From the course: CompTIA Security+ (SY0-701) Cert Prep

Elliptic-curve and quantum cryptography

From the course: CompTIA Security+ (SY0-701) Cert Prep

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Elliptic-curve and quantum cryptography

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- [Narrator] Let's take a look at two more encryption technologies that are covered on the exam, but they're a little less commonly used, elliptic curve cryptography and quantum cryptography. All public key cryptography is based upon the difficulty of solving complex mathematical problems. In the case of the RSA algorithm, the security of the algorithm depends upon the difficulty of factoring the product of two large prime numbers. You might recall from a math class that prime numbers are those that are divisible only by themselves and the number one. Common examples of prime numbers include 2, 3, 5, 7 and 11. Now, if I told you that I was going to multiply two prime numbers together and provide you with the answer, you might think that you'd be able to perform that calculation. For example, if I tell you that 15 is the product of two prime numbers, you can easily determine that those numbers are three and five. Or if I asked you to perform the prime factorization of 21, you'd quickly figure out that the two prime numbers are three and seven. RSA and other cryptographic algorithms that depend upon the difficulty of factoring prime numbers, use much larger prime numbers however. What if I showed you this product and asked you to identify the two prime numbers that went into it? Now, that's a little more difficult, isn't it? Currently, there is no effective way to solve the prime factorization problem efficiently for large numbers. If someone discovered an efficient way to do this, all of the cryptographic algorithms that depend upon prime factorization would immediately become insecure. Elliptic curve cryptography, or ECC, does not depend upon the prime factorization problem. It uses a completely different problem, known as the elliptic curve discreet logarithm problem. Now, explaining that problem is a lot more difficult than the prime factorization problem, but fortunately, you won't need to understand how ECC works on the exam, just to remember that it uses a different approach than the prime factorization problem. Quantum computing is an emerging field that attempts to use quantum mechanics to perform computing tasks. It's still mostly a theoretical field, but if it advances to the point where that theory becomes practical to implement, quantum cryptography may be able to defeat cryptographic algorithms that depend upon factoring large prime numbers. Unfortunately, the use of elliptic curve cryptography would not provide protection against quantum attacks. Elliptic curve approaches are even more susceptible to quantum attack than prime factorization algorithms. At the same time, quantum computing may be used to develop even stronger cryptographic algorithms that would be far more secure than modern approaches. We'll have to wait and see how those develop to provide us with strong quantum communications in a post quantum era.

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