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Yes, this is secure, it is largely compatible with KDF1 and KDF2 which basically use a 4 byte big endian encoding of the counter instead of a direct ASCII conversion to a byte. However, if you want to use the latest and greatest, you could use HKDF, possibly even augmented with a salt for session keys.


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Depends on what you mean by Keccak. There is actually a slight issue here that not all 256-bit Keccak variants have 256-bit preimage resistance. SHA3-256 (in the current SHA-3 draft) does have 256-bit preimage, but if you are using Keccak with 256-bit capacity it only has 128-bit preimage resistance. At least some of the earlier documents had 256-bit output ...



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