The biases in the RC4 keystream, particularly short-term biases, generally decrease as more initial bytes are discarded (i.e., as ( N ) increases in RC4-dropN). However, research indicates that these biases do not strictly diminish monotonically in all cases, nor do they stabilize at a non-zero minimum for finite ( N ).

Key points:

1. Bias Reduction Trend: Empirical and theoretical analy...

Short answer No. Dropping one more byte does not always reduce the bias, and there is no finite “magic” drop length that makes the remaining RC4 keystream essentially unbiased. After a few thousand bytes the “early/transient” (short‑term) effects largely die out, but the generator exhibits persistent, position‑dependent (periodic) long‑term biases of roughly constant magnitude thereafter. So beyon...

This is an excellent question about the asymptotic behavior of biases in RC4's keystream. Let me address this comprehensively.

The Nature of RC4 Biases

RC4 exhibits several types of biases:

1. Short-term biases: Most prominent in the initial keystream bytes
2. Long-term biases: Persist throughout the keystream (like the double-byte bias)
3. Key-dependent biases: Vary based on the...

Short answer
No. After the very first kilobytes the large, easy-to-see biases get smaller, but they never vanish, they are not monotonic, and nothing is known (and nothing seems likely) that would let you point to a single number N and say “from here on the bias is minimal”. “RC4-drop-N” therefore has no magic value of N that turns RC4 into an unbiased generator – it only trades big early weak...

RC4 Biases and the Effect of Dropping Initial Bytes

The question asks if biases in the RC4 stream cipher continually decrease as more initial bytes are dropped, or if there's a point beyond which no further improvement occurs.

Understanding RC4 Biases

RC4 has two types of biases:

1. Short-term biases: These occur in the initial portion of the keystream and are caused by imperfect mixi...

Excellent question. It cuts to the core of understanding why RC4 is considered broken and what mitigations like RC4-dropN can and cannot do.

Let's break this down. The short answer is:

No, there is no N that results in a minimum, "as-good-as-it-gets" bias. The profile of biases is constantly evolving. While the initial, strong biases are smoothed out, the underlying state never reaches a s...

Terminology
Let

δt  = maxx |Pr[ Zt = x ] – 1/256|

be the (single-byte) bias of the t-th keystream byte Zt, and let

Δt  = maxx,y |Pr[ Zt = x , Zt+1 = y ] – 1/256²|

be the largest two-byte bias, and so on.
RC4-dropN means that we throw away the first N bytes and start counting with t = 1 afterwards; its remaining single-byte bias is therefore δN+1 , its largest two-byte bias is Δ...

Key points from the question:

• The most severe bias is in the second byte (bias towards...

Here is the short answer. Let δₖ be the largest single‐byte bias in the k-th output word of RC4, i.e.
δₖ = maxₓ ∣Pr[Sₖ = x] – 1/256∣.
All of the classical “short-term” RC4 biases (including the famous 1/128 bias in byte 2) satisfy
δₖ = Θ(1/k)
for large k. In particular one shows by careful counting (see Mantin & Shamir, Paul & Maitra, AlFardan & Paterson, etc.) that for k≫1
...