After Ralph Merkle, Whitfield Diffie and Martin Hellman, Michael O. Rabin is the most important of the creators of public-key cryptography.

The RSA team (Ron Rivest, Adi Shamir and Leonard Adleman) is better known than Michael O. Rabin, but that is entirely due to marketing and advertising, because they founded a successful business.

In reality the RSA algorithm is superfluous and suboptimal. If the RSA team had never discovered this algorithm, that would have had a null impact on the practice of cryptography. Public-key cryptography would have been developed equally well, because the algorithms discovered by Merkle, Diffie, Hellman and Rabin are necessary and sufficient.

On the other hand, while without the publications of RSA, cryptography would have evolved pretty much in the same way, without the publications of Michael O. Rabin from the late seventies the development of public-key cryptography would have been delayed by some years, until someone else would have made the same discoveries.

Together with Ralph Merkle, Michael O. Rabin was the one who discovered the need for secure cryptographic hash functions, i.e. one-way hash functions, which are now critical for many applications, including digital signatures. Thus Rabin is the one who has shown how the previously proposed methods of digital signing must be used in practice. For example, the original signing algorithm proposed by RSA could trivially be broken and it became secure only in the modified form described by Rabin, i.e. with the use of a one-way hash function.

Originally, Merkle defined 2 conditions for one-way hash functions, of resistance to first preimage attacks and second preimage attacks, while Rabin defined 1 condition, of resistance to collision attacks. Soon after that it was realized that all 3 conditions are mandatory, so the 2 definitions, of Merkle and of Rabin, have been merged into the modern definition of such hash functions.

Unfortunately, both Merkle and Rabin have overlooked a 4th condition, of resistance to length extension attacks. This should have always been included in the definition of secure hash functions.

Because this 4th condition was omitted, the US Secure Hash Algorithm Standards defined algorithms that lack this property, which has forced many applications to use workarounds, like the HMAC algorithm, which for many years have wasted time and energy wherever encrypted communications were used, until more efficient authentication methods have been standardized, which do not use one-way hash functions, for instance GCM, which is today the most frequently used authentication algorithm on the Internet.

Rabin Fingerprinting is one of my favorites of his contributions. It's a "rolling hash" that allows you to quickly compute a 32-bit (or larger) hash at *every* byte offset of a file. It is used most notably to do file block matching/deduplication when those matching blocks can be at any offset. It's tragically underappreciated.

I've been meaning to write up a tutorial as part of my Galois Field series. Someday..

Thank you again!

Interesting. Some people are lucky enough to find their vocation quite early in life.

https://youtu.be/L3FZzGU3n14

A friend of mine was one of his graduate students and a teaching assistant for the class. He pointed out to me once that Professor Rabin would state many of his points during lecture twice. Once I started listening more carefully, I found this to be true. It was both subtle and pedagogically effective.

English was not his first language, but he enjoyed his struggles with it. I remember him stumbling over the pronunciation of a word during class. Giving up with a smile, he said, "This is a word I know only from books."

Also, as a teen he was taught mathematics by a certain Elisha Netanyahu, who was an uncle of the current Israeli Prime Minister. What an unexpected connection, at least for me.

We are all in his debt.