Security and Efficiency
The Blum-Goldwasser scheme is semantically-secure based on the hardness of predicting the keystream bits given only the final BBS state and the public key . However, ciphertexts of the form are vulnerable to an adaptive chosen ciphertext attack in which the adversary requests the decryption of a chosen ciphertext . The decryption of the original ciphertext can be computed as .
Depending on plaintext size, BG may be more or less computationally expensive than RSA. Because most RSA deployments use a fixed encryption exponent optimized to minimize encryption time, RSA encryption will typically outperform BG for all but the shortest messages. However, as the RSA decryption exponent is randomly distributed, modular exponentiation may require a comparable number of squarings/multiplications to BG decryption for a ciphertext of the same length. BG has the advantage of scaling more efficiently to longer ciphertexts, where RSA requires multiple separate encryptions. In these cases, BG may be significantly more efficient.
Read more about this topic: Blum–Goldwasser Cryptosystem
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