It is a bad engineering practice to reinvent the wheel. Engineers who do this are falling victim to the “Not Invented Here” bias, which can cause a lot of damage when it is a security critical system.
SSL/TLS which is behind HTTPS is absolutely vital in maintaining a secure connection between a website and a browser. Public wifi networks put users at risk, and when used correctly, HTTPS is the only tool that can protect user accounts from this vulnerability.
In the case of two clients that need secure end-to-end (e2e) encryption then there is the open source and vetted Signal Protocol which has received number opens source ports on github and a wide adoption from popular apps like WhatsApp. There is no need to brew your own, these protocols work well for a reason.
If your host doesn’t support HTTPS then a service like Cloudflare Universal SSL can be used to ensure all browsers connect to your site using HTTPS, even if your server doesn’t support SSL/TLS. The connection between Cloudflare and your website will still be unprotected, but this Cloudflare service is intended to protect users against threats found on public wifi networks. From the perspective of a penetration tester, not providing HTTPS is highly suspect, if you aren’t providing a basic security requirement as delivering traffic, then what other security requirements are you missing? HTTPS certificates can be obtained for free using Let’s Encrypt or Start SSL, there is no legitimate reason not to support HTTPS.
HTTPS is vital because it does lot more than just “encrypt passwords”. Another important role is that it should prevent the user from giving logging into a malicious server that is impersonating a real server. Using a system to protect the password alone is still a violation of OWASP A9 – Insufficient Transport Layer Protection because you would still be transmitting session credentials in plain text which is all the attacker needs (Firesheep).
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JavaScript-based cryptography cannot be used to construct a secure transport layer.
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“Tokenize logins”: If an attacker is sniffing
the traffic, they’ll have the plain text username/password and then
they can just login with these new credentials. (Replay attack) -
“Somehow encrypt the transmitted password”: After the person has logged in
an attacker can sniff the traffic to get the valid session id
(cookie) and then just use this instead of logging in. If the
entire session was protected with SSL/TLS then this is not a problem.
There are other more complex attacks that affect both this system and our current SSL infrastructure. The SSLStrip attack goes into greater detail. I highly recommend watching Moxie Marlinspike’s Blackhat 2009 talk, which lead to the HTTP-Strict-Transport-Security standard.