This survey explores techniques for recovering cryptographic keys from partial information, focusing on RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman. Side-channel attacks often reveal indirect or incomplete information about secret keys, requiring additional cryptanalytic methods to recover the full key. The paper categorizes known techniques based on the type of information an attacker can obtain and provides simplified examples to illustrate the underlying principles. Key recovery methods include lattice-based algorithms, which are effective for recovering RSA keys when partial information is known. For example, lattice reduction techniques like LLL and BKZ can be used to find small roots of polynomials modulo integers, enabling the recovery of secret keys. These methods are particularly useful when large contiguous portions of the secret key are known, such as bits of the private exponent or factors of the modulus. The paper also discusses scenarios where partial information about the secret key is not contiguous, such as non-consecutive bits. In these cases, branch-and-prune algorithms can be used to iteratively solve for unknown bits, starting from the least significant bits and pruning branches that do not satisfy the required relationships. This approach is effective when a significant portion of the bits of the secret key is known, even if they are not contiguous. For RSA, techniques such as lattice-based methods can be applied to recover the private exponent $ d $ when partial information about $ d_p $ and $ d_q $ is known. These methods leverage the mathematical relationships between the public and private keys to efficiently recover the full key. The paper also addresses the challenges of recovering RSA keys from multiple chunks of bits of $ p $, highlighting the trade-offs between the number of chunks and the complexity of the lattice construction. Additionally, it discusses the limitations of current methods when dealing with non-consecutive bits and the open problem of recovering RSA keys from many non-consecutive bits. Overall, the survey provides a comprehensive overview of the techniques used in key recovery from partial information, emphasizing the importance of lattice-based methods and the adaptability of these techniques to different scenarios in public-key cryptography.This survey explores techniques for recovering cryptographic keys from partial information, focusing on RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman. Side-channel attacks often reveal indirect or incomplete information about secret keys, requiring additional cryptanalytic methods to recover the full key. The paper categorizes known techniques based on the type of information an attacker can obtain and provides simplified examples to illustrate the underlying principles. Key recovery methods include lattice-based algorithms, which are effective for recovering RSA keys when partial information is known. For example, lattice reduction techniques like LLL and BKZ can be used to find small roots of polynomials modulo integers, enabling the recovery of secret keys. These methods are particularly useful when large contiguous portions of the secret key are known, such as bits of the private exponent or factors of the modulus. The paper also discusses scenarios where partial information about the secret key is not contiguous, such as non-consecutive bits. In these cases, branch-and-prune algorithms can be used to iteratively solve for unknown bits, starting from the least significant bits and pruning branches that do not satisfy the required relationships. This approach is effective when a significant portion of the bits of the secret key is known, even if they are not contiguous. For RSA, techniques such as lattice-based methods can be applied to recover the private exponent $ d $ when partial information about $ d_p $ and $ d_q $ is known. These methods leverage the mathematical relationships between the public and private keys to efficiently recover the full key. The paper also addresses the challenges of recovering RSA keys from multiple chunks of bits of $ p $, highlighting the trade-offs between the number of chunks and the complexity of the lattice construction. Additionally, it discusses the limitations of current methods when dealing with non-consecutive bits and the open problem of recovering RSA keys from many non-consecutive bits. Overall, the survey provides a comprehensive overview of the techniques used in key recovery from partial information, emphasizing the importance of lattice-based methods and the adaptability of these techniques to different scenarios in public-key cryptography.