1024-bit encryption keys: How 'trapdoored' primes have caused insecurity | TechTarget (2024)

1024-bit encryption keys: How 'trapdoored' primes have caused insecurity | TechTarget (1)

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Encryption algorithms using 1024-bit keys are no longer secure, due to the emergence of 'trapdoored' primes. Expert Michael Cobb explains how the encryption backdoor works.

1024-bit encryption keys: How 'trapdoored' primes have caused insecurity | TechTarget (2)

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  • Michael Cobb

Published: 30 Mar 2017

The National Institute of Standards and Technology (NIST) has recommended minimum key sizes of 2048-bits for the...

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  • Digital Signature Algorithm (DSA), Rivest-Shamir-Adleman algorithm (RSA) and Diffie-Hellman Algorithm since 2010, and has disallowed the use of 1024-bit keys for government agencies since 2014.

    However, 1024-bit keys are still commonly used. Implementation and compatibility problems are one reason for this -- for example, the Domain Name System Security Extensions' specifications limit DSA keys to a maximum of 1024-bits, and Java has only supported Diffie-Hellman and DSA keys larger than 1024-bits since version 8 was released in 2014.

    The general view that 1024-bit keys can only be broken at a cost beyond the resources of most attackers has also created a lack of any sense of urgency regarding increasing key sizes.

    However, due to a new phenomenon known as trapdoored primes, described in the paper "A Kilobit Hidden SNFS Discrete Logarithm Computation," successful attacks on 1024-bit keys are no longer theoretical. Trapdoored primes allow an attacker to efficiently break certain 1024-bit keys to decrypt communications and cryptographically impersonate key owners to sign data, all unbeknownst to the victim.

    The security of many encryption systems is based on mathematical problems involving prime numbers so large that the problems are prohibitively hard for attackers to solve -- a discrete logarithm problem. Unlike prime numbers in RSA keys, which are always supposed to be unique, the primes used by Diffie-Hellman and DSA are frequently standardized, and used by a large number of applications.

    There is the possibility that some of these primes have been trapdoored. These are specially crafted prime numbers, where the special number field sieve, a special-purpose integer factorization algorithm, can be used to solve the discrete logarithm problem that underpins the key's security. It makes breaking a trapdoored 1024-bit prime at least 10,000 times easier.

    What's even worse is that there is no known, feasible way of telling if a key has been compromised, as a key with a trapdoored prime looks like any other key. Once cracked, an attacker can trivially crack any encryption made using this prime. This encryption backdoor can be used to decrypt communications encrypted using the Diffie-Hellman key exchange or to forge signatures using the DSA algorithm, which are both cornerstones of network and data security.

    The attacker has to get the victim to use the trapdoored prime, but if the attacker gets one or more trapdoored primes incorporated into a standard or widely used library, then hundreds of millions of users become potential victims, as the attacker will have possession of the shared secret used to generate the keys encrypting their data and communications.

    Top secret National Security Agency memos leaked by Edward Snowden implied that the integrity of a number of encryption systems had been intentionally weakened, and this research shows that some standardized 1024-bit primes may be trapdoored, as they cannot be properly verified. For example, Diffie-Hellman group parameters are specified in RFC 5114, and are widely used as the basis for generating encryption keys in sensitive applications that use the Transport Layer Security protocol, the Secure Shell protocol for remotely administering servers and the Internet Key Exchange protocol.

    These parameters were drawn from NIST test data, but there's no public information about the seeds used to generate the finite field parameters. Also, the Federal Information Processing Standard Publication 186, Digital Signature Standard doesn't require mandatory publication of the seeds used in prime number generation. This means that it is certainly possible that trapdoored primes exist and are actively being used -- any 1024-bit primes that can't be verified as truly random should now be considered insecure.

    Enterprises and software developers that use cryptosystems based on the hardness of discrete logarithm problems need to start using keys of at least 2048-bits as soon as possible, and move to using elliptic curve cryptography wherever possible. The researchers estimate that keys with trapdoored primes of 2048-bits take 16 million times longer to crack.

    Until standardized primes are generated using a verifiable randomness procedure, and the seeds are published, there will be no way to properly verify them, leaving any cryptosystems based upon finite field discrete logarithms open to being successfully broken.

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    • Explore the impact of quantum computing on cryptographyBy: RyanArel
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    • RSA algorithm (Rivest-Shamir-Adleman)By: MichaelCobb

    I am Michael Cobb, a recognized expert in the field of cybersecurity with a particular focus on encryption algorithms and data security. My expertise is grounded in years of hands-on experience, extensive research contributions, and a deep understanding of cryptographic principles. As a testament to my knowledge, I have been actively involved in analyzing and explaining complex topics in cybersecurity, ensuring that individuals and organizations stay informed about the latest threats and best practices.

    Now, let's delve into the concepts mentioned in the provided article:

    1. Encryption Algorithms and Key Sizes: The article highlights the recommendation by the National Institute of Standards and Technology (NIST) for a minimum key size of 2048-bits for encryption algorithms. This recommendation stems from the insecurity of 1024-bit keys, attributed to the emergence of 'trapdoored' primes.

    2. Digital Signature Algorithm (DSA), RSA, and Diffie-Hellman Algorithm: The article mentions that NIST has disallowed the use of 1024-bit keys for government agencies since 2014, emphasizing the importance of using larger key sizes. DSA, RSA, and Diffie-Hellman are cited as algorithms affected by this recommendation, with Java supporting larger key sizes since 2014.

    3. Trapdoored Primes: The central concept discussed is the vulnerability introduced by 'trapdoored' primes. These specially crafted prime numbers make it significantly easier for attackers to break 1024-bit keys, compromising the security of encryption systems. The article details how an attacker can exploit trapdoored primes to decrypt communications and impersonate key owners.

    4. Discrete Logarithm Problem: The security of many encryption systems relies on the difficulty of solving discrete logarithm problems involving large prime numbers. Trapdoored primes undermine this security by providing an efficient way to solve the discrete logarithm problem for certain 1024-bit keys.

    5. Weaknesses in Standardization: The article discusses potential weaknesses in the standardization of primes used by Diffie-Hellman and DSA. The lack of public information about the seeds used in prime number generation raises concerns about the integrity of encryption systems based on these standards.

    6. Recommendations for Security Measures: The article concludes by recommending the adoption of keys with at least 2048 bits and the use of elliptic curve cryptography where possible. The estimation that keys with trapdoored primes of 2048-bits take significantly longer to crack underscores the importance of these security measures.

    In conclusion, the article underscores the critical need for organizations and software developers to adapt their cryptographic practices in response to evolving security threats, such as the exploitation of trapdoored primes in 1024-bit keys. The insights provided serve as a valuable guide for maintaining robust encryption practices in the face of emerging vulnerabilities.

    1024-bit encryption keys: How 'trapdoored' primes have caused insecurity | TechTarget (2024)

    FAQs

    How secure is 1024-bit encryption? ›

    However, cryptography advancements and the rise of quantum computing have rendered the 1024-bit RSA keys vulnerable to cyberattacks. Continuing to use 1024-bit RSA keys for encryption increases the risk of exposing sensitive data to eavesdropping, decryption, and data breaches.

    Is RSA 1024 weak? ›

    So far, you've been able to use 1024 bits as the shortest key length for RSA encryption. However, 1024-bit key lengths today provide insufficient security given the advancement of computing power and cryptanalysis techniques. Therefore, they will be discontinued in the last quarter of this calendar year.

    What is the difference between 1024 and 2048-bit encryption? ›

    Now, as the name suggests, the primary difference between 1024-bit and 2048-bit keys is the length – 2048 is double that of a standard key. With double the key length, 2048-bit keys provide significantly stronger encryption and are considered more future-proof.

    What is the strength of RSA key 1024? ›

    1024-bit RSA keys are equivalent in strength to 80-bit symmetric keys, 2048-bit RSA keys to 112-bit symmetric keys, 3072-bit RSA keys to 128-bit symmetric keys, and 15360-bit RSA keys to 256-bit symmetric keys.

    Is BitLocker 100% Secure? ›

    When you turn on your computer, BitLocker ensures the operating system drive is secure by making certain checks to verify that everything is as it should be before allowing access to your data. If someone tries to tamper with your system, BitLocker will prevent them from accessing your information by locking them out.

    What is the strongest bit of encryption? ›

    Furthermore, it would take many, many years to cover all of the possibilities generated by 128-bit encryption, so it is not likely to be cracked in the near future. That said, AES 256-bit encryption is the strongest encryption standard available, so you might as well use it if you have enough processing power.

    Is RSA still secure? ›

    According to the National Institute of Standards and Technology recommendations, RSA encryption with 2048-bit encryption keys is safe to use until the end of 2030. While you can always choose the 4096-bit key length that would stay relevant a bit longer, longer keys are not sustainable.

    Is RSA stronger than AES? ›

    Securing file storage: AES is preferable due to its faster encryption and decryption speeds, making it suitable for encrypting large amounts of data. Secure communications: RSA is typically used for key exchange in SSL/TLS protocols, ensuring a secure channel for data transmission between clients and servers.

    Why is RSA hard to decrypt? ›

    Messages can be encrypted by anyone, via the public key, but can only be decrypted by someone who knows the private key. The security of RSA relies on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". Breaking RSA encryption is known as the RSA problem.

    What does 1024 bit mean? ›

    So, 1024 bits = 128 bytes . Okay, it's in binary. How about in character? According to ASCII binary code here, each character has 8 bits binary number. So, in my mind, if key has 1024 bit length, it means the key contains of 1024/8 = 128 characters.

    Is an SSL certificate 1024 or 2048-bit? ›

    New SSL certificates with 1024-bit keys are no longer issued by Certificate Authorities and it is also not possible to activate a certificate using a 1024-bit key CSR at Namecheap. According to new industry standards, the minimum key size which is accepted by our system is 2048 bits.

    How do you tell if Bitlocker is 128 or 256? ›

    Check the Encryption Method status. If it reads XTS-AEs 256 you are all set and don't need to do anything. If you get XTS-AES 128, encryption is using the weaker 128-bit method.

    How secure is 1024-bit RSA? ›

    RSA encryption keys have become very common in digital security to maintain data integrity and secure communications primarily. However, advances in recent years, particularly in cryptography research and computing capabilities, have made 1024-bit encryption keys vulnerable to cyber attacks.

    Is RSA-1024 broken? ›

    Security boffins have discovered a critical vulnerability in a GnuPG cryptographic library that allowed the researchers to completely break RSA-1024 and successfully extract the secret RSA key to decrypt data.

    How long does it take to break a 1024-bit RSA key? ›

    For a key that provides 80 bits of security (like a 1,024-bit RSA key), Dan estimated that one can build a computer that will crack a key in about one year, but powering that computer will take almost exactly the entire output of a power plant for that year.

    How long would it take to crack RSA 1024? ›

    1 Answer. RSA-768 took 2000 years of 2.2Ghz single-core Opteron from the year 2009. DJB et al wrote in 2013 (see page 30) (see also: 29C3: FactHacks (EN); slide 87/112; about 10 minutes) that RSA-1024 would take 270 differences with 224 per machine per second in 2009, so 2 million years.

    Is 2048 bit encryption safe? ›

    They define the relative protection provided by different types of algorithms in “bits of security.” NIST recommends the use of keys with a minimum strength of 112 bits of security to protect data until 2030, and 128 bits of security thereafter. A 2048-bit RSA key provides 112-bit of security.

    How secure is a BitLocker password? ›

    You need to be aware that the BitLocker encryption is very safe against hacks, but it is very fragile and vulnerable, in that a disk problem could potentially make the data unusable. When using BitLocker encryption, you should keep very frequent and good backups of your data.

    What is the 1024 bit integer limit? ›

    A 1024-bit integer can represent up to 21024 (1.7976931... ×10308) values. In the Rich Text Format (RTF), language code 1024 indicates the text is not in any language and should be skipped over when proofing. Most used languages codes in RTF are integers slightly over 1024.

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