The current hashing algorithm of IOTA is Kerl—a ternary version of Keccak algorithm. But the IOTA foundation is still researching on Curl to develop Curl-P.
So, which major advantages does one expect from Curl-P over Kerl?
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Kerl uses SHA-3 Keccak at its core, which is a binary hashing algorithm. This means that the trinary 'trits' which IOTA normally operates on are converted to bits before being absorbed by Keccak, whose output is converted back from bits to trits after being squeezed out.
This extra radix conversion step is clearly suboptimal in terms of performance, so IOTA's hope is to achieve a purely ternary cryptographic hash function which can meet the cryptographic standards of state-of-the-art mainstream hash functions.