HFE Variations
Hidden Field Equations has four basic variations namely +,-,v and f and it is possible to combine them in various way. The basic principle is the following:
- 01. The + sign consists of linearity mixing of the public equations with some random equations.
- 02. The - sign is due to Adi Shamir and intends to remove the redundancy 'r' of the public equations.
- 03. The f sign consists of fixing some input variables of the public key.
- 04. The v sign is defined as a construction and sometimes quite complex such that the inverse of the function can be found only if some v of the variables called vinegar variables are fixed. This idea is due to Jacques Patarin.
The operations above preserve to some extent the trapdoor solvability of the function.
HFE- and HFEv are very useful in signature schemes as they prevent from slowing down the signature generation and also enhance the overall security of HFE whereas for encryption both HFE- and HFEv will lead to a rather slow decryption process so neither too many equations can be removed (HFE-) nor too many variables should be added (HFEv). Both HFE- and HFEv were used to obtain Quartz.
For encryption, the situation is better with HFE+ since the decryption process takes the same amount of time, however the public key has more equations than variables.
Read more about this topic: Hidden Field Equations
Famous quotes containing the word variations:
“I may be able to spot arrowheads on the desert but a refrigerator is a jungle in which I am easily lost. My wife, however, will unerringly point out that the cheese or the leftover roast is hiding right in front of my eyes. Hundreds of such experiences convince me that men and women often inhabit quite different visual worlds. These are differences which cannot be attributed to variations in visual acuity. Man and women simply have learned to use their eyes in very different ways.”
—Edward T. Hall (b. 1914)