ROCA vulnerability

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The ROCA vulnerability is a cryptographic weakness that allows the private key of a key pair to be recovered from the public key in keys generated by devices with the vulnerability. "ROCA" is an acronym for "Return of the Coppersmith Attack".[1] The vulnerability has been given the identifier CVE-2017-15361.

The vulnerability arises from a problem with an approach to RSA key generation used in a software library, RSALib, provided by Infineon, and incorporated in many smart cards and Trusted Platform Module (TPM) implementations. The same vulnerability appears in recent Yubikey 4 tokens, often used to generate PGP keys. Keys of lengths 512, 1024, and 2048 bits generated using the Infineon library are vulnerable to a practical ROCA attack.[2][3] The research team that discovered the attack (all with Masaryk University and led by Matúš Nemec and Marek Sýs)[2] estimate that it affects around one-quarter of all current TPM devices globally.[4] Millions of smartcards are believed to be affected.[1]

The team informed Infineon of the RSALib problem in February 2017, but withheld public notice until mid-October, citing responsible disclosure. At that time they announced the attack and provided a tool to test public keys for vulnerability. They published the details of the attack in November.[2]

Technical details[edit]

Generating an RSA key involves selecting two large randomly-generated prime numbers, a process that can be time-consuming, particularly on small devices, such as smart cards. In addition to being primes, the numbers should have certain other properties for best security. The vulnerable RSALib selection process quickly creates primes of the desired type by only testing for primality numbers of the form:

k*M + (65537a mod M)

where M is the product of the first n successive primes (2, 3, 5, 7, 11, 13,...), and n is a constant that only depends on the desired key size. The security is based on the secret constants k and a. The ROCA attack exploits this particular format for primes using a variation of the Coppersmith method. In addition, public keys generated this way have a distinctive fingerprint that can be quickly recognized by attempting to compute the discrete logarithm of the public key mod M to base 65537. Computing discrete logarithms in a large group is usually extremely difficult, but in this case it can be done efficiently using the Pohlig–Hellman algorithm because M is a smooth number. A test site is available on the Internet.[2][5][6][7]

Mitigation[edit]

The ROCA authors consider public keys of length 512, 1024 and 2048-bits generated by RSALib to be vulnerable. Because the details of key generation differ for different key lengths, shorter keys are not necessarily more vulnerable than longer keys. For example a 1952-bit RSAlib key is stronger than a 2048-bit key and a 4096-bit key is weaker than a 3072-bit key.

The best mitigation, according to the authors, is to generate RSA keys using a stronger method, such as by OpenSSL. If that is not possible, the ROCA authors suggest using key lengths that are less susceptible to ROCA such as 3936-bit, 3072-bit or 1952-bits if there is a 2048-bit key size maximum.[2]:Sec 5.1

See also[edit]

References[edit]

  1. ^ a b Goodin, Dan (2017-10-23). "Crippling crypto weakness opens millions of smartcards to cloning". Ars Technica. Retrieved 2017-10-25. 
  2. ^ a b c d e The Return of Coppersmith’s Attack: Practical Factorization of Widely Used RSA Moduli, Matus Nemec, Marek Sys, Petr Svenda, Dusan Klinec,Vashek Matyas, November 2017
  3. ^ Khandelwal, Swati. "Serious Crypto-Flaw Lets Hackers Recover Private RSA Keys Used in Billions of Devices". The Hacker News. Retrieved 2017-10-25. 
  4. ^ Leyden, John (16 October 2017). "Never mind the WPA2 drama... Details emerge of TPM key cockup that hits tonnes of devices". United Kingom: The Register. Retrieved 2017-10-25. 
  5. ^ "ROCA: Infineon TPM and Secure Element RSA Vulnerability Guidance". www.ncsc.gov.uk. United Kingdom. Retrieved 2017-10-25. 
  6. ^ "ROCA: Vulnerable RSA generation (CVE-2017-15361)". Czech Republic: Centre for Research on Cryptography and Security, Faculty of Informatics, Masaryk University. Retrieved 2017-10-25. 
  7. ^ "Information on software update of RSA key generation function". Infineon Technologies AG. Retrieved 2017-10-25. 

External links[edit]