名处事，但在Wisdom Chain上则是将其作为一个尺度成果。这对付想要实现多重签名成果的自动化编程者而言，也意味着用户可以或许通过接口就可以实现多重签名成果。在Wisdom Chain上，支持的模式是MN，这意味着一个法则最多可以有M个签名，可是同时可以有N个签名时可以对其举办签名（请留意，N必需小于或便是M）。
Allow each signer to sign his or her own message.
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