RSA Calculator

Interactive walkthrough of RSA public-key encryption and decryption

This tool walks through the mechanics of RSA encryption step by step. It uses small numbers for clarity — no provisions are made for high-precision arithmetic or efficient handling of large values, so keep your choices modest.

Summary of Steps

Generate N and r

Pick two primes p and q. N = p×q becomes the modulus; r = (p−1)(q−1) is used to find valid key pairs.

Find a factorable K

From the list of candidates equal to 1 mod r, pick one (K) that factors into two usable numbers.

Choose e and d

Split K's factors into e and d, both relatively prime to r, so that e×d ≡ 1 (mod r).

Encrypt / decrypt

Use e and N to encrypt a numeric message, then d and N to decrypt the ciphertext back to the original.

Compute N as the product of two prime numbers p and q

Enter values for p and q, then click to compute N and r.

The values of p and q you provided yield a modulus N, and also a number r = (p−1)(q−1), which is very important. You will need to find two numbers e and d whose product is a number equal to 1 mod r. Below appears a list of some numbers which equal 1 mod r. You will use this list in Step 2.

N = p×q

r = (p−1)×(q−1)

Candidates (1 mod r)

Find a number equal to 1 mod r which can be factored

Enter a candidate value K, then click to factor it.

Factors of K

Find two numbers e and d that are relatively prime to N and for which e×d ≡ 1 mod r

Use the factorization info above to split K into two numbers, e and d. Click the button to check correctness.

Consistency check

If your choices of e and d are acceptable, you should see the messages "e*d mod r = 1", "e and r are relatively prime", and "d and r are relatively prime" at the end of this box.

Use e and d to encode and decode messages

Enter a message in numeric form. Click the button to encode and decode it. Break your message into small chunks so that the Msg codes are not larger than N. (See the ASCII Reference Table below for ASCII code equivalences.)

Message → Numeric Converter

Type text below to see its ASCII codes. Copy one value at a time into the Msg field — each chunk must be smaller than N.

Text message

ASCII codes

Msg

Bit-Level View (for comparison, not part of RSA math)

RSA itself encrypts using modular exponentiation (Cipher = Msg^e mod N), not XOR. This panel just shows what a simple XOR cipher would look like using Msg as plaintext and e as the key, so you can see how it differs from RSA.

Plaintext bits (Msg)

Key bits (e)

Msg ⊕ e (XOR)

Encrypted Cipher = (Msg)^e mod N

Decrypted Msg = (Cipher)^d mod N

ASCII Reference Table

Printable characters 32–126 with their decimal codes. Use these values when converting a message character by character, or with the Message → Numeric converter above.

32Space

33!

34"

35#

36$

37%

38&

39'

40(

41)

42*

43+

44,

45-

46.

47/

480

491

502

513

524

535

546

557

568

579

58:

59;

60<

61=

62>

63?

64@

65A

66B

67C

68D

69E

70F

71G

72H

73I

74J

75K

76L

77M

78N

79O

80P

81Q

82R

83S

84T

85U

86V

87W

88X

89Y

90Z

91[

92\

93]

94^

95_

96`

97a

98b

99c

100d

101e

102f

103g

104h

105i

106j

107k

108l

109m

110n

111o

112p

113q

114r

115s

116t

117u

118v

119w

120x

121y

122z

123{

124|

125}

126~