Cryptography

**flinted** · May 17th 2008, 08:07 AM

I was also wondering if someone could help me find the answers to these simple problems

$-16 mod 3$

$-52 mod 19$

is there a formula to follow for these problems?

Could someone help me get a solution to this probelm.

Compute $2^{1000000} mod 7$

Repeated Square method might do it.

**Moo** · May 17th 2008, 08:10 AM

Hello,

Originally Posted by flinted

Could someone help me get a solution to this probelm.

Compute $2(^1000000) mod 7$

$2^3=8=1 \mod 7$

1000000=3k+1

Therefore, $2^{1000000}=2^{3k+1}=2 \cdot (2^3)^k \equiv 2 \cdot 1^k \mod 7$

$\boxed{2^{1000000} = 2 \mod 7}$

**Isomorphism** · May 17th 2008, 08:12 AM

Originally Posted by flinted

Could someone help me get a solution to this probelm.

Compute $2(^)((1000000)) mod 7$

To find $2^{1000000} mod 7$ , observe that $2^3 = 1 mod 7$ . This means $2^{999999} = (2^3)^{333333} = 1^{333333} mod 7$ . $2^{999999} = 1 mod 7 \Rightarrow 2^{1000000} = 2 mod 7$

**flinted** · May 17th 2008, 08:17 AM

thanks but i dont undertand where you got the $k + 1$ formula from

**Moo** · May 17th 2008, 08:21 AM

1000000=3x333333+1
I substitute 333333 by k.

**flinted** · May 17th 2008, 08:26 AM

thanks alot

**flinted** · May 19th 2008, 07:16 AM

*bump*

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