Yes, it is possible in theory to forge the Web Server Certificate that is used in SSL/TLS communication. This is because the certificate is signed by a certificate authority that your browser trusts using a cryptographic hashing algorithm of a specific length. The hashing algorithms that have been used to sign certificates are (from newest to oldest) SHA256, SHA1, and MD5. The output of a MD5 hash function is 128 bits, while a SHA1 digest is 160 bits, and a SHA256 is (you guessed it) 256 bits. One of the design features of a cryptographic hashing algorithm is that it is infeasible to predict the output (the “digest”) based on its input. However, for any hash function, there are only a limited number of possible outputs, although this is a very large number. The number of possible digests doubles for every additional bit added to the length of the digest.
When two different inputs to a given hash function generate the same digest, it is called a “collision.” At a conceptual level, the fact that collisions are possible should make sense because there are literally an infinite number of possible inputs but only a large, but finite number of outputs of a hash function. However, even though collisions are theoretically possible, in practice they are computationally expensive to determine, particularly when trying to identify a second certificate that creates the same digest of the certificate that you are attempting to forge.
As an example, Bruce Schneier, a crypto expert wrote a blog post in 2012 projecting that it would take about $700,000 to generate a bogus SHA1 Web Server Certificate in 2015 using Amazon EC2 pricing. More importantly, he predicted that the price would drop to about $43k by 2021. (See When Will We See Collisions for SHA-1?)
It is for this reason that the internet community is moving away from SHA1 Certificates to SHA256 Certificates. In 2008, a group of security researchers actually published details on how they forged the MD5 certificate of a Certificate Authority using a collision-based attack. (See MD5 considered harmful today.) This research hastened the move away from MD5 to SHA1. There are other innovations that such as Certificate Transparency and Certificate Pinning that also help to mitigate the threat of a forged web server certificate in practice. But those are potential topics for future posts.
NOTE: This has been cross-posted from Quora.com