A method comprising: a secure encryption element negotiating cryptographic session keys with remote devices using, in a normal operation mode, secret keys it generates randomly, and encrypting and decrypting data with the negotiated session keys during communication sessions with the remote devices; the secure encryption element receiving and authenticating a legal intercept mode command from a service provider, and responsively both transitioning from the normal-operation mode to a legal-intercept mode and negotiating a predictable cryptographic session key at least in part by: accessing a first key-negotiation parameter stored within the secure encryption element, the first key-negotiation parameter originating from by a secure-encryption-element provider and a second key-negotiation parameter stored within the secure encryption element, the second key-negotiation parameter originating from the service provider, wherein the first key-negotiation parameter is not known to the service provider and the second key-negotiation parameter is not known to the secure-encryption-element provider; generating a pseudorandom secret key based on the first and second key-negotiation parameters; generating and sharing a first shared intermediate value based on the pseudorandom secret key; receiving a second shared intermediate value from a remote device; generating the predictable cryptographic session key based on the pseudorandom secret key and the second shared intermediate value; and encrypting and decrypting data with the generated predictable cryptographic session key during a communication session with the remote device. a secure encryption element negotiating cryptographic session keys with remote devices using, in a normal operation mode, secret keys it generates randomly, and encrypting and decrypting data with the negotiated session keys during communication sessions with the remote devices; the secure encryption element receiving and authenticating a legal intercept mode command from a service provider, and responsively both transitioning from the normal-operation mode to a legal-intercept mode and negotiating a predictable cryptographic session key at least in part by: accessing a first key-negotiation parameter stored within the secure encryption element, the first key-negotiation parameter originating from by a secure-encryption-element provider and a second key-negotiation parameter stored within the secure encryption element, the second key-negotiation parameter originating from the service provider, wherein the first key-negotiation parameter is not known to the service provider and the second key-negotiation parameter is not known to the secure-encryption-element provider; generating a pseudorandom secret key based on the first and second key-negotiation parameters; generating and sharing a first shared intermediate value based on the pseudorandom secret key; receiving a second shared intermediate value from a remote device; generating the predictable cryptographic session key based on the pseudorandom secret key and the second shared intermediate value; and encrypting and decrypting data with the generated predictable cryptographic session key during a communication session with the remote device. accessing a first key-negotiation parameter stored within the secure encryption element, the first key-negotiation parameter originating from by a secure-encryption-element provider and a second key-negotiation parameter stored within the secure encryption element, the second key-negotiation parameter originating from the service provider, wherein the first key-negotiation parameter is not known to the service provider and the second key-negotiation parameter is not known to the secure-encryption-element provider; generating a pseudorandom secret key based on the first and second key-negotiation parameters; generating and sharing a first shared intermediate value based on the pseudorandom secret key; receiving a second shared intermediate value from a remote device; generating the predictable cryptographic session key based on the pseudorandom secret key and the second shared intermediate value; and encrypting and decrypting data with the generated predictable cryptographic session key during a communication session with the remote device.