Signatures let us communicate information in public, while still ensuring that the information itself has not been tampered with.

Multiple Signatures

One drawback of the simple version of signatures described above is that it is limited to a single sender. When that sender is the one individual that is producing the message, that’s okay. In certain cases, however, the message can be from a group, and in those cases using simple signatures requires trusting one member of the group. That is, if Alice’s family wants to send Bob’s family a message, and they decide that Evelyn, Alice’s mischievous 12-year-old daughter, will be the one to sign the message, Evelyn can sign a different message, send it and its signature to Bob’s family, and they will be none the wiser that this wasn’t the intended message.

The simple way to solve the above problem is to ask for more than one signature. Rather than just let Evelyn sign the message, Evelyn and Alice both sign the message, and Bob can check both to make sure everything was right. As a bonus, this makes sure that Alice can’t secretly include any embarassing stories about Evelyn in the family message.

One downside of this is that it can require a lot of extra work and data. Say that Evelyn’s soccer team wants to send Bob’s family a thank you note for the jerseys they helped them buy. That team is all 12-year-olds, so trusting any one of them to send the right note can be a real leap of faith. If the whole team signs, however, with 11 players and 10 on the bench, that’s 21 people who have to sign, and the message now has to include 21 signatures! As if that’s not enough hassle, Bob’s family has to then check the message against all 21 of those signatures to be certain none of Evelyn’s teammates worked together to tamper with the message.