Suppose that the only public key cryptography schemes that we knew were [Diffie Hellman][1], [RSA][2] and [ElGamal][3]. How much would this set civilization back? Are there important applications of elliptic curve cryptography [specifically] without viable substitutes? [Edit: I came across [this question][4] which gives some information, but I'm looking for more. Specifically, I would like to know *how* much better elliptic curve cryptography is/(would be) than more classical encryption schemes for the applications where elliptic curve cryptography is superior. [1]: http://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange [2]: http://en.wikipedia.org/wiki/RSA_%28algorithm%29 [3]: http://en.wikipedia.org/wiki/ElGamal_encryption [4]: https://crypto.stackexchange.com/questions/1190/why-is-elliptic-curve-cryptography-not-widely-used-compared-to-rsa?rq=1