Question

I am creating an encryption strategy for a lab project and want to know if there exists the capability to create a public key from just the private key?

Otherwise, can the public key only be created at the same time as the private key from some key generator?

P.S. A quick google didnt really help.

Answer 1

Private and public key are created together. Also, the standard storage format for a RSA private key includes all the public key fields, because it is useful for optimized implementations and masking (protection against some side-channel attacks). See the RSA standard itself: PKCS#1.

Edit: question has been edited, it was originally RSA-only. For other asymmetric algorithm, there is no requirement that the public key may be derived from the private key, nor is there any requirement of the contrary. For discrete logarithm-based algorithms (Diffie-Hellman, El-Gamal, DSA, and the elliptic curve variants of all of these), the public key is easily computed from the private key. It is possible to conceive a degenerate RSA in which knowledge of the private key does not allow reconstruction of the public key, but this requires not storing a few key elements which are needed for good performance (in full details, storing the RSA modulus factors allows for a 4x speed enhancement through the Chinese Remainder Theorem, so everybody stores the factors). On a more conceptual basis, the public key is, well, public, so it is assumed that “everybody” knows it; in practical terms, private key storage format almost always include provisions for storing the public key as well, or at least sufficient data to rebuild the public key.