This decision of November 30, 2010 may be interesting for the cryptography-acquainted reader. While mathematical methods as such are excluded from patentability at the EPO, the question underlying the decision was whether this also applies to the employment of mathematics in **cryptography** applications:

### Catchwords (inofficial translation)

Methods for encrypting/decrypting or signing electronic messages have to be classified as technical methods even though they are based substantially on mathematical methods(reasons no. 7).

### From the reasons (inofficial translation)

5. According to established case law the subject-matter of all claims has technical character and is thus in agreement with Art. 52(2) and (3) since it concerns a computer-implemented method (see T 258/03, Hitachi; Headnote 1; Official Journal EPO, 2004, 575; and G 3/08; Reasons No. 10.7).

5.4 The board thus considers it appropriate to examine within its authority under Art. 111(1) EPC 1973 whether the methods of claims 1–4 provide a technical effect that goes beyond the fact that they are computer-implemented.

6. RSA is an asymmetric crypto system which can be used both for encryption and digital signing. It uses a pair of keys consisting of a private key which is used for decrypting or signing data and a public key serving for encrypting or validating of signatures. The private key is confidential and cannot, or only with extremely high efforts, be derived from the public key.

6.1 Keys and messages are represented as numbers and both the determination of the key pair and the encrypting/decrypting or signing of messages is characterized by methematical operations: the choice of two large prime numbers P and Q and the calculation of N=P*Q and M=(P-1)*(Q-1), the choice of a number E coprime to M and the determination of the modular inverse of E modulus M (for the determination of the key pair), as well as the potentialization modulo N (during encrypting/decrypting or signing). Furthermore, the confidentiality of the private key is based on the reasoned mathematical assumption that the prime factorization is in principle a difficult problem, and in particular that the factorization of N into its prime factors P and Q is practically impossible. **Therefore, RSA appears to be in a large part a purely mathematical method.**

6.2 **On the other hand, asymmetric cryptography deals with the specific task of ensuring a secure exchange of electronic messages which at the same time facilitates the key exchange and secrecy.** Unlike symmetric cryptography, in asymmetric cryptography each user of the system has to keep only its own private key secret.

6.3 **The board is of the opinion that the secure exchange of electronic messages is a technical effect the provision of which has to be considered a technical problem.**

6.4 RSA solves this problem with mathematical means. With RSA a breakthrough in the development of cryptography was achieved: RSA is acknowledged to be the first practicable and specifically implementable asymmetric crypto system and is nowadays a central component in various cryptographic security systems. **The mathematics underlying RSA thus directly serve the solution of a specific technical problem.**

7. **For this reason the board is of the opinion that methods for encrypting/decrypting or signing electronic messages using RSA have to be classified as technical methods even though they are based substantially on mathematical methods.**

*Read the whole decision (in German only) **here**.*

*Originally published at **www.europeansoftwarepatents.com** on February 26, 2015.*