Disclosed are various embodiments for certificate-free cryptosystems that achieve significant computational and communication efficiency as compared to prior systems. A private key generator (PKG) generates a master public key and a master private key unique to the PKG; receives identifying information for at least one client device; generates a public key for the at least one client device; generates a private key for the at least one client device by: performing a hash of the identifying information using the public key generated for the at least one client device to generate a plurality of indices; identifying values corresponding to the indices from the master private key; and deriving the private key based at least in part on a summation of the values corresponding to the indices; and sends the public key and the private key to the at least one client device.
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