The invention discloses a multivariable public key encryption method. According to the multivariable public key encryption method, when a key is generated, a matrix is constructed according to an iterative method, the length of the key is greatly reduced, and the key can be managed conveniently; a probability encryption method is adopted, random parameters are introduced into encryption, the random parameters must be solved by a deciphering party through a deciphering process, the random parameters take part in decryption of a plaintext, the plaintext can be deciphered only under the condition that the random parameters are known, the difficulty of ciphertext decryption by an attacker is increased, ciphertexts are different even if public keys are the same, the public keys can be released in the forms such as telephone numbers, and encryption security is improved; based on the combinatorial optimization difficulty and multivariable quadratic polynomial, attack of a quantum computer can be resisted, both the encryption speed and the decryption speed are high, and the method can be applied to mobile terminals such as mobile phones; based on calculation on a finite field, the calculation process is simplified; the addition homomorphism and the subtraction homomorphism are achieved, the multiplication homomorphism can be achieved under special conditions, and the method can be applied to the newly-developed fields such as cloud computing.