Motivation: Understanding how viruses co-evolve with their hosts and adapt various genomic level strategies in order to ensure their fitness may have essential implications in unveiling the secrets of viral evolution, and in developing new vaccines and therapeutic approaches. Here, based on a novel genomic analysis of 2625 different viruses and 439 corresponding host organisms, we provide evidence of universal evolutionary selection for high dimensional 'silent' patterns of information hidden in the redundancy of viral genetic code. Results: Our model suggests that long substrings of nucleotides in the coding regions of viruses from all classes, often also repeat in the corresponding viral hosts from all domains of life. Selection for these substrings cannot be explained only by such phenomena as codon usage bias, horizontal gene transfer and the encoded proteins. Genes encoding structural proteins responsible for building the core of the viral particles were found to include more ost-repeating substrings, and these substrings tend to appear in the middle parts of the viral coding regions. In addition, in human viruses these substrings tend to be enriched with motives related to transcription factors and RNA binding proteins. The host-repeating substrings are possibly related to the evolutionary pressure on the viruses to effectively interact with host's intracellular factors and to efficiently escape from the host's immune system.