While many people still shop online on Cyber Monday, a lot of them are still concerned about security, according to a new survey from the National Cyber Security Alliance. 

According to the study, 64 percent of respondents in a survey said they have not made an online purchase from a specific website because they were worried about how safe it was. Of those 64 percent, 60 percent said they did not that think that site was secure, 51 percent were worried about the information requested and 48 percent thought the site was requesting too much information.

To me they are showing awareness that they are about to engage in a commercial financial transaction and as we've seen in other surveys, they have a fear of financial loss. Their answers don't mean the site is or isn't secure, but to them something didn't feel right when they went there, said Michael Kaiser, NCSA executive director.

Kaiser said despite the concerns, online shopping remains a popular activity for most respondents as close to 68 percent said they made recent purchases via the web. There are some brands, he says, which are able to parlay their trust in the physical world to the web. For the brands not known in brick-and-mortar stores, it's not as easy to make that transition.

I think that's powerful for consumers when making purchasing decisions, when you do a search and see the best prices from some place you never heard of, doesn't mean it's not trustworthy, it just means you might be more hesitant to do business. You do that in brick-and-mortar stores, if you walk into a store and don't know about it, you'll look around before deciding to do business, Kaiser said.

Kaiser said the lack of certainty felt by consumers for online shopping can be an opportunity for these retailers. He said companies should present to consumers what they are doing to protect their information, why they collect certain information and just try and make them feel comfortable.  

Growth in online shopping is good for the economy and good for the country. Anything that deters people from making purchases is probably hurtful to economy. I think we are still emerging into the detail age. People's comfort level may not be 100 percent with some online payment systems and authentication methods. This will start to change as more rigorous ways of protecting online come into play, Kaiser said.

The study also found more people are shopping via their smartphone. Eight percent of people surveyed made online payments from their mobile phones, doubling last year's total. Meanwhile, 16 percent of people surveyed researched potential purchases from their phone, up from last year's nine percent.