Electrum seems very user friendly, thin and convenient, but is it cryptographically secure? One of the ways to attack any cryptographic system is to exploit weaknesses in the key generation algorithm. Electrum uses a deterministic algorithm based on a pseudo-random seed to derive the public and private keys. Is this a cryptographically secure way of generating keys?
The seed generated by Electrum is a 128-bit random number. It is encoded as a sequence of 12 words, for the purpose of memorization. However, it is important to understand that it has 128-bits of entropy.