nly passive listening. If k1 and k2 are equal, the system is symmetric. Otherwise, it is said to be asymmetric. To guarantee security, k2 must always be kept secret, whereas k1 can be made public, provided it is infeasible to derive k2 from k1. If indeed this is the case, then the system is called a public key system. Public key systems offer many interesting possibilities. For instance, anyone can send an encrypted credit card number to an online shop using the shop's public k1. Since only the shop possesses k2, no one but the shop can determine the number. If a symmetric system were used, the shop would have to exchange unique keys - privately and in advance - with every potential customer. The security of public key systems is always based on the difficulty of solving certain mathematical problems, whereas symmetric schemes are more ad hoc in nature. The main drawback of public key systems is that their mathematical nature always makes them less efficient than symmetric systems; in particular, because the size of keys in public key systems is measured in kilobits - the keys of symmetrical systems are only one-tenth as large. Thus, the choice of encryption method depends on the intended application. The most widespread symmetric system is the data encryption standard (DES), which was developed by IBM in the mid-1970s. The DES used a key size of 56 bits. With recent hardware developments, however, a 56-bit key size space can be entirely searched by advanced machines within hours or even minutes. For this reason, the National Institute of Standards and Technology (NIST) initiated the development of the advanced encryption standard (AES), which supports 128- to 256-bit keys. Moreover, unlike the development of DES, the AES design process is open to the public. A key length of 128 bits is considered secure. IPsec applies AES encryption. Security 6.10.3 ELECTRONIC SIGNATURES Electronic signatures enable the recipient of information to verify the authenticity of the information's origin, and also verify the integrity