数字签名是什么
数字签名是什么? - justjavac(迷渡) - ITeye技术网站
今天,我读到一篇。
它用图片通俗易懂地解释了,"数字签名"(digital signature)和"数字证书"(digital certificate)到底是什么。
我对这些问题的理解,一直是模模糊糊的,很多细节搞不清楚。读完这篇文章后,发现思路一下子就理清了。为了加深记忆,我把文字和图片都翻译出来了。
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数字签名是什么?
作者:David Youd
翻译:阮一峰
鲍勃有两把钥匙,一把是公钥,另一把是私钥。
鲍勃把公钥送给他的朋友们----帕蒂、道格、苏珊----每人一把。
苏珊要给鲍勃写一封保密的信。她写完后用鲍勃的公钥加密,就可以达到保密的效果。
鲍勃收信后,用私钥解密,就看到了信件内容。这里要强调的是,只要鲍勃的私钥不泄露,这封信就是安全的,即使落在别人手里,也无法解密。
鲍勃给苏珊回信,决定采用"数字签名"。他写完后先用Hash函数,生成信件的摘要(digest)。
然后,鲍勃使用私钥,对这个摘要加密,生成"数字签名"(signature)。
鲍勃将这个签名,附在信件下面,一起发给苏珊。
苏珊收信后,取下数字签名,用鲍勃的公钥解密,得到信件的摘要。由此证明,这封信确实是鲍勃发出的。
苏珊再对信件本身使用Hash函数,将得到的结果,与上一步得到的摘要进行对比。如果两者一致,就证明这封信未被修改过。
复杂的情况出现了。道格想欺骗苏珊,他偷偷使用了苏珊的电脑,用自己的公钥换走了鲍勃的公钥。此时,苏珊实际拥有的是道格的公钥,但是还以为这是鲍勃的公钥。因此,道格就可以冒充鲍勃,用自己的私钥做成"数字签名",写信给苏珊,让苏珊用假的鲍勃公钥进行解密。
后来,苏珊感觉不对劲,发现自己无法确定公钥是否真的属于鲍勃。她想到了一个办法,要求鲍勃去找"证书中心"(certificate authority,简称CA),为公钥做认证。证书中心用自己的私钥,对鲍勃的公钥和一些相关信息一起加密,生成"数字证书"(Digital Certificate)。
鲍勃拿到数字证书以后,就可以放心了。以后再给苏珊写信,只要在签名的同时,再附上数字证书就行了。
苏珊收信后,用CA的公钥解开数字证书,就可以拿到鲍勃真实的公钥了,然后就能证明"数字签名"是否真的是鲍勃签的。
下面,我们看一个应用"数字证书"的实例:https协议。这个协议主要用于网页加密。
首先,客户端向服务器发出加密请求。
服务器用自己的私钥加密网页以后,连同本身的数字证书,一起发送给客户端。
客户端(浏览器)的"证书管理器",有"受信任的根证书颁发机构"列表。客户端会根据这张列表,查看解开数字证书的公钥是否在列表之内
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)
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