This should be the flow of the description of RSA
- RSA is a public key crypto system that everyone in the room who doesn't live in a cave uses pretty much every day. If you are using a computer to get on the internet, chances are you use RSA a lot.
- Being a public key crypto system that means there is a public key that everyone knows and can use to encrypt messages and send them to you. Decrypting those messages is done using a private key that only you have. Pictures of Alice and Bob are always helpful here.
- RSA works by using numbers of the form $N=p\cdot q$ where $p$ and $q$ are prime. If I have $p$ and $q$, then computing $N$ is really easy. But if I give you $N$, it turns out that breaking $N$ apart into the primes $p$ and $q$ is really hard.
Everyone can understand the math in that description. If someone has a hard time believing that breaking $N$ into $p$ and $q$ is really hard, then show them this
cb 12 fd 3b 32 8c 65 17 ff 39 2f 25 27 e3 80 ba bf d7 e4 5f 9a 65 a9 96 70 96 ef f9 49 36 79 97 e4 22 23 4c 9d af 5b 27 56 ef 6a 36 3f 4a 5d d1 44 fb 5d ca 21 7a f3 7c 39 cb ab 07 1c 6a ec 2c 21 64 37 1d 16 11 73 3f 7e 1f 68 a9 ea b5 bd 7a 05 6d 38 05 8d ef ee 23 1c e2 cf ec aa 22 d9 4e 84 47 38 c2 cd bc 1b 72 51 a3 64 46 f0 55 95 57 ee de 87 db 39 96 57 c0 42 58 1b 48 bc 5c 79 20 d9 96 4e e9 49 86 67 78 4f fe 4b 66 b0 f6 7d b9 e7 07 de c6 da d8 20 96 65 a0 de 4e a0 c4 76 f3 41 e7 e4 de c0 32 47 8d 5f a9 96 09 b8 46 5e e8 c0 3e d1 d0 69 e8 4c 26 3c 8e 69 1c 01 eb 61 ec ec 77 f0 e9 c2 fe 2a bf 8d 68 c2 1a 55 7d 61 ac 85 c8 f7 16 e2 a0 73 97 ff 26 5c 05 38 e6 e1 a7 89 13 d6 ac 13 aa 7e 44 87 83 07 ab f2 da a6 cf 38 a7 6b cb 17 07 62 08 a9 10 8e 58 8d 73 c6 e9
That is the $N$ that Bank of America uses and tell them that if they really think you are wrong, then the two of you should get together after the presentation so that you can go make a lot of money.
Personally I also like to show off pictures like this
Those are the inventors of RSA (Rivest, Shamir, and Adleman). By their picture they are obviously very smart, so the audience should just trust you that they know what they are doing.
In other words, if the audience doesn't need to understand all of the details of RSA, don't even try. Give them just enough that they can understand what they need to know. If they want more, deflect and take it offline as much as possible. Otherwise you will loose everyone else and probably the person asking the question.
Use lots of pictures and try to add some humor.