## Choosing an Implementation Approach

May 10, 2018
What one man can do, another can do!--The Edge (1997) Choose the hill you want to die on.--Common saying attributed to the United States Marine Corps Planning out an FPGA Implementation

In my first article, I gave a high-level view of the project that brings me into the world of FPGA development. At the end, I tried to break down the areas of development that would be involved, and some of the knowledge and expertise I would probably have to gain in order to make it a...

## Dealing With Fixed Point Fractions

Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow.  If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions.  When integers overflow, they lose data off the most significant bits.  When fractions overflow, they lose data off...

## Elliptic Curve Digital Signatures

December 9, 2015

A digital signature is used to prove a message is connected to a specific sender.  The sender can not deny they sent that message once signed, and no one can modify the message and maintain the signature. The message itself is not necessarily secret. Certificates of authenticity, digital cash, and software distribution use digital signatures so recipients can verify they are getting what they paid for.

Since messages can be of any length and mathematical algorithms always use fixed...

## Elliptic Curve Key Exchange

December 3, 2015

Elliptic Curve Cryptography is used to create a Public Key system that allows two people (or computers) to exchange public data so that both sides know a secret that no one else can find in a reasonable time.  The simplest method uses a fixed public key for each person.  Once cracked, every message ever sent with that key is open.  More advanced key exchange systems have "perfect forward secrecy" which means that even if one message key is cracked, no other message will...

## Polynomial Inverse

One of the important steps of computing point addition over elliptic curves is a division of two polynomials.  When working in $GF(2^n)$ we don't have large enough powers to actually do a division, so we compute the inverse of the denominator and then multiply.  This is usually done using Euclid's method, but if squaring and multiplying are fast we can take advantage of these operations and compute the multiplicative inverse in just a few steps.

The first time I ran across this...

## One Clock Cycle Polynomial Math

Error correction codes and cryptographic computations are most easily performed working with $GF(2^n)$  polynomials.  By using very special values of $n$ we can build circuits which multiply and square in one clock cycle on an FPGA. These circuits come about by flipping back and forth between a standard polynomial basis and a normal basis representation of elements in $GF(2^n)$.

A normal basis is yet another form of polynomial but instead of adding powers of $\beta$ we add...

## Elliptic Curve Cryptography

Secure online communications require encryption.  One standard is AES (Advanced Encryption Standard) from NIST.  But for this to work, both sides need the same key for encryption and decryption.  This is called Private Key encryption.  Public Key encryption is used to create a private key between two sides that have not previously communicated.  Compared to the history of encryption, Public Key methods are very recent having been started in the 1970's.  Elliptic...

## Polynomial Math

Elliptic Curve Cryptography is used as a public key infrastructure to secure credit cards, phones and communications links. All these devices use either FPGA's or embedded microprocessors to compute the algorithms that make the mathematics work. While the math is not hard, it can be confusing the first time you see it.  This blog is an introduction to the operations of squaring and computing an inverse over a finite field which are used in computing Elliptic Curve arithmetic. ...

## MyHDL Interface Example

MyHDL Interfaces Example

With the next release of MyHDL, version 0.9, conversion of interfaces will be supported.  In this context an interface is any object with a Signal attribute.  This can be used to simplify connection between modules and port definitions.  For example, if I want to define a simple memory-map bus, the Signals for the bus can be defined as follows:

class BareBoneBus: def __init__(self): self.wr = Signal(False) self.rd =...

## BGA and QFP at Home 1 - A Practical Guide.

It is almost universally accepted by the hobbyists that you can't work with high-density packages at home.  That is entirely incorrect.  I've been assembling and reflowing BGA circuit boards at home for a few years now.  BGAs and 0.5mm-pitch QFPs are well within the realm of a determined amateur.

This series of articles presents practical information on designing and assembling boards with high-density packages at home.  While the focus is on FPGA packages, most of...

## MyHDL FPGA Tutorial I (LED Strobe)

Last updated 05-Nov-2015

Introduction

From many perspectives the latest FPGA offerings from 'X' and 'A' are large devices - mucho programmable logic resources.  Even the devices that one can get for sub \\$10 are relatively large.  Because of the size of these FPGAs they are implemented using an HDL.  To manually configure each circuit would be a long and tedious task.  It is not feasible to program an FPGA by manually defining the logic for each LUT and manually...

## BGA and QFP at Home 1 - A Practical Guide.

It is almost universally accepted by the hobbyists that you can't work with high-density packages at home.  That is entirely incorrect.  I've been assembling and reflowing BGA circuit boards at home for a few years now.  BGAs and 0.5mm-pitch QFPs are well within the realm of a determined amateur.

This series of articles presents practical information on designing and assembling boards with high-density packages at home.  While the focus is on FPGA packages, most of...

## Introduction to FPGA Technology

May 12, 2011
Overview

FPGA stands for Field Programmable Gate Array. An FPGA is an integrated circuit (IC) that can be programmed and configured by the embedded system developer in the field after it has been manufactured. FPGA is a semi-conductor device which is not limited to any pre-defined hardware function; it is rather highly flexible in its functionality and may be configured by the embedded system developer according to his design requirements. FPGAs use pre-built logic blocks and programmable...

## MyHDL FPGA Tutorial II (Audio Echo)

July 18, 2012
Introduction

This tutorial will walk through an audio echo that can be implemented on an FPGA development board.  This tutorial is quite a bit more involved than the previous MyHDL FPGA tutorial.  This project will require an FPGA board with an audio codec and the interface logic to the audio codec.

Review the Previous Tutorial

The previous MyHDL FPGA tutorial I posted a strobing LED on an FPGA board.  In that tutorial we introduced the basics of a MyHDL module....

## Shared-multiplier polyphase FIR filter

Keywords: FPGA, interpolating decimating FIR filter, sample rate conversion, shared multiplexed pipelined multiplier

Discussion, working code (parametrized Verilog) and Matlab reference design for a FIR polyphase resampler with arbitrary interpolation and decimation ratio, mapped to one multiplier and RAM.

Introduction

A polyphase filter can be as straightforward as multirate DSP ever gets, if it doesn't turn into a semi-deterministic, three-legged little dance between input, output and...

## Elliptic Curve Cryptography

Secure online communications require encryption.  One standard is AES (Advanced Encryption Standard) from NIST.  But for this to work, both sides need the same key for encryption and decryption.  This is called Private Key encryption.  Public Key encryption is used to create a private key between two sides that have not previously communicated.  Compared to the history of encryption, Public Key methods are very recent having been started in the 1970's.  Elliptic...

## Dealing With Fixed Point Fractions

Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow.  If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions.  When integers overflow, they lose data off the most significant bits.  When fractions overflow, they lose data off...

## How to start in FPGA development? - Some tips

Introduction

The aim of this tutorial is to show some useful tips for people like me that one day started from zero to work with FPGA's. Why FPGA's? Because they are easy to use and they are not too expensive, and they are usually used in lab courses to let students "play" with them.

1: How to choose the right FPGA?

As you may know there are a lot of different FPGA's, brands and models. How to choose the right one? It's very difficult to say that before knowing which will be the...