Abstract: The invention discloses a calculation method and device for elliptic curve digital signature to resist memory disclosure attacks aiming signing private keys, which belongs to the field of cryptography technology. The method described in the invention includes the following steps. During initialization phase happened in a trusted environment, the key of symmetric cryptographic algorithm is used to encrypt the random number k1 and the private key used for signing, the scalar multiplication k1×G is calculated. At each signing phase, the plaintext data used to calculate s is calculated based on the selected signature algorithm and the value of scalar multiplication k1×G. The plaintext data used to calculate s include r or the data calculated based on r. Inside registers, s is calculated based on the above plaintext data and the ciphertext of random number k1 and the ciphertext of the private key. The signature of the message is (r, s).