Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

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Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 = 13·19 and e = 25.

What is her secret key and what is her signature corresponding to the message M = 63?

n=247=13 x 19

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Answer 1

Answer #1

n = 247 = 13 * 19
so,
p = 13 & q = 19

$\phi$ ( n ) = (13-1) * (19 -1) = 216

e =25

secret key is d such that

e*d = 1 mod 216

using eucledian theorem

d is multiplicative inverse of e in Z₂₁₆

q	r1	r2	r	t1	t2	t
8	216	25	16	0	1	-8
1	25	16	9	1	-8	9
1	16	9	7	-8	9	-17
1	9	7	2	9	-17	26
3	7	2	1	-17	26	-95
2	2	1	0	26	-95	216
	1	0		-95	216

t = t₁ -q*t₂

t₁ = t₂

t₂ = t

value of t = -95 or (216 - 95) = 121

so d =121

where secret key = (d,n) = (121 , 247)

signature = m^d mod n

= 63¹²¹ mod 247 = 232

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Answer 2

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Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

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q	r1	r2	r	t1	t2	t
8	216	25	16	0	1	-8
1	25	16	9	1	-8	9
1	16	9	7	-8	9	-17
1	9	7	2	9	-17	26
3	7	2	1	-17	26	-95
2	2	1	0	26	-95	216
	1	0		-95	216

q	r1	r2	r	t1	t2	t
8	216	25	16	0	1	-8
1	25	16	9	1	-8	9
1	16	9	7	-8	9	-17
1	9	7	2	9	-17	26
3	7	2	1	-17	26	-95
2	2	1	0	26	-95	216
	1	0		-95	216

Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

Homework Answers

Add Answer to: Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

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Earn Coins

Add Answer to:
Exercise 1 (2 pts). Alice has her RSA public key (n,e) where n = 247 =...

q	r1	r2	r	t1	t2	t
8	216	25	16	0	1	-8
1	25	16	9	1	-8	9
1	16	9	7	-8	9	-17
1	9	7	2	9	-17	26
3	7	2	1	-17	26	-95
2	2	1	0	26	-95	216
	1	0		-95	216