## 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

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

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 ExampleWith 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...

## Windows XP and Win32 - the Platform of the Future!

Over the past decade I often wondered why anyone uses Windows. It's just so... proprietary. And pedestrian. As I grew up my OS of choice went nothing to CPM to DOS (on Apple ][), GEM on Atari ST, MS-DOS, DOS extenders, Mac OS, Windows NT, Windows XP, Linux... Now, I again find myself a fan of Windows XP, the platform of the future. (I am still a fan of bare metal, of course).Maybe I am not totally serious, but I, a self-proclaimed freedom lover and...

## MyHDL FPGA Tutorial I (LED Strobe)

Last updated 05-Nov-2015

IntroductionFrom 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...

## 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...

## MyHDL FPGA Tutorial II (Audio Echo)

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

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

IntroductionThe 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...

## Introduction to FPGA Technology

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...

## 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.

IntroductionA 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...

## FPGA or DSP Processor - Parameters to Make the Right Choice

Introduction

Digital Signal Processing (DSP) has a huge global market that is growing fast day by day with rapidly evolving sophisticated modern electronics applications like 3G wireless, voice over internet protocol (VoIP), multimedia systems, radar and satellite systems, medical systems, image-processing applications and consumer electronics. These sophisticated DSP applications pose many conflicting challenges to system designers and application developers in terms of cost and...

## Learning VHDL - Basics

Since FPGA are becoming more accessible to the hobbyist, learning how to use them can be really useful for certain applications, like DSP and video generation; moreover, engineers that are able to code in VHDL/Verilog are always requested on the job market.

In this tutorial I will cover the basics of Xilinx ISE and VHDL. I willl base my code on the Basys2 board from Digilent: it is really cheap (especially for students) and has a lot of features on board, as you can see from the picture...

## MyHDL Resources

Last updated 26-Oct-2015

MyHDL ResourcesIf you want to dive into MyHDL (digital hardware description in Python) there are many resources available. Below is a list of MyHDL resources, including some of the past blogs here on fpgarelated.

The MyHDL manual is a great (probably the best) place to get started.

The manual is an in-depth introduction to MyHDL. The concepts are well explained and there are examples to test while working through the...

## MyHDL FPGA Tutorial I (LED Strobe)

Last updated 05-Nov-2015

IntroductionFrom 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...

## MyHDL FPGA Tutorial II (Audio Echo)

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

## 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...

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

IntroductionThe 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...

## Introduction to FPGA Technology

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...

## 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.

IntroductionA 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...

## Learning VHDL - Basics

Since FPGA are becoming more accessible to the hobbyist, learning how to use them can be really useful for certain applications, like DSP and video generation; moreover, engineers that are able to code in VHDL/Verilog are always requested on the job market.

In this tutorial I will cover the basics of Xilinx ISE and VHDL. I willl base my code on the Basys2 board from Digilent: it is really cheap (especially for students) and has a lot of features on board, as you can see from the picture...

## FPGA or DSP Processor - Parameters to Make the Right Choice

Introduction

Digital Signal Processing (DSP) has a huge global market that is growing fast day by day with rapidly evolving sophisticated modern electronics applications like 3G wireless, voice over internet protocol (VoIP), multimedia systems, radar and satellite systems, medical systems, image-processing applications and consumer electronics. These sophisticated DSP applications pose many conflicting challenges to system designers and application developers in terms of cost and...

## binary hello world

Python + Ohio + MyHDL + FPGARecently I had the opportunity to coordinate a hands-on programmable hardware (FPGA) workshop (open-space) at a regional Python conference - @pyohio. The workshop was for those that had little to no exposure to programmable hardware. For this situation I used two basic examples: two versions of a binary hello world.

The binary hello world -- blinking an LED -- is a good starting point to introduce programmable hardware, hardware descriptions languages,...