Homomorphic encryption

A homomorphic encryption has homomorphic properties, whereby calculations can be performed on the ciphertext corresponding to mathematical operations on the corresponding plain text.

With the help of homomorphic cryptography, calculations can be distributed to different systems (e.g. servers ) that do not trust each other. This could play a role in cloud computing in the future and promises a great gain in data protection. Encrypted data is stored in a cloud. There they can be searched or processed without being decrypted. The result is sent back in encrypted form. As a result, the cloud provider knows neither the data nor the results.

There are a number of cryptosystems that allow at least partially homomorphic encryption with reasonable effort. In addition, there are also fully homomorphic encryption systems, which, however, have not yet been used due to their complex design and computational intensity.

Examples of homomorphic encryption systems are:

• Goldwasser-Micali cryptosystem
• Benaloh cryptosystem
• Paillier cryptosystem
• Okamoto Uchiyama cryptosystem

Craig Gentry found the first candidates for fully homomorphic encryption methods in his doctoral thesis in 2009.

properties

Homomorphic cryptosystems can be classified by their homomorphic properties.

So there are additively homomorphic systems (partial) with the following property.

${\displaystyle m(a)\oplus m(b)=m(a+b)}$

Multiplicatively homomorphic systems (partial) with the following property.

${\displaystyle m(a)\otimes m(b)=m(a\times b)}$

In addition, there are fully homomorphic systems that have both additive and multiplicative homomorphic properties.

literature

• Dr. Michael Brenner: Encrypted calculations with homomorphic encryption . In: c't . No. 6 , 2016, p. 176–178 ( heise.de [accessed January 11, 2020]).

Individual evidence

1. ↑ Craig Stuntz: What is Homomorphic Encryption, and Why Should I Care? March 18, 2010, archived from the original on February 4, 2016 . 
2. ↑ Fraunhofer FOKUS Competence Center Public IT: The ÖFIT trend sonar in IT security - homomorphic cryptography. April 2016 . 
3. ↑ Craig Gentry: A Fully Homomorphic Encryption Scheme. (PDF; 952 kB) Stanford Crypto Group, August 1, 2009, pp. 169–178 (English).