[wrong][spam] Cracking PGP

[Karl]

>
> ===Key generation===
>>>> The keys for the RSA algorithm are generated in the following way:
>>>> # Choose two distinct [[prime number]]s ''p'' and ''q''.
>>>>
>>>
>>> #* ''p'' and ''q'' are kept secret.
>>>> # Compute 'n'' = ''pq''
>>>>
>>>
>>> public n = private p * private q
>>> n is keylength bits long.
>>>
>>> # Compute ''λ''(''n''), where ''λ'' is Carmichael's totient function.
>>>> Since ''n'' = ''pq'', ''λ''(''n'') = lcm(''λ''(''p''),''λ''(''q'')), and
>>>> since ''p'' and ''q'' are prime, ''λ''(''p'') = ''φ''(''p'') = ''p'' − 1
>>>> where φ is the Euler totient function, and likewise ''λ''(''q'') =
>>>> ''q'' − 1. Hence ''λ''(''n'') = lcm(''p'' − 1, ''q'' − 1)
>>>>
>>>
>>> private lambda(n) is calculated and has a number of relevant algebraic
>>> identities associated
>>>
>>> #* The lcm may be calculated through the Euclidean algorithm, since
>>>> lcm(''a'',''b'') = ''|ab|''/gcd(''a'',''b'').
>>>> # Choose an integer ''e'' such that 1 < ''e'' < ''λ''(''n'') and
>>>> gcd(''e'', ''λ''(''n'')) = 1; that is, ''e'' and ''λ''(''n'') are coprime.
>>>>
>>>
>> #* ''e'' having a short bit-length and small Hamming weight results in
>>>> more efficient encryption -- the most commonly chosen value for ''e'' is
>>>> 2**16 + 1 = 65,537. The smallest (and fastest) possible value for ''e'' is
>>>> 3, but such a small value for ''e'' has been shown to be less secure in
>>>> some settings.
>>>> #*''e'' is released as part of the public key.
>>>>
>>>
> public e is often a very simple reused constant
>
> # Determine ''d'' as ''d'' ≡ ''e''**−1 (mod ''λ''(''n'')); that is, ''d''
>>>> is the modular multiplicative inverse of ''e'' modulo ''λ''(''n'').
>>>>
>>>
> #* This means: solve for ''d'' the equation ''d''⋅''e'' ≡ 1 (mod
>>>> ''λ''(''n'')); ''d'' can be computed efficiently by using the Extended
>>>> Euclidean algorithm, since, thanks to ''e'' and ''λ''(''n'') being coprime,
>>>> said equation is a form of Bézout's identity, where ''d'' is one of the
>>>> coefficients.
>>>> #* ''d'' is kept secret as the ''private key exponent''.
>>>> The ''public key'' consists of the modulus ''n'' and the public (or
>>>> encryption) exponent ''e''. The ''private key'' consists of the private (or
>>>> decryption) exponent ''d'', which must be kept secret. ''p'', ''q'', and
>>>> ''λ''(''n'') must also be kept secret because they can be used to calculate
>>>> ''d''. In fact, they can all be discarded after ''d'' has been computed.
>>>>
>>>
Okay!  I removed all the wiki markup!

>
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