{"id":8307,"date":"2019-01-21T13:31:38","date_gmt":"2019-01-21T18:31:38","guid":{"rendered":"https:\/\/www.thesslstore.com\/blog\/?p=8307"},"modified":"2021-03-12T15:28:12","modified_gmt":"2021-03-12T20:28:12","slug":"is-it-still-safe-to-use-rsa-encryption","status":"publish","type":"post","link":"https:\/\/www.thesslstore.com\/blog\/is-it-still-safe-to-use-rsa-encryption\/","title":{"rendered":"Is it still safe to use RSA Encryption?"},"content":{"rendered":"\n

RSA could potentially be cracked by careless implementation, but does that mean\nit\u2019s broken?<\/h2>\n\n\n\n

Let\u2019s talk about RSA encryption. Last month we wrote about an exploit called Bleichenbacher\u2019s CAT<\/a> that could impact RSA key generation. Today we\u2019re going to discuss how poorly configured RSA can lead to cracked public keys.<\/p>\n\n\n\n

This actually isn\u2019t new research, it stems from a 2012 research paper<\/a>,\nbut a blog post by William Kuszmaul on Algorithm Soup last week kicked the\ntires on it. You\ncan find that post here<\/a>, it\u2019s very well written, William is an MIT PHD\nstudent that specializes in computer science and algorithms. <\/p>\n\n\n\n

Or, if that sounds a bit daunting you can let me hash it out\nfor you.<\/p>\n\n\n\n

Either way, today we\u2019ll be discussing the RSA cryptosystem, its\nweaknesses and why random number generators may not be so random after all. <\/p>\n\n\n\n

Let\u2019s hash it out. <\/span><\/p>\n\n\n\n

Let\u2019s start with RSA<\/h2>\n\n\n\n
\"Encryption\"<\/figure><\/div>\n\n\n\n

RSA stands for Rivest-Shamir-Adleman, the surnames of its creators. As we\u2019ve discussed before, Public Key cryptography<\/a> was actually \u201cdiscovered\u201d twice, once by the UK\u2019s GCHQ in 1973 \u2013 at the time it was deemed impractical \u2013 and then by Whitfield Diffie and Martin Hellman (with an assist from Ralph Merkle) in 1976. <\/p>\n\n\n\n

At that point things were still fairly theoretical, nobody\nhad been able to make the encryption a one-way function, one that was nearly\nimpossible to reverse engineer. <\/p>\n\n\n\n

Ron Rivest, Adi Shamir and Leonard Adleman set out to accomplish that in 1977. Rivest and Shamir were both computer scientists while Adleman was a mathematician. Eventually after several failed approaches (and having nearly lost all hope), they arrived at prime factorization as a method for one-way encryption.<\/p>\n\n\n\n

[Prime numbers – for those who slept through high school math – are numbers greater than one that are only divisible by one and themselves (factors).<\/em>] <\/p>\n\n\n\n

Remember, public key encryption, one-way encryption, asymmetric encryption \u2013 whatever you feel like calling it \u2013 is what facilitates key exchange with SSL\/TLS. We\u2019ve given an over-the-top look at this before, today we\u2019ll dive a little bit deeper.<\/p>\n\n\n\n<\/span><\/span>\n\n\n\n

When we mention prime factorization, what\u2019s meant is that RSA uses two large random prime numbers (p<\/em> and q<\/em>) \u2013 we\u2019re talking huge, hundreds of bits long \u2013 and multiplies them to create a public key. <\/p>\n\n\n\n

So, p * q = x<\/em><\/p>\n\n\n\n

And, x = Public Key<\/em><\/p>\n\n\n\n

Anyone can take the public key and use it to encrypt a piece of data. Typically in the context of SSL\/TLS what\u2019s being encrypted is the session key<\/a>. However, without knowing the values of the two prime numbers, p<\/em> and q<\/em>, nobody else can decrypt the message.<\/p>\n\n\n\n

To give you a better idea of the computational hardness of RSA, factoring a 232-digit number took a group of researchers<\/a> over 1,500 years of computing time (distributed across hundreds of computers). You can also check out this video.<\/p>\n\n\n\n

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