Methods, apparatus, and articles of manufacture to encode auxiliary data into relational database keys and methods, apparatus, and articles of manufacture to obtain encoded data from relational database keys

A non-transitory computer readable storage medium comprising computer readable instructions which;

• when executed, cause a machine to at least:
• access network communications to obtain a relational database key value, a first base number, and a second base number, the relational database key value corresponding to encoded auxiliary data;
• divide the relational database key value into a first number of groups;
• determine first remainders for respective ones of the groups based on corresponding first incremental values;
• modify the first remainders using the first base number to generate first encoded values;
• when the first encoded values do not correspond to first auxiliary data:
• determine second remainders for respective ones of the groups based on corresponding second incremental values;
• and
• modify the second remainders using the second base number to obtain the encoded auxiliary data.

A method to decode auxiliary data from relational data, the method comprising:

• accessing network communications to obtain a relational database key value, a first base number, and a second base number, the relational database key value corresponding to encoded auxiliary data;
• dividing, by executing an instruction with a processor, the relational database key value into a first number of groups;
• determining, by executing an instruction with the processor, first remainders for respective ones of the groups based on corresponding first incremental values;
• modifying, by executing an instruction with the processor, the first remainders using the first base number to generate first encoded values;
• and
• when the first encoded values do not correspond to a first result;
• determining second remainders for respective ones of the groups based on corresponding second incremental values;
• and
• modifying the second remainders using the second base number to obtain the encoded auxiliary data.