Object orientation is in many ways a natural style of programming whose techniques are reinvented constantly by every programer (Coplien 1992). Object notation consolidates these techniques, so that much of the tedious programming necessary to use them is automatically handled by the interpreter. An object can be thought of as an abstract data type that is very useful in separating the idea of what a thing does from the details of the way it goes about doing it. Support for objects in hoc came late to NEURON, after the notion of cable sections, and as a consequence there are several types of variables (e.g. sections, mechanisms, range variables) that are clearly treated as objects from a conceptual point of view but grew up without a uniform syntax.

In hoc, an object is a collection of functions, procedures, and data, where the data defines the state of the object. There is just enough extra syntax in hoc to support a subset of the object-oriented programming paradigm: specifically, it supports information hiding and polymorphism, but not inheritance. Yet this subset is sufficient to greatly increase the user's ability to maintain conceptual control of complex programs.

Introduction

The need to authenticate both the contents and origin of a message is crucial in any communications network. Consider the following problematic situations in which Alice and Bob face the forger Fred. In each case we suppose that Bob is Alice's banker.

1. (1) Suppose Fred sends Bob a message claiming to come from Alice asking him to transfer $1000 into Fred's account. If Bob has no way of verifying the origin of this message then Alice is in trouble.

2. (2) Suppose Fred intercepts a message from Alice to Bob asking him to transfer $1000 into Carol's account. If Fred can alter the message so that ‘Carol’ is replaced by ‘Fred’ then again there is trouble.

3. (3) Suppose Fred intercepts a message from Alice to Bob asking him to transfer $1000 into Fred's account. Fred stores the message and resends it to Bob whenever he is short of cash!

In each case Fred can succeed if no proper system of message authentication is in place.

Historically the handwritten signature has been the preferred method for authentication of messages. A digital signature is a method for achieving this based on cryptography.

In Chapter 2 we remarked that a conceptual model is an absolute prerequisite for the scientific application of computational modeling. But if a computational model is to be a fair test of our conceptual model, we must take special care to establish a direct correspondence between concept and implementation. To this end, the research use of NEURON involves all of these steps:

1. Implement a computational model of the biological system

2. Instrument the model

3. Set up controls for running simulations

4. Save the model with instrumentation and run controls

5. Run simulation experiments

6. Analyze results

These steps are often applied iteratively. We first encountered them in Chapter 1, and we will return to each of them repeatedly in the remainder of this book.

Graphical user interface vs. hoc code: which to use, and when?

At the core of NEURON is an interpreter which is based on the hoc programming language (Kernighan and Pike 1984).

The basic problems

We saw in Chapter 5 that the one-time pad is a cryptosystem that provides perfect secrecy, so why not use it? The obvious reason is that the key needs to be as long as the message and the users need to decide on this secret key in advance using a secure channel.

Having introduced public key cryptography in Chapter 7 one might wonder why anyone would want to use a symmetric cryptosystem. Why not simply use RSA or some other public key cryptosystem and dispense with the need to exchange secret keys once and for all?

The problem with this approach is that symmetric cryptosystems are generally much faster. For example in 1996, DES was around 1000 times faster than RSA. In situations where a large amount of data needs to be encrypted quickly or the users are computationally limited, symmetric cryptosystems still play an important role. A major problem they face is how to agree a common secret key to enable communications to begin.

This basic ‘key exchange problem’ becomes ever more severe as communication networks grow in size and more and more users wish to communicate securely. Indeed while one could imagine. Alice and Bob finding a way to exchange a secret key securely the same may not be true if you have a network with 1000 users.

Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. The mechanisms that generate these signals and regulate their interactions are marked by a wide diversity of properties, differing across neuronal cell class, developmental stage, and species (e.g. Chapter 7 in (Johnston and Wu 1995); also see (McCormick 1998)). To be useful in research, a simulation environment must provide a flexible and powerful means for incorporating new biophysical mechanisms in models. It must also help the user remain focused on the model instead of programming.

Such a means is provided to NEURON by NMODL, a high level language that was originally implemented for NEURON by Michael Hines and later extended by him and Upinder Bhalla to generate code suitable for linking with GENESIS (Wilson and Bower 1989).

Modeling and understanding

Modeling can have many uses, but its principal benefit is to improve understanding. The chief question that it addresses is whether what is known about a system can account for the behavior of the system. An indispensable step in modeling is to postulate a conceptual model that expresses what we know, or think we know, about a system, while omitting unnecessary details. This requires considerable judgment and is always vulnerable to hindsight and revision, but it is important to keep things as simple as possible. The choice of what to include and what to leave out depends strongly on the hypothesis that we are studying. The issue of how to make such decisions is outside the primary focus of this book, although from time to time we may return to it briefly.

The task of building a computational model should only begin after a conceptual model has been proposed. In building a computational model we struggle to establish a match between the conceptual model and its computational representation, always asking the question: would the conceptual model behave like the simulation? If not, where are the errors? If so, how can we use NEURON to help understand why the conceptual model implies that behavior?

Introducing NEURON

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data.

In search of a definition

Having considered classical symmetric cryptography in the previous chapter we now introduce the modern complexity theoretic approach to cryptographic security.

Recall our two characters Alice and Bob who wish to communicate securely. They would like to use a cryptosystem, in which encryption (by Alice) and decryption (by Bob using his secret key) are computationally easy but the problem of decryption for Eve (who does not know Bob's secret key) should be as computationally intractable as possible.

This complexity theoretic gap between the easy problems faced by Alice and Bob and the hopefully impossible problems faced by Eve is the basis of modern cryptography. In order for such a gap to exist there must be a limit to the computational capabilities of Eve. Moreover it would be unrealistic to suppose that any limits on the computational capabilities of Eve did not also apply to Alice and Bob. This leads to our first assumption:

• Alice, Bob and Eve can only perform probabilistic polynomial time computations.

So for Alice and Bob to be able to encrypt and decrypt easily means that there should be (possibly probabilistic) polynomial time algorithms for both procedures.

But exactly how should we formalise the idea that Eve must face a computationally intractable problem when she tries to decrypt an intercepted cryptogram without Bob's secret key?