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Elliptic Curve Cryptography (ECC): Encryption & Example

Instructor: David Gloag

David has over 40 years of industry experience in software development and information technology and a bachelor of computer science

Security methods and strength are increasing at a rate that matches the processing power and capabilities computers can bring to bear. In this lesson, we'll look at one such method, public key encryption, and an improvement, elliptic curve cryptography.

Securing Information Systems

With the processing power of computers increasing at such a rapid rate, it makes sense that the security of information systems will begin to falter. In response, new methods will have to be developed to counteract this trend.

Companies like IBM and Hewlett Packard are already at work testing existing methods and developing new ones. But there already exists several methods that do a good job resisting attacks. One such method is elliptic curve cryptography.

What Is Encryption?

Encryption is the process of taking information in one form (usually human-readable), and converting it to another form (not usually human-readable). It is mathematically based, and it makes use of an external piece of information, known as a key, to perform this conversion.

There are several different types of encryption, and they are used for various things. Common examples include:

  • storing personal information for bank and credit card accounts
  • calls and data sent to and from your cell phone
  • login credentials stored on your personal computer

In each case, encryption is behind the scenes, working to protect you and your information.

What Is Cryptography?

Cryptography is the science of reading and writing secret messages. And based on this definition, one might think that it can be used interchangeably with encryption. In fact, they often are. But actually, they are not the same.

Encryption is a specific part of cryptography. For example, if we consider encryption to be the equivalent of a type of car, say a BMW, then cryptography would be equivalent to all cars, regardless of type.

What is Elliptic Curve Cryptography?

Elliptic curve cryptography, or ECC is an extension to well-known public key cryptography. In public key cryptography, two keys are used, a public key, which everyone knows, and a private key, which only you know.

To encrypt, the public key is applied to the target information, using a predefined operation (several times), to produce a pseudo-random number. To decrypt, the private key is applied to the pseudo-random number, using a different predefined operation (several times), to get the target information back. The algorithm relies on the fact that encryption is easy, and decryption is hard, making decryption impractical without the key. It was the first system to allow secure information transfer without a shared key.

The problem is that with today's computers getting faster and faster, there will come a point where we can't make the pseudo-prime large enough to thwart an attack. That is where elliptic curve cryptography comes in. This extension uses the properties of an elliptical curve, the same pair of keys, and some funky math (which I won't get into here), to encrypt and decrypt the target information.

An elliptic curve is a graph that represents the points generated by the following equation:

y2 = x3 + ax + b

Or in pictorial form:


An Elliptic Curve
Elliptic-Curve


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