I recall the craze in the 1990s for Magic Eye posters and books. People would gaze and squint at these multicoloured, seemingly random, patterns to discern 3d images of dolphins, elephants, temples, and spaceships. The method of display was a variation on what I experienced as a child, as I gazed at my bedroom wallpaper…More

## Secrets of the overhead projector

All transmission of data across digital networks now involves encryption. It’s interesting to read articles from the 1990s in which cryptography was applied usually to messages only requiring high levels of security. A seminal 1995 article by Moni Naor and Adi Shamir began “In this paper we consider the problem of encrypting written material (printed…More

## Truth, lies and architecture

Do buildings lie? The UK Trade Descriptions Act prohibits sellers from circulating false or misleading descriptions of their goods and services. Legislation across most countries echoes the spirit of the UK Act. Informal reference to the challenge of false trade descriptions circulates amongst professional and consumer stakeholders within retail, education, health, and the built environment.…More

## Key exchange: It’s a wrap!

In an earlier post (Elliptic trapdoors) I did my best to explain addition and multiplication along an elliptic curve. The diagram showed a point P doubled to produce 2P, then added to itself to produce 3P, and added again to produce 4P. The dotted lines indicated the mirror reflection operation to arrive at the final…More

## Elliptic fields

One property of algebraic equations is that you can perform the same simple arithmetical operation on both sides of the equation and the equivalence still holds for the same x and y values, e.g. y = 2x has the same values if both sides are multiplied by the same number e.g. 6y = 12x. The…More

## Sharing a secret number

Here’s a naive method for two people to agree a secret number. The number to be shared is simply an integer, which is a key for some other encrypted communication channel. It could even be a PIN to a bank account, an access code for a door or the combination code to a shared locker…More

## Elliptic trapdoors

Elliptic curves are amongst a family of curves that make up the alluring surfaces of much contemporary organically-inspired architecture. They are also the basis of encryption methods that secure digital communications. A trapdoor is a one-way portal. You can go through it easily in one direction, but it’s difficult to come out again in the…More

## RSA public key encryption

I’m continuing this dive into public-private key encryption. As outlined in a helpful blog post by Nick Sullivan, the kind of encryption I described in the last two posts relies on a simple property of numbers. It’s easy to multiply two numbers, even if very large, but more difficult to factor a number, i.e. find…More

## Asymmetric key encryption

An encryption key is a string of characters that you feed into an encryption algorithm to either encrypt or decrypt a message. An asymmetric key system has two keys. There’s a public key to encrypt a message. It’s public because anyone can see it and use that key. But once the message is encrypted using…More

## Primes

Some secure encryption methods make use of prime numbers. I’ll examine the method in the next post, but here’s some properties of primes relevant to encryption, presented via simple grid geometry. Hopefully that connects this esoteric field with spatial shapes such as rectangular rooms on a gridded plan. Composites A composite number is a positive…More