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Salsa12 is in eStream portfolio. How many random bits one can generate in Salsa12 using single key? Is it $512\times 2^{128}$?

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Salsa20 (and its variants) has 512 bit blocks, a 64-bit counter and a 64-bit nonce. So it can produce $2^{64}$ independent streams consisting of $512 \cdot 2^{64}$ bits each, for a total of $512 \cdot 2^{128}$ bits.

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