Method for the secure execution of programs (smart contracts) implemented between a first wallet node (WN) (WN1) and a second wallet node (WN2), at least the second WN being implemented in an enclave of a processor, and the WNs being capable of executing programs designated in the messages that reach them, the method comprising the following steps: a) sending by WN1 to WN2 of a pre-message; b1) in response to this pre-message, execution in the enclave of a first program (WNRoT); b2) generation by the enclave of a certificate of authenticity of said first program and of the integrity of its execution; b3) sending said certificate to WN1; c) verification by WN1 of said certificate; d) in the event of successful verification, sending by WN1 to WN2 of a message intended to trigger the execution of a given program in WN2, and e) execution of said program in WN2.