Published in ASecuritySite: When Bob Met Alice·PinnedMember-onlyThe Strange Tale of Dual_EC_DRBGJulian Assange being arrested recently brought back memories of how he leaked Edward Snowden’s memos around the possible existence of an NSA-sourced cryptographic backdoor — the Dual EC standard (Dual_EC_DRBG). So let’s dive into the method and the trap door, and see the “magic” behind it. With Elliptic Curve methods…Security5 min read
Published in ASecuritySite: When Bob Met Alice·12 hours agoMember-onlyWhere Would You Find Both ECC and RSA Working Well Together? Well, In Virtually Every Web ConnectionDon’t you sometimes worry that we use the Internet and don’t actually understand how it works? Well, let’s dive into the wonderful world of key exchanges, and which are the core of every TLS connection that we make to the Web. ECDH (Elliptic Curve Diffie Hellman) For key exchange, we started with the wonderful Diffie-Hellman…Cryptography3 min read
Published in ASecuritySite: When Bob Met Alice·1 day agoMember-onlyRSA Is Alive And Kicking in Nearly Every TLS Connection: Creating Fast RSA SignaturesWhile elliptic curve methods have taken over with key exchange and in digital signing with Bitcoin and Ethereum, the RSA signature method is still one of the most popular methods for signing. Sullivan et al [1], for example, found that ECDHE with RSA was by far the most popular way…Cybersecurity4 min read
Published in ASecuritySite: When Bob Met Alice·1 day agoMember-onlyBeware of RSA Fault Attacks — They May Comprise Your Trust InfrastructureIn a brilliant paper published at USENIX 2022, Sullivan et al [1] show that real-life RSA signatures can be cracked for their private key — if the signature contains a fault. In a previous article, I outlined how faults in ECDSA can cause compromises: https://medium.com/asecuritysite-when-bob-met-alice/ecdsa-signatures-can-be-cracked-with-one-good-signature-and-one-bad-one-2d8bc71949e9?sk=b2d77913f1420d2a72952c1f2395d379Cryptography5 min read
Published in ASecuritySite: When Bob Met Alice·1 day agoMember-onlySo What Are dQ, dP, and InvQ Used For In RSA?If you look at a private key in RSA, you will see p and q — the core prime numbers, and the modulus N (and which is p times q). But you will also see dQ, dP and InvQ. Overall, they make the decryption process faster and use Chinese Remainer…Cybersecurity3 min read
Published in ASecuritySite: When Bob Met Alice·2 days agoMember-onlyDoes ElGamal Encryption Do Homomorphic Addition and Subtraction?Well, yes, but with a small modification … — Homomorphic encryption provides us with a way to encrypt values and then to be able to process them. Let’s say we have Bob the Data Processor and Alice the Consumer. With this, Alice could encrypt the values that she has with her public key, and then Bob can process these…Cryptography4 min read
Published in ASecuritySite: When Bob Met Alice·2 days agoMember-onlyHomomorphic Encryption with ElGamal Using Python (Multiplication and Division)We live in a 20th Century world of data, and where often do not protect our data. In a future data world, all of our values could be encrypted, and where we can still operate on them. This will be a world of homomorphic encryption. Meet Taher Elgamal Taher Elgamal is one of…Cryptography5 min read
Published in ASecuritySite: When Bob Met Alice·3 days agoMember-onlyOur Paper-based World of SecretsAnd, so, the media were red hot last week with the FBI’s search of Donald Trump’s home:Cryptography5 min read
Published in ASecuritySite: When Bob Met Alice·3 days agoMember-onlyCrypto Magic: Recovering Alice’s Public Key From An ECDSA SignatureThe core of the security of the Internet is based on one thing: PKI (Public Key Infrastructure). With this, Alice has a key pair: a public key and a private key. This can either be an RSA key pair or an Elliptic Curve key pair. If Alice wants to prove…Cryptography5 min read
Published in ASecuritySite: When Bob Met Alice·4 days agoMember-onlySatoshi Selected ECDSA with The Secp256k1 Curve and SHA-256. Are Other Options Available?Over 10 years ago, Satoshi Nakamoto wrote a classic white paper on Bitcoin, and the rest is history:Cryptography4 min read