Elliptic Curve Cryptography

Joe Hendrix — Mon, 08 Apr 2013 15:10:49 +0000

When it comes to public key cryptography, most systems today are still stuck in the 1970s. On December 14, 1977, two events occurred that would change the world: Paramount Pictures released Saturday Night Fever, and MIT filed the patent for RSA. Just as Saturday Night Fever helped popularize disco through its choreography and soundtrack, RSA helped popularize cryptography by allowing two parties to communicate securely without a shared secret.

Public key techniques, such as RSA, have revolutionized cryptography and form the basis for Web site encryption via SSL/TLS, server administration via SSH, secure e-mail and IP encryption (IPsec). They do this by splitting the shared secret key used in traditional cryptography into two parts: a public key for identifying oneself and a secret key for proving an identity electronically. Although the popularity of disco has waned, most Web sites today that use encryption still are using RSA.

Since the 1970s, newer techniques have been developed that offer better security with smaller key sizes than RSA. One major breakthrough is the development of cryptography based on the mathematical theory of elliptic curves, called ECC (Elliptic Curve Cryptography). Although ECC has a reputation for being quite complex, it has been integrated into popular open-source cryptographic software including OpenSSH and OpenSSL, and it's not inherently any more difficult to use than RSA. In this article, I describe ECC and show how it can be used with recent versions of OpenSSH and OpenSSL.

Not all cryptographic algorithms are equal. For a fixed key or output length, one algorithm may provide much more security than another. This is particularly true when comparing different types of algorithms, such as comparing public and symmetric key algorithms. To help make sense of this, the National Institute of Standards and Technology (NIST) reviews the academic literature on attacking cryptographic algorithms and makes recommendations on the actual security provided by different algorithms (see Table 1 from 2011).

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