Homomorphic Encryption with ElGamal Using Python (Multiplication and Division)
We live in a 20th Century world of data, and where often do not protect our data. In a future data world, all of our values could be encrypted, and where we can still operate on them. This will be a world of homomorphic encryption.
Meet Taher Elgamal
Taher Elgamal is one of the giants of cybersecurity. His work on Netscape led to the creation of SSL, and on which much of our Web security is still built on. Along with this, he published this paper in 1985 [here]:
It was true classic and has been referenced over 11,700 times. Within the paper, Tahir outlined an encryption method and a digital signature method. His ‘base’ was to take John Napier’s logarithms, and make them discrete. This discrete element meant that we only dealt with positive integer values and where we worked within a finite field. This field was defined by a prime number (p).
While the core ElGamal encryption method was overtaken in its usage by RSA, and then by ECC (Elliptic Curve Cryptography), the signature method was adopted as the Digital Signature Standard (DSS) by NIST. This has since…
