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Fix xor
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Andre Henriques 2023-11-03 13:00:42 +00:00
parent 1b2ee7fc14
commit f132feca53
1 changed files with 2 additions and 2 deletions
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cw/cw.tex
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@ -53,8 +53,8 @@
if the message is only one block long: if the message is only one block long:
$$H=E$$ $$H=E$$
$$m\ne m'$$ $$m\ne m'$$
$$H(m)=E(K, IV \xor m) = C_1$$ $$H(m)=E(K, IV \oplus m) = C_1$$
$$H(m')=E(K, IV \xor m') = C_2$$ $$H(m')=E(K, IV \oplus m') = C_2$$
And if there the hashing function was not collision resistant that would imply And if there the hashing function was not collision resistant that would imply
$$C_1=C_2\implies D(C_1)=D(C_2) \impies m=m'$$ $$C_1=C_2\implies D(C_1)=D(C_2) \impies m=m'$$
and since $m !=m'$ the hash function is collision resistant, for messages with 1 block. and since $m !=m'$ the hash function is collision resistant, for messages with 1 block.