Cracking RSA — A Challenge Generator

RSA Encryption parameters. Public key: [e,N].
e: 65537
N: 498702132445864856509611776937010471
Cipher: 96708304500902540927682601709667939
We are using 60 bit primes
Can you find the value of the message?

Example

Encryption parameters
e: 65537
N: 1034776851837418228051242693253376923
Cipher: 582984697800119976959378162843817868
We are using 60 bit primes
Factors
-------
1,034,776,851,837,418,228,051,242,693,253,376,923 = 1,086,027,579,223,696,553 x 952,809,000,096,560,291
>>>p=1086027579223696553
>>>q=952809000096560291
>>> print (p-1)*(q-1)
1034776851837418226012406113933120080
Inverse of  65537  mod  1034776851837418226012406113933120080
Result: 568411228254986589811047501435713
>>> d=568411228254986589811047501435713
>>> cipher=582984697800119976959378162843817868
>>> N=1034776851837418228051242693253376923
>>> print pow(cipher,d,N)
345
>>> m=345
>>> e=65537
>>> N=1034776851837418228051242693253376923
>>> print pow(m,e,N)
582984697800119976959378162843817868

Conclusions

RSA Encryption parameters. Public key: [e,N].
e: 65537
N: 911844725340031776516886332975892441
Cipher: 801127314512167104045686292190207406
We are using 60 bit primes
Can you find the value of the message?
RSA Encryption parameters. Public key: [e,N].
e: 65537
N: 1157170973102575683016736411062049761643292045397
Cipher: 398616441584847118291875619819339172891325623639
We are using 80 bit primes
Can you find the value of the message?

RSA Encryption parameters. Public key: [e,N].
e: 65537
N: 49141939931137261116843775362783398673931258031923895283286320973486872970729
Cipher: 14199123787046830048066972290052136769415356824981695836360604590953658335413
We are using 128 bit primes
Can you find the value of the message?

Answers

ASecuritySite: When Bob Met Alice

This publication brings together interesting articles related to cyber security.

Prof Bill Buchanan OBE

Written by

Prof at Napier. Serial innovator. Crypto Punk. Believer in fairness, justice & freedom. EU Citizen. Auld Reekie native. Old World Breaker. New World Creator.

ASecuritySite: When Bob Met Alice

This publication brings together interesting articles related to cyber security.