6.1. Introduction

Public-key cryptographic protocols deal with sets like the ring of integers modulo n, the multiplicative group of units in a finite field or the group of points in an elliptic curve over a finite field. Messages that need to be encrypted or signed are, on the other hand, usually human-readable text or numbers or keys of secret-key cryptographic protocols, which are typically represented in computers in the form of sequences of bits (or bytes). It is necessary to convert such bit stings (or byte strings) to mathematical elements before the cryptographic algorithms are applied. This conversion is referred to as encoding. The reverse transition, that is, converting mathematical entities back to bit strings is called decoding.

If Alice and Bob were the only two parties involved in deploying public-key protocols, they could have agreed upon a set of private (not necessarily secret) encoding and decoding rules. In practice, however, when many entities interact over a public network, it is impractical, if not impossible, to have an individual encoding scheme for every pair of communicating parties. This is also unnecessary, because the security of the protocols comes from the encryption process and not from encoding. On the contrary, poorly designed encoding schemes may endanger the security of the underlying protocols.

We, therefore, need a set of standard ways of converting data between various logical formats. This promotes interoperability, removes ambiguities, facilitates simplicity in handling cryptographic data and thereby enhances the applicability and acceptability of public-key algorithms. IEEE (The Institute of Electrical and Electronics Engineers, Inc., pronounced eye-triple-e) and the RSA laboratories have published extensive documents standardizing data conversion and encoding for many popular public-key cryptosystems. Here we summarize the contents of some of these documents. This exposition is meant mostly for software engineers intending to develop cryptographic tool-kits that conform to the accepted standards.