Discussion:
RSA fail when e=2
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v***@chelnydom.ru
2008-03-01 22:13:15 UTC
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e=2
d=((p-1)*(q-1),e)=2
m=p*q-1
E(p*q-1)=1
D(1)=1
p*q-1 is not equal to 1.
Neil - Salem, MA USA
2008-03-02 17:16:37 UTC
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Post by v***@chelnydom.ru
e=2
d=((p-1)*(q-1),e)=2
m=p*q-1
E(p*q-1)=1
D(1)=1
p*q-1 is not equal to 1.
This is cryptic (no pun intended) as far as I can see.

In most papers written about RSA, "p" represents a prime number, "q"
represents another prime number, "e" is the encryption exponent, and "d" is
the decryption exponent.

e is chosen such that it has no factors in common with (p-1)*(q-1)

...but, since p is prime, then p-1 is an even number, and
...since q is prime, then q-1 is an even number, therefore
...(p-1)*(q-1) = an even number and has 2 as one of its factors

Since e must have no factors in common with (p-1)*(q-1), then 2 cannot be a
factor of e. In other words, e must be an odd number.

Neil - Salem, MA USA
v***@chelnydom.ru
2008-03-04 05:25:29 UTC
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Post by Neil - Salem, MA USA
e=2
In most papers written about RSA, "p" represents a prime number, "q"
represents another prime number, "e" is the encryption exponent, and "d" is
the decryption exponent.
e is chosen such that it has no factors in common with (p-1)*(q-1)
I know such paper which describe that e is e[i]. (a,b) is maximal
common divisor of two numbers.
Post by Neil - Salem, MA USA
...but, since p is prime, then p-1 is an even number, and
2 is prime number.
Post by Neil - Salem, MA USA
...since q is prime, then q-1 is an even number, therefore
...(p-1)*(q-1) = an even number and has 2 as one of its factors
Since e must have no factors in common with (p-1)*(q-1), then 2 cannot be a
d=((p-1)*(q-1),e) divide both (p-1)*(q-1) and e.
Post by Neil - Salem, MA USA
factor of e. In other words, e must be an odd number.
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