There are two distinct encryption technologies referred to as 'genetic encryption': one in which sequences of genetic material are used to carry the message, the other in which they are used for the key. Both of these techs started to be developed in the Information Age.
DNA as message carrier
Standard DNA and RNA have four possible nucleotides for each base pair; thus, non-protein-coding areas of a genetic strand can be used to encode two bits worth of data in each base pair. Given the possibility of mutations, to ensure fidelity of a message, it is a good idea to use redundancy and error correction so that even multiple mutations will not result in any significant data loss.
DNA as cryptographic key generator
When creating a cryptographic key, it should be as random as possible, to avoid allowing any ways of making it easier to ferret out the key than simple brute force computation. The more random something is, the more entropy it is said to have specifically, 'information entropy'). Certain aspects of DNA, such as random mutations, are one potential source of such entropy.
However, most truly random physical phenomena that are used to generate bits rarely generate 0's and 1's in equal amounts. There are various ways to 'even them out', creating a truly random stream of bits to encode with, one of which is to XOR the original random stream with a "pseudorandom" stream. When used correctly, a DNA sequence can serve as such a pseudorandom stream.
Cryptography - Text by Anders Sandberg The art of creating and using cryptosystems. A cryptosystem (or cipher system) is a method of disguising messages so that only certain people can see through the disguise, e.g, encryption. Cryptanalysis is the art of breaking cryptosystems - seeing through the disguise even when you're not supposed to be able to. Cryptology is the study of both cryptography and cryptanalysis. Very popular in the Cyberian worlds, where there is an obsession with personal privacy.
Cryptotechnology - Text by M. Alan Kazlev The design of tech intended, deliberately or by accident, to be obscure. Theoretically, anything, even macroscale dumbtech, can be cryptotech. The term however is more often applied to more dramatic high ultratech, transapientech or godtech creations. And while many cryptotechnologists tend to be higher toposophic minds whose motives and logic are often incomprehensible to lower beings, it is also possible for a dedicated and highly augmented ordinary sapient to design simpler forms of cryptotech; perhaps as a hobby, a joke, a unique craft, or a form of memegineering.
DNA Computing - Text by M. Alan Kazlev A form of computing dating back to the Information Age, in which DNA molecules are used to solve complex mathematical problems or generate virtual worlds. DNA computers allow trillions of computations to be performed simultaneously. However, they are slower than standard nanocomputers.
Genetic Algorithm - Text by Anders Sandberg in his Transhumanist Terminology Any algorithm which seeks to solve a problem by considering numerous possibilities at once, ranking them according to some standard of fitness, and then combining ("breeding") the fittest in some way. In other words, any algorithm which imitates natural selection.
Genetics - Text by M. Alan Kazlev The study of heredity, genes, and the genome, both terragen and alien (this latter is sometimes called xenogenetics). Includes also the mapping of the genotype with the phenotype, simulation of past and future inheritance and evolutionary paths, and the basic theory behind gengineering.