Forbidden Salamanders

+ Forbidden Salamanders + at cyfraeviolae.org +

+ source code + · + aes-gcm nonce reuse + · + aes-gcm nonce truncation + · + aes-gcm key commitment +

+ The FIPS-compliant sorcerer Roseacrucis uses the Advanced Encryption Standard in Galois/Counter Mode + to correspond with his retinue. The Library’s cryptanalysts + have intercepted the communication channel, but we need your + help to exploit their broken protocols. +

+ Choose one of the following missions. +

+ Nonce + reuse. Due to rising entropy prices, Roseacrucis has + started to reuse nonces. You must perform the Forbidden Attack in order to + recover the authentication key and forge arbitrary ciphertext. +

+ Nonce truncation. The sorcerer + aims to conserve bandwidth by truncating nonces from twelve bytes + to four. Use the enemy as a decryption oracle to once again, + recover the authentication key and forge arbitrary ciphertext. +

+ Key commitment. One of + our agents has infiltrated Roseacrucis’ inner circle, but all + secret keys are required to be surrendered to the + counterintelligence authority. Help her send ciphertexts to the + Library that decrypt to confidential information under one key, but + innocuous banter under another. +

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+

+ Though it is not required to complete your missions, we now + review the construction of AES-GCM. +

+ AES-GCM is a block cipher that accepts a key of 16 bytes, + a nonce of 12 bytes, plaintext, and additional authenticated data. + It returns ciphertext and a message authentication code (MAC). +

+ The ciphertext is computed as in counter mode, whereas the MAC is computed using the algorithm GMAC. +

+ Let + \[ + m = \alpha^{128}+\alpha^7 + \alpha^2 + \alpha + 1 + \] + \[ + \mathbb{K} = \mathbb{F}(2^{128})/m. + \] +

+ The finite field \(\mathbb{K}\) can be + interpreted as the set of polynomials with coefficients in \(\mathbb{F}_2\) + of degree less than \(128\). Multiplication + is performed modulo \(m\). This field is of characteristic 2; + e.g., \((\alpha^5 + 1)+(\alpha^5 + 1) = 0\). +

+ We interpret 16-byte blocks as elements in \(\mathbb{K}\) + in little-endian bit order: + \[ + b_0b_1b_2\ldots{}b_{127} \mapsto + b_0 + b_1\alpha + b_2\alpha^2 + \ldots + b_{127}\alpha^{127}, + \] + where \(b_0\) is the least significant bit of the first byte of + the block. +

+ 12-byte nonces are interpreted as 96-bit integers in big-endian + byte order. Let \(\operatorname{Byte} = [0, 2^8-1]\) and + \(x_i\) refer to the \(i\)th 16-byte chunk of the bytestring + \(x\). +

+ \(\operatorname{encode_{big}}(x, n)\) encodes an integer \(x\) into \(n\) bytes in big-endian + byte order. \(\operatorname{pad_n}(x, p)\) pads the length of + the bytestring \(x\) to the nearest multiple of \(n\) with the + byte \(p\). \(\operatorname{AES}(k, x)\) refers to + the 128-bit AES block cipher. +

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+

\(\operatorname{GMAC}(h\in \mathbb{K}, s\in \mathbb{K}, aad\in \operatorname{Byte}^{y}, c\in \operatorname{Byte}^{z})\)

\( len = \operatorname{encode_{big}}(8y, 8) \mathbin\Vert \operatorname{encode_{big}}(8z, 8) \)
\( blocks = \operatorname{pad}_{16}(aad, 0) \mathbin\Vert \operatorname{pad}_{16}(c, 0) \mathbin\Vert len \mathbin\Vert s \)
\( N = \frac{\vert blocks \vert}{16} \)
\( \operatorname{return} \sum\limits_{i=1}^{N} blocks_{N-i} h^{i-1}\)

+
+
+

\(\operatorname{AES-GCM}(k\in \operatorname{Byte}^{16}, n\in \operatorname{Byte}^{12}, aad\in \operatorname{Byte}^{y}, m\in \operatorname{Byte}^{z})\)

\( r = \mathop{\Vert}\limits_{n'=2^{32}n+2}^{2^{32}n+2^{32}-1} \operatorname{AES}(k, n') \)
\( c = r \oplus m \)
\( h = \operatorname{AES}(k, 0) \)
\( s = \operatorname{AES}(k, 2^{32}n + 1) \)
\( \operatorname{return} c, \operatorname{GMAC}(h, s, aad, c) \)

+ + + + + + + + -- cgit v1.2.3